:: LATTICE5 semantic presentation

REAL is V56() V57() V58() V62() V74() V75() V77() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V56() V57() V58() V59() V60() V61() V62() V63() V72() V74() cardinal limit_cardinal Element of bool REAL
bool REAL is non empty set
COMPLEX is V56() V62() set
RAT is V56() V57() V58() V59() V62() set
INT is V56() V57() V58() V59() V60() V62() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V56() V57() V58() V59() V60() V61() V62() V63() V72() V74() cardinal limit_cardinal set
bool NAT is non empty non empty-membered V63() set
bool NAT is non empty non empty-membered V63() set
[:COMPLEX,COMPLEX:] is Relation-like set
bool [:COMPLEX,COMPLEX:] is non empty set
[:COMPLEX,REAL:] is Relation-like set
bool [:COMPLEX,REAL:] is non empty set
K322(NAT) is V89() set
{} is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V37() ext-real V43() V56() V57() V58() V59() V60() V61() V62() V63() V74() V75() V76() V77() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V91() set
the empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V37() ext-real V43() V56() V57() V58() V59() V60() V61() V62() V63() V74() V75() V76() V77() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V91() set is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V37() ext-real V43() V56() V57() V58() V59() V60() V61() V62() V63() V74() V75() V76() V77() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V91() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real positive V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
{{},1} is non empty V56() V57() V58() V59() V60() V61() V72() V74() set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is Relation-like set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty set
[:REAL,REAL:] is Relation-like set
bool [:REAL,REAL:] is non empty set
[:[:REAL,REAL:],REAL:] is Relation-like set
bool [:[:REAL,REAL:],REAL:] is non empty set
[:RAT,RAT:] is Relation-like set
bool [:RAT,RAT:] is non empty set
[:[:RAT,RAT:],RAT:] is Relation-like set
bool [:[:RAT,RAT:],RAT:] is non empty set
[:INT,INT:] is Relation-like set
bool [:INT,INT:] is non empty set
[:[:INT,INT:],INT:] is Relation-like set
bool [:[:INT,INT:],INT:] is non empty set
[:NAT,NAT:] is non empty Relation-like V63() set
[:[:NAT,NAT:],NAT:] is non empty Relation-like V63() set
bool [:[:NAT,NAT:],NAT:] is non empty non empty-membered V63() set
K475() is set
K576() is non empty strict LattStr
the carrier of K576() is non empty set
K579() is V56() V57() V58() V59() V60() V61() V74() Element of bool NAT
[:K579(),K579():] is Relation-like set
[:[:K579(),K579():],K579():] is Relation-like set
bool [:[:K579(),K579():],K579():] is non empty set
2 is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real positive V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
3 is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real positive V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V62() V63() V74() V75() V76() V77() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V91() Element of NAT
4 is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real positive V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
5 is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real positive V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
L is Relation-like Function-like set
proj1 L is set
A is Relation-like Function-like Function-yielding V91() set
proj2 A is set
union (proj2 A) is set
doms A is Relation-like Function-like set
proj2 (doms A) is set
union (proj2 (doms A)) is set
D is set
L . D is set
[D,(L . D)] is V18() set
{D,(L . D)} is non empty set
{D} is non empty trivial 1 -element set
{{D,(L . D)},{D}} is non empty set
S is set
proj1 A is set
FS is set
A . FS is Relation-like Function-like set
proj1 (doms A) is set
(doms A) . FS is set
proj1 (A . FS) is set
D is set
S is set
proj1 (doms A) is set
FS is set
(doms A) . FS is set
proj1 A is set
A . FS is Relation-like Function-like set
FS is Relation-like Function-like set
proj1 (A . FS) is set
FS . D is set
[D,(FS . D)] is V18() set
{D,(FS . D)} is non empty set
{D} is non empty trivial 1 -element set
{{D,(FS . D)},{D}} is non empty set
L is non empty set
union L is set
A is non empty set
union A is set
[:(union L),(union A):] is Relation-like set
{ [:b₁,b₂:] where b₁ is Element of L, b₂ is Element of A : ( b₁ in L & b₂ in A ) } is set
union { [:b₁,b₂:] where b₁ is Element of L, b₂ is Element of A : ( b₁ in L & b₂ in A ) } is set
S is set
FS is set
FS is set
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
FD is set
f is set
z is Element of L
w is Element of A
[:z,w:] is Relation-like set
S is set
FS is set
FS is Element of L
FD is Element of A
[:FS,FD:] is Relation-like set
f is set
w is set
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
L is non empty set
union L is set
[:(union L),(union L):] is Relation-like set
{ [:b₁,b₁:] where b₁ is Element of L : b₁ in L } is set
union { [:b₁,b₁:] where b₁ is Element of L : b₁ in L } is set
{ [:b₁,b₂:] where b₁, b₂ is Element of L : ( b₁ in L & b₂ in L ) } is set
union { [:b₁,b₂:] where b₁, b₂ is Element of L : ( b₁ in L & b₂ in L ) } is set
S is set
FS is set
FS is Element of L
FD is Element of L
[:FS,FD:] is Relation-like set
[:FD,FD:] is Relation-like set
[:FS,FS:] is Relation-like set
S is set
FS is Element of L
[:FS,FS:] is Relation-like set
L is set
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt L) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt L) is non empty set
K559((EqRelLatt L)) is Relation-like the carrier of (EqRelLatt L) -defined the carrier of (EqRelLatt L) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt L),K559((EqRelLatt L)) #) is strict RelStr
L is set
(L) is reflexive transitive antisymmetric RelStr
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt L) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt L) is non empty set
K559((EqRelLatt L)) is Relation-like the carrier of (EqRelLatt L) -defined the carrier of (EqRelLatt L) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt L),K559((EqRelLatt L)) #) is strict RelStr
A is set
L is set
(L) is non empty reflexive transitive antisymmetric with_suprema with_infima RelStr
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt L) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt L) is non empty set
K559((EqRelLatt L)) is Relation-like the carrier of (EqRelLatt L) -defined the carrier of (EqRelLatt L) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt L),K559((EqRelLatt L)) #) is strict RelStr
the carrier of (L) is non empty set
[:L,L:] is Relation-like set
bool [:L,L:] is non empty set
the carrier of (LattPOSet (EqRelLatt L)) is non empty set
D is Element of the carrier of (LattPOSet (EqRelLatt L))
% D is Element of the carrier of (EqRelLatt L)
{ b₁ where b₁ is Relation-like L -defined L -valued Element of bool [:L,L:] : b₁ is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:] } is set
S is Relation-like L -defined L -valued Element of bool [:L,L:]
D is Element of the carrier of (EqRelLatt L)
S is Element of the carrier of (L)
L is set
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
the carrier of (EqRelLatt L) is non empty set
A is Element of the carrier of (EqRelLatt L)
D is Element of the carrier of (EqRelLatt L)
[:L,L:] is Relation-like set
bool [:L,L:] is non empty set
S is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
FS is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
S /\ FS is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
A "/\" D is Element of the carrier of (EqRelLatt L)
the L_meet of (EqRelLatt L) is Relation-like [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] -defined the carrier of (EqRelLatt L) -valued Function-like quasi_total Element of bool [:[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):], the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
[:[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):], the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [:[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):], the carrier of (EqRelLatt L):] is non empty non empty-membered set
the L_meet of (EqRelLatt L) . (S,FS) is set
[S,FS] is V18() set
{S,FS} is non empty set
{S} is non empty trivial 1 -element set
{{S,FS},{S}} is non empty set
the L_meet of (EqRelLatt L) . [S,FS] is set
L is set
(L) is non empty reflexive transitive antisymmetric with_suprema with_infima RelStr
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt L) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt L) is non empty set
K559((EqRelLatt L)) is Relation-like the carrier of (EqRelLatt L) -defined the carrier of (EqRelLatt L) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt L),K559((EqRelLatt L)) #) is strict 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)
FS is Element of the carrier of (EqRelLatt L)
FS % is Element of the carrier of (LattPOSet (EqRelLatt L))
the carrier of (LattPOSet (EqRelLatt L)) is non empty set
FS is Element of the carrier of (EqRelLatt L)
FS % is Element of the carrier of (LattPOSet (EqRelLatt L))
FS is Element of the carrier of (EqRelLatt L)
FS is Element of the carrier of (EqRelLatt L)
FS % is Element of the carrier of (LattPOSet (EqRelLatt L))
the carrier of (LattPOSet (EqRelLatt L)) is non empty set
FS % is Element of the carrier of (LattPOSet (EqRelLatt L))
L is non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet L is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of L is non empty set
K559(L) is Relation-like the carrier of L -defined the carrier of L -valued total reflexive antisymmetric transitive Element of bool [: the carrier of L, the carrier of L:]
[: the carrier of L, the carrier of L:] is non empty Relation-like set
bool [: the carrier of L, the carrier of L:] is non empty non empty-membered set
RelStr(# the carrier of L,K559(L) #) is strict RelStr
the carrier of (LattPOSet L) is non empty set
A is Element of the carrier of (LattPOSet L)
D is Element of the carrier of (LattPOSet L)
A "/\" D is Element of the carrier of (LattPOSet L)
% A is Element of the carrier of L
% D is Element of the carrier of L
(% A) "/\" (% D) is Element of the carrier of L
S is Element of the carrier of L
FS is Element of the carrier of L
S "/\" FS is Element of the carrier of L
(S "/\" FS) % is Element of the carrier of (LattPOSet L)
FS % is Element of the carrier of (LattPOSet L)
FD is Element of the carrier of (LattPOSet L)
S % is Element of the carrier of (LattPOSet L)
f is Element of the carrier of (LattPOSet L)
w is Element of the carrier of L
w % is Element of the carrier of (LattPOSet L)
L is set
(L) is non empty reflexive transitive antisymmetric with_suprema with_infima RelStr
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt L) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt L) is non empty set
K559((EqRelLatt L)) is Relation-like the carrier of (EqRelLatt L) -defined the carrier of (EqRelLatt L) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt L),K559((EqRelLatt L)) #) is strict 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)
A "/\" D is Element of the carrier of (L)
A /\ D is set
[:L,L:] is Relation-like set
bool [:L,L:] is non empty set
S is Element of the carrier of (EqRelLatt L)
FS is Element of the carrier of (EqRelLatt L)
S "/\" FS is Element of the carrier of (EqRelLatt L)
the L_meet of (EqRelLatt L) is Relation-like [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] -defined the carrier of (EqRelLatt L) -valued Function-like quasi_total Element of bool [:[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):], the carrier of (EqRelLatt L):]
[:[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):], the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [:[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):], the carrier of (EqRelLatt L):] is non empty non empty-membered set
FS is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
FD is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
the L_meet of (EqRelLatt L) . (FS,FD) is set
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
the L_meet of (EqRelLatt L) . [FS,FD] is set
S /\ FS is set
the carrier of (LattPOSet (EqRelLatt L)) is non empty set
FS is Element of the carrier of (LattPOSet (EqRelLatt L))
S is Element of the carrier of (LattPOSet (EqRelLatt L))
FS is Element of the carrier of (EqRelLatt L)
FS % is Element of the carrier of (LattPOSet (EqRelLatt L))
% (FS %) is Element of the carrier of (EqRelLatt L)
FD is Element of the carrier of (EqRelLatt L)
FD % is Element of the carrier of (LattPOSet (EqRelLatt L))
% (FD %) is Element of the carrier of (EqRelLatt L)
FS "/\" FD is Element of the carrier of (EqRelLatt L)
L is non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet L is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of L is non empty set
K559(L) is Relation-like the carrier of L -defined the carrier of L -valued total reflexive antisymmetric transitive Element of bool [: the carrier of L, the carrier of L:]
[: the carrier of L, the carrier of L:] is non empty Relation-like set
bool [: the carrier of L, the carrier of L:] is non empty non empty-membered set
RelStr(# the carrier of L,K559(L) #) is strict RelStr
the carrier of (LattPOSet L) is non empty set
A is Element of the carrier of (LattPOSet L)
D is Element of the carrier of (LattPOSet L)
A "\/" D is Element of the carrier of (LattPOSet L)
% A is Element of the carrier of L
% D is Element of the carrier of L
(% A) "\/" (% D) is Element of the carrier of L
S is Element of the carrier of L
FS is Element of the carrier of L
S "\/" FS is Element of the carrier of L
(S "\/" FS) % is Element of the carrier of (LattPOSet L)
FS % is Element of the carrier of (LattPOSet L)
S % is Element of the carrier of (LattPOSet L)
FD is Element of the carrier of (LattPOSet L)
f is Element of the carrier of (LattPOSet L)
w is Element of the carrier of L
w % is Element of the carrier of (LattPOSet L)
L is set
(L) is non empty reflexive transitive antisymmetric with_suprema with_infima RelStr
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt L) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt L) is non empty set
K559((EqRelLatt L)) is Relation-like the carrier of (EqRelLatt L) -defined the carrier of (EqRelLatt L) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt L),K559((EqRelLatt L)) #) is strict RelStr
the carrier of (L) is non empty set
[:L,L:] is Relation-like set
bool [:L,L:] is non empty set
A is Element of the carrier of (L)
D is Element of the carrier of (L)
A "\/" D is Element of the carrier of (L)
S is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
FS is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
S "\/" FS is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
the carrier of (LattPOSet (EqRelLatt L)) is non empty set
FD is Element of the carrier of (LattPOSet (EqRelLatt L))
FS is Element of the carrier of (LattPOSet (EqRelLatt L))
f is Element of the carrier of (EqRelLatt L)
f % is Element of the carrier of (LattPOSet (EqRelLatt L))
% (f %) is Element of the carrier of (EqRelLatt L)
w is Element of the carrier of (EqRelLatt L)
w % is Element of the carrier of (LattPOSet (EqRelLatt L))
% (w %) is Element of the carrier of (EqRelLatt L)
f "\/" w is Element of the carrier of (EqRelLatt L)
the L_join of (EqRelLatt L) is Relation-like [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] -defined the carrier of (EqRelLatt L) -valued Function-like quasi_total Element of bool [:[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):], the carrier of (EqRelLatt L):]
[:[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):], the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [:[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):], the carrier of (EqRelLatt L):] is non empty non empty-membered set
the L_join of (EqRelLatt L) . (f,w) is Element of the carrier of (EqRelLatt L)
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
the L_join of (EqRelLatt L) . [f,w] is set
L is non empty RelStr
the carrier of L is non empty set
bool the carrier of L is non empty non empty-membered set
A is Element of bool the carrier of L
{ b₁ where b₁ is Element of the carrier of L : b₁ is_<=_than A } is set
S is Element of the carrier of L
FS is Element of the carrier of L
FS is Element of the carrier of L
FD is Element of the carrier of L
f is Element of the carrier of L
FS is Element of the carrier of L
A is set
{ b₁ where b₁ is Element of the carrier of L : A is_<=_than b₁ } is set
S is set
FS is Element of the carrier of L
S is Element of the carrier of L
FS is Element of the carrier of L
FS is Element of the carrier of L
FD is Element of the carrier of L
FS is Element of the carrier of L
L is set
(L) is non empty reflexive transitive antisymmetric with_suprema with_infima RelStr
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt L) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt L) is non empty set
K559((EqRelLatt L)) is Relation-like the carrier of (EqRelLatt L) -defined the carrier of (EqRelLatt L) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt L),K559((EqRelLatt L)) #) is strict RelStr
the carrier of (L) is non empty set
bool the carrier of (L) is non empty non empty-membered set
A is Element of bool the carrier of (L)
A /\ the carrier of (L) is Element of bool the carrier of (L)
[:L,L:] is Relation-like set
bool [:L,L:] is non empty Element of bool (bool [:L,L:])
bool [:L,L:] is non empty set
bool (bool [:L,L:]) is non empty non empty-membered set
S is set
S is Element of bool (bool [:L,L:])
Intersect S is Relation-like L -defined L -valued Element of bool [:L,L:]
FS is Relation-like L -defined L -valued Element of bool [:L,L:]
FS is set
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
FD is set
FS is Relation-like L -defined L -valued Element of bool [:L,L:]
dom FS is Element of bool L
bool L is non empty set
field FS is set
FD is set
f is set
w is set
[FD,f] is V18() set
{FD,f} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,f},{FD}} is non empty set
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
[FD,w] is V18() set
{FD,w} is non empty set
{{FD,w},{FD}} is non empty set
z is set
FD is set
f is set
[FD,f] is V18() set
{FD,f} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,f},{FD}} is non empty set
[f,FD] is V18() set
{f,FD} is non empty set
{f} is non empty trivial 1 -element set
{{f,FD},{f}} is non empty set
w is set
FD is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
f is Element of the carrier of (L)
w is Element of the carrier of (L)
c₁₁ is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
z is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
dq9 is set
q is set
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
w is Element of the carrier of (L)
z is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
c₁₁ is Element of the carrier of (L)
c₁₁ is set
dq9 is set
L is non empty reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of L is non empty set
A is non empty reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of A is non empty set
[: the carrier of L, the carrier of A:] is non empty Relation-like set
bool [: the carrier of L, the carrier of A:] is non empty non empty-membered set
the Element of the carrier of A is Element of the carrier of A
the carrier of L --> the Element of the carrier of A is non empty Relation-like the carrier of L -defined the carrier of A -valued Function-like constant total quasi_total Element of bool [: the carrier of L, the carrier of A:]
{ the Element of the carrier of A} is non empty trivial 1 -element set
[: the carrier of L,{ the Element of the carrier of A}:] is non empty Relation-like set
S 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 Element of the carrier of L
FS is Element of the carrier of L
FS "/\" FS is Element of the carrier of L
S . (FS "/\" FS) is Element of the carrier of A
S . FS is Element of the carrier of A
S . FS is Element of the carrier of A
(S . FS) "/\" (S . FS) is Element of the carrier of A
the Element of the carrier of A "/\" the Element of the carrier of A is Element of the carrier of A
(S . FS) "/\" the Element of the carrier of A is Element of the carrier of A
FS is Element of the carrier of L
FS is Element of the carrier of L
FS "\/" FS is Element of the carrier of L
S . (FS "\/" FS) is Element of the carrier of A
S . FS is Element of the carrier of A
S . FS is Element of the carrier of A
(S . FS) "\/" (S . FS) is Element of the carrier of A
the Element of the carrier of A "\/" the Element of the carrier of A is Element of the carrier of A
(S . FS) "\/" the Element of the carrier of A is Element of the carrier of A
L is non empty reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of L is non empty set
the Element of the carrier of L is Element of the carrier of L
{ the Element of the carrier of L} is non empty trivial 1 -element Element of bool the carrier of L
bool the carrier of L is non empty non empty-membered set
[:{ the Element of the carrier of L},{ the Element of the carrier of L}:] is non empty Relation-like set
bool [:{ the Element of the carrier of L},{ the Element of the carrier of L}:] is non empty non empty-membered set
the Relation-like { the Element of the carrier of L} -defined { the Element of the carrier of L} -valued Element of bool [:{ the Element of the carrier of L},{ the Element of the carrier of L}:] is Relation-like { the Element of the carrier of L} -defined { the Element of the carrier of L} -valued Element of bool [:{ the Element of the carrier of L},{ the Element of the carrier of L}:]
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
"\/" ({S,FS},L) is Element of the carrier of L
the Element of the carrier of L "\/" the Element of the carrier of L is Element of the carrier of L
the InternalRel of 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:]
[: the carrier of L, the carrier of L:] is non empty Relation-like set
bool [: the carrier of L, the carrier of L:] is non empty non empty-membered set
S is set
FS is set
FS is set
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
[ the Element of the carrier of L, the Element of the carrier of L] is V18() Element of [: the carrier of L, the carrier of L:]
{ the Element of the carrier of L, the Element of the carrier of L} is non empty set
{ the Element of the carrier of L} is non empty trivial 1 -element set
{{ the Element of the carrier of L, the Element of the carrier of L},{ the Element of the carrier of L}} is non empty set
RelStr(# { the Element of the carrier of L}, the Relation-like { the Element of the carrier of L} -defined { the Element of the carrier of L} -valued Element of bool [:{ the Element of the carrier of L},{ the Element of the carrier of L}:] #) is non empty trivial V125() 1 -element strict RelStr
S is strict SubRelStr of L
FS is Element of the carrier of L
FS is Element of the carrier of L
{FS,FS} is non empty Element of bool the carrier of L
"/\" ({FS,FS},L) is Element of the carrier of L
the Element of the carrier of L "/\" the Element of the carrier of L is Element of the carrier of L
L is non empty reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of L is non empty set
A is non empty reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of A is non empty set
[: the carrier of L, the carrier of A:] is non empty Relation-like set
bool [: the carrier of L, the carrier of A:] is non empty non empty-membered set
D is Relation-like the carrier of L -defined the carrier of A -valued Function-like quasi_total meet-preserving join-preserving Element of bool [: the carrier of L, the carrier of A:]
Image D is strict reflexive transitive antisymmetric V184(A) SubRelStr of A
rng D is Element of bool the carrier of A
bool the carrier of A is non empty non empty-membered set
subrelstr (rng D) is strict reflexive transitive antisymmetric V184(A) SubRelStr of A
the carrier of (subrelstr (rng D)) is set
dom D is Element of bool the carrier of L
bool the carrier of L is non empty non empty-membered set
FS is Element of the carrier of A
FS is Element of the carrier of A
{FS,FS} is non empty Element of bool the carrier of A
"\/" ({FS,FS},A) is Element of the carrier of A
FD is set
D . FD is set
f is set
D . f is set
w is Element of the carrier of L
z is Element of the carrier of L
{w,z} is non empty Element of bool the carrier of L
D .: {w,z} is Element of bool the carrier of A
"\/" ((D .: {w,z}),A) is Element of the carrier of A
"\/" ({w,z},L) is Element of the carrier of L
D . ("\/" ({w,z},L)) 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 non empty Element of bool the carrier of A
"/\" ({FS,FS},A) is Element of the carrier of A
FD is set
D . FD is set
f is set
D . f is set
w is Element of the carrier of L
z is Element of the carrier of L
{w,z} is non empty Element of bool the carrier of L
D .: {w,z} is Element of bool the carrier of A
"/\" ((D .: {w,z}),A) is Element of the carrier of A
"/\" ({w,z},L) is Element of the carrier of L
D . ("/\" ({w,z},L)) is Element of the carrier of A
L is non empty set
L is non empty set
A is set
D is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
D |-> A is Relation-like NAT -defined Function-like V63() D -element FinSequence-like FinSubsequence-like set
Seg D is V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() D -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= D ) } is set
(Seg D) --> A is Relation-like Seg D -defined Seg D -defined {A} -valued Function-like constant total total quasi_total V63() FinSequence-like FinSubsequence-like Element of bool [:(Seg D),{A}:]
{A} is non empty trivial 1 -element set
[:(Seg D),{A}:] is Relation-like set
bool [:(Seg D),{A}:] is non empty set
S is Relation-like set
FS is Relation-like set
FS is non empty Relation-like NAT -defined L -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of L
dom FS is non empty V56() V57() V58() V59() V60() V61() V72() V74() Element of bool NAT
FS . 1 is set
len FS is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
FD is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS . FD is set
FD + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS . (FD + 1) is set
[(FS . FD),(FS . (FD + 1))] is V18() set
{(FS . FD),(FS . (FD + 1))} is non empty set
{(FS . FD)} is non empty trivial 1 -element set
{{(FS . FD),(FS . (FD + 1))},{(FS . FD)}} is non empty set
Seg (len FS) is non empty V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() len FS -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len FS ) } is set
Seg (len FS) is non empty V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() len FS -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len FS ) } is set
FS . (len FS) is set
L is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
D is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A + D is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
L is non empty set
A is set
D is set
S is Relation-like set
FS is Relation-like set
FS is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FD is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
f is non empty Relation-like NAT -defined L -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of L
len f is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
f . (len f) is set
dom f is non empty V56() V57() V58() V59() V60() V61() V72() V74() Element of bool NAT
rng f is non empty Element of bool L
bool L is non empty non empty-membered set
FD - FS is V37() ext-real V43() set
z is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
w is Element of L
z |-> w is Relation-like NAT -defined L -valued Function-like V63() z -element FinSequence-like FinSubsequence-like Element of z -tuples_on L
z -tuples_on L is non empty functional FinSequence-membered FinSequenceSet of L
L * is non empty functional FinSequence-membered FinSequenceSet of L
{ b₁ where b₁ is Relation-like NAT -defined L -valued Function-like V63() FinSequence-like FinSubsequence-like Element of L * : len b₁ = z } is set
Seg z is V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() z -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= z ) } is set
(Seg z) --> w is Relation-like Seg z -defined Seg z -defined L -valued {w} -valued Function-like constant total total quasi_total V63() FinSequence-like FinSubsequence-like Element of bool [:(Seg z),{w}:]
{w} is non empty trivial 1 -element set
[:(Seg z),{w}:] is Relation-like set
bool [:(Seg z),{w}:] is non empty set
c₁₁ is Relation-like NAT -defined L -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of L
dq9 is non empty Relation-like NAT -defined L -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of L
dom dq9 is non empty V56() V57() V58() V59() V60() V61() V72() V74() Element of bool NAT
f ^ dq9 is non empty Relation-like NAT -defined L -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of L
q is non empty Relation-like NAT -defined L -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of L
len q is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
len dq9 is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
(len f) + (len dq9) is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS + (FD - FS) is V37() ext-real V43() set
q . 1 is set
f . 1 is set
q . (len q) is set
q . ((len f) + (len dq9)) is set
dq9 . (len dq9) is set
Q is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
q . Q is set
Q + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
q . (Q + 1) is set
[(q . Q),(q . (Q + 1))] is V18() set
{(q . Q),(q . (Q + 1))} is non empty set
{(q . Q)} is non empty trivial 1 -element set
{{(q . Q),(q . (Q + 1))},{(q . Q)}} is non empty set
Seg (len f) is non empty V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() len f -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len f ) } is set
f . (Q + 1) is set
f . Q is set
dq9 . 1 is set
(len f) + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
Q - (len f) is V37() ext-real V43() set
(Q - (len f)) + (len f) is V37() ext-real V43() set
0 + (len f) is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
((len f) + (len dq9)) - (len f) is V37() ext-real V43() set
u is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
u + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
(Q + 1) - (len f) is V37() ext-real V43() set
dq9 . ((Q + 1) - (len f)) is set
dq9 . (u + 1) is set
Seg (len dq9) is non empty V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() len dq9 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len dq9 ) } is set
dq9 . u is set
(len f) + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
f . (Q + 1) is set
f . Q is set
dq9 . 1 is set
(len f) + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
Q - (len f) is V37() ext-real V43() set
(Q - (len f)) + (len f) is V37() ext-real V43() set
0 + (len f) is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
((len f) + (len dq9)) - (len f) is V37() ext-real V43() set
u is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
u + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
(Q + 1) - (len f) is V37() ext-real V43() set
dq9 . ((Q + 1) - (len f)) is set
dq9 . (u + 1) is set
Seg (len dq9) is non empty V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() len dq9 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len dq9 ) } is set
dq9 . u is set
(len f) + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
L is non empty set
(L) is non empty reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V183() RelStr
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt L) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt L) is non empty set
K559((EqRelLatt L)) is Relation-like the carrier of (EqRelLatt L) -defined the carrier of (EqRelLatt L) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt L),K559((EqRelLatt L)) #) is strict RelStr
[:L,L:] is non empty Relation-like set
bool [:L,L:] is non empty non empty-membered set
A is meet-inheriting join-inheriting SubRelStr of (L)
the carrier of A is set
id L is non empty Relation-like L -defined L -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:L,L:]
D is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
S is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : S₁[b₁] } is set
FS is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
FD is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
field D is set
f is set
w is set
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
FS "\/" FD is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
z is non empty Relation-like NAT -defined L -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of L
len z is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
z . 1 is set
z . (len z) is set
1 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
c₁₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V63() cardinal set
2 + c₁₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
dq9 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
dq9 + 2 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
q is non empty V56() V57() V58() V59() V60() V61() V72() V74() Element of bool NAT
min q is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
(min q) + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
u is non empty Relation-like NAT -defined L -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of L
len u is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
u . 1 is set
u . (len u) is set
1 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
1 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
(min q) - 1 is V37() ext-real V43() set
((min q) - 1) + 2 is V37() ext-real V43() set
(min q) -' 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real non negative V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
((min q) + 1) - 1 is V37() ext-real V43() set
u is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
u + 2 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
v is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
a is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
b is set
e is set
[b,e] is V18() set
{b,e} is non empty set
{b} is non empty trivial 1 -element set
{{b,e},{b}} is non empty set
v "\/" a is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
FS is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS + 2 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS + 2 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FD is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
f is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
w is set
z is set
[w,z] is V18() set
{w,z} is non empty set
{w} is non empty trivial 1 -element set
{{w,z},{w}} is non empty set
FD "\/" f is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
field f is set
field FD is set
c₁₁ is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
dq9 is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
q is set
Q is set
[q,Q] is V18() set
{q,Q} is non empty set
{q} is non empty trivial 1 -element set
{{q,Q},{q}} is non empty set
c₁₁ "\/" dq9 is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
field dq9 is set
field c₁₁ is set
1 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS + (1 + 1) is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
(FS + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
u is non empty Relation-like NAT -defined L -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of L
len u is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
1 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS + (1 + 1) is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
(FS + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
u is non empty Relation-like NAT -defined L -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of L
len u is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
L is non empty set
(L) is non empty reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V183() RelStr
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt L) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt L) is non empty set
K559((EqRelLatt L)) is Relation-like the carrier of (EqRelLatt L) -defined the carrier of (EqRelLatt L) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt L),K559((EqRelLatt L)) #) is strict RelStr
[:L,L:] is non empty Relation-like set
bool [:L,L:] is non empty non empty-membered set
id L is non empty Relation-like L -defined L -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:L,L:]
A is meet-inheriting join-inheriting SubRelStr of (L)
the carrier of A is set
(L,A) is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
D is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
D + 2 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
D + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
S is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V63() cardinal set
(D + 1) + S is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
(D + 1) + FS is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
((D + 1) + FS) + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
D + FS is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
(D + FS) + 2 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
FS is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
FD is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
f is set
w is set
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
FS "\/" FD is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
(D + 2) + FS is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
field FD is set
field FS is set
z is non empty Relation-like NAT -defined L -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of L
len z is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
L is non empty set
[:L,L:] is non empty Relation-like set
A is 1-sorted
the carrier of A is set
[:[:L,L:], the carrier of A:] is Relation-like set
bool [:[:L,L:], 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
FS is Element of L
D . (S,FS) is set
[S,FS] is V18() set
{S,FS} is non empty set
{S} is non empty trivial 1 -element set
{{S,FS},{S}} is non empty set
D . [S,FS] is set
[S,FS] is V18() Element of [:L,L:]
FS is Element of [:L,L:]
D . FS is Element of the carrier of A
L is non empty set
[:L,L:] is non empty Relation-like set
A is 1-sorted
the carrier of A is set
[:[:L,L:], the carrier of A:] is Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
Bottom A is Element of the carrier of A
[:L,L:] --> (Bottom A) is non empty Relation-like [:L,L:] -defined the carrier of A -valued Function-like constant total quasi_total Element of bool [:[:L,L:], the carrier of A:]
{(Bottom A)} is non empty trivial 1 -element set
[:[:L,L:],{(Bottom A)}:] is non empty Relation-like 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
FS is Element of L
[S,FS] is V18() Element of [:L,L:]
{S,FS} is non empty set
{S} is non empty trivial 1 -element set
{{S,FS},{S}} is non empty set
D . [S,FS] is Element of the carrier of A
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
FS is Element of L
(L,A,S,FS,FS) is Element of the carrier of A
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
S . [FS,FS] is set
(L,A,S,FS,FS) is Element of the carrier of A
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
S . [FS,FS] is set
FS is Element of L
FD is Element of L
(L,A,S,FS,FD) is Element of the carrier of A
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
S . [FS,FD] is set
FS is Element of L
(L,A,S,FS,FS) is Element of the carrier of A
[FS,FS] is V18() set
{FS,FS} is non empty set
{{FS,FS},{FS}} is non empty set
S . [FS,FS] is set
(L,A,S,FS,FD) is Element of the carrier of A
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
S . [FS,FD] is set
(L,A,S,FS,FS) "\/" (L,A,S,FS,FD) is Element of the carrier of A
FS is Element of L
(L,A,S,FS,FS) is Element of the carrier of A
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
S . [FS,FS] is set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
(L) is non empty reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V183() RelStr
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt L) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt L) is non empty set
K559((EqRelLatt L)) is Relation-like the carrier of (EqRelLatt L) -defined the carrier of (EqRelLatt L) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt L),K559((EqRelLatt L)) #) is strict RelStr
the carrier of (L) is non empty set
[: the carrier of A, the carrier of (L):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (L):] is non empty non empty-membered set
bool [:L,L:] is non empty non empty-membered set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total (L,A) (L,A) (L,A) Element of bool [:[:L,L:], the carrier of A:]
S is Element of the carrier of A
FS is Relation-like L -defined L -valued Element of bool [:L,L:]
FS is set
FD is set
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
[FD,FS] is V18() set
{FD,FS} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,FS},{FD}} is non empty set
w is Element of L
f is Element of L
(L,A,D,w,f) is Element of the carrier of A
[w,f] is V18() set
{w,f} is non empty set
{w} is non empty trivial 1 -element set
{{w,f},{w}} is non empty set
D . [w,f] is set
(L,A,D,f,w) is Element of the carrier of A
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
D . [f,w] is set
FS is set
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
Bottom A is Element of the carrier of A
FD is Element of L
(L,A,D,FD,FD) is Element of the carrier of A
[FD,FD] is V18() set
{FD,FD} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,FD},{FD}} is non empty set
D . [FD,FD] is set
dom FS is Element of bool L
bool L is non empty non empty-membered set
field FS is set
FS is set
FD is set
f is set
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
[FD,f] is V18() set
{FD,f} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,f},{FD}} is non empty set
[FS,f] is V18() set
{FS,f} is non empty set
{{FS,f},{FS}} is non empty set
w is Element of L
z is Element of L
(L,A,D,w,z) is Element of the carrier of A
[w,z] is V18() set
{w,z} is non empty set
{w} is non empty trivial 1 -element set
{{w,z},{w}} is non empty set
D . [w,z] is set
c₁₁ is Element of L
(L,A,D,z,c₁₁) is Element of the carrier of A
[z,c₁₁] is V18() set
{z,c₁₁} is non empty set
{z} is non empty trivial 1 -element set
{{z,c₁₁},{z}} is non empty set
D . [z,c₁₁] is set
(L,A,D,w,z) "\/" (L,A,D,z,c₁₁) is Element of the carrier of A
(L,A,D,w,c₁₁) is Element of the carrier of A
[w,c₁₁] is V18() set
{w,c₁₁} is non empty set
{{w,c₁₁},{w}} is non empty set
D . [w,c₁₁] is set
FS is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
FD is Element of the carrier of (L)
f is Element of the carrier of (L)
S is Relation-like the carrier of A -defined the carrier of (L) -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of (L):]
S is Relation-like the carrier of A -defined the carrier of (L) -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of (L):]
FS is Relation-like the carrier of A -defined the carrier of (L) -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of (L):]
f is Element of the carrier of A
S . f is Element of the carrier of (L)
FS . f is Element of the carrier of (L)
w is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
z is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
c₁₁ is Element of L
dq9 is Element of L
[c₁₁,dq9] is V18() Element of [:L,L:]
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
(L,A,D,c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
D . [c₁₁,dq9] is set
c₁₁ is set
dq9 is set
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
field w is set
q is Element of L
Q is Element of L
[q,Q] is V18() Element of [:L,L:]
{q,Q} is non empty set
{q} is non empty trivial 1 -element set
{{q,Q},{q}} is non empty set
field z is set
q is Element of L
Q is Element of L
[q,Q] is V18() Element of [:L,L:]
{q,Q} is non empty set
{q} is non empty trivial 1 -element set
{{q,Q},{q}} is non empty set
FS is Relation-like the carrier of A -defined the carrier of (L) -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of (L):]
FD is Relation-like the carrier of A -defined the carrier of (L) -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of (L):]
f is set
FS . f is set
FD . f is set
L is non empty set
[:L,L:] is non empty Relation-like set
(L) is non empty reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V183() RelStr
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt L) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt L) is non empty set
K559((EqRelLatt L)) is Relation-like the carrier of (EqRelLatt L) -defined the carrier of (EqRelLatt L) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt L),K559((EqRelLatt L)) #) is strict RelStr
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total (L,A) (L,A) (L,A) Element of bool [:[:L,L:], the carrier of A:]
(L,A,D) is Relation-like the carrier of A -defined the carrier of (L) -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of (L):]
the carrier of (L) is non empty set
[: the carrier of A, the carrier of (L):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (L):] is non empty non empty-membered set
S is Element of the carrier of A
FS is Element of the carrier of A
{S,FS} is non empty Element of bool the carrier of A
bool the carrier of A is non empty non empty-membered set
(L,A,D) .: {S,FS} is Element of bool the carrier of (L)
bool the carrier of (L) is non empty non empty-membered set
bool [:L,L:] is non empty non empty-membered set
S "/\" FS is Element of the carrier of A
(L,A,D) . (S "/\" FS) is Element of the carrier of (L)
FD is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
(L,A,D) . FS is Element of the carrier of (L)
f is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
(L,A,D) . S is Element of the carrier of (L)
w is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
w /\ f is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
z is Element of L
c₁₁ is Element of L
[z,c₁₁] is V18() Element of [:L,L:]
{z,c₁₁} is non empty set
{z} is non empty trivial 1 -element set
{{z,c₁₁},{z}} is non empty set
(L,A,D,z,c₁₁) is Element of the carrier of A
[z,c₁₁] is V18() set
D . [z,c₁₁] is set
z is set
c₁₁ is set
[z,c₁₁] is V18() set
{z,c₁₁} is non empty set
{z} is non empty trivial 1 -element set
{{z,c₁₁},{z}} is non empty set
field w is set
field f is set
(field w) /\ (field f) is set
L /\ (field f) is set
L /\ L is set
field (w /\ f) is set
dq9 is Element of L
q is Element of L
[dq9,q] is V18() Element of [:L,L:]
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
field FD is set
dq9 is Element of L
q is Element of L
[dq9,q] is V18() Element of [:L,L:]
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
dom (L,A,D) is Element of bool the carrier of A
"/\" (((L,A,D) .: {S,FS}),(L)) is Element of the carrier of (L)
{((L,A,D) . S),((L,A,D) . FS)} is non empty Element of bool the carrier of (L)
"/\" ({((L,A,D) . S),((L,A,D) . FS)},(L)) is Element of the carrier of (L)
((L,A,D) . S) "/\" ((L,A,D) . FS) is Element of the carrier of (L)
"/\" ({S,FS},A) is Element of the carrier of A
(L,A,D) . ("/\" ({S,FS},A)) is Element of the carrier of (L)
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total (L,A) (L,A) (L,A) Element of bool [:[:L,L:], the carrier of A:]
(L,A,D) is Relation-like the carrier of A -defined the carrier of (L) -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of (L):]
(L) is non empty reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V183() RelStr
EqRelLatt L is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt L) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt L) is non empty set
K559((EqRelLatt L)) is Relation-like the carrier of (EqRelLatt L) -defined the carrier of (EqRelLatt L) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):]
[: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt L), the carrier of (EqRelLatt L):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt L),K559((EqRelLatt L)) #) is strict RelStr
the carrier of (L) is non empty set
[: the carrier of A, the carrier of (L):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (L):] is non empty non empty-membered set
rng D is Element of bool the carrier of A
bool the carrier of A is non empty non empty-membered set
FS is Element of the carrier of A
(L,A,D) . FS is Element of the carrier of (L)
FS is Element of the carrier of A
(L,A,D) . FS is Element of the carrier of (L)
FD is set
D . FD is set
f is set
w is set
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
dq9 is set
D . dq9 is set
q is set
Q is set
[q,Q] is V18() set
{q,Q} is non empty set
{q} is non empty trivial 1 -element set
{{q,Q},{q}} is non empty set
bool [:L,L:] is non empty non empty-membered set
a is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
b is Relation-like L -defined L -valued total reflexive symmetric transitive Element of bool [:L,L:]
u is Element of L
v is Element of L
(L,A,D,u,v) is Element of the carrier of A
[u,v] is V18() set
{u,v} is non empty set
{u} is non empty trivial 1 -element set
{{u,v},{u}} is non empty set
D . [u,v] is set
[u,v] is V18() Element of [:L,L:]
z is Element of L
c₁₁ is Element of L
(L,A,D,z,c₁₁) is Element of the carrier of A
[z,c₁₁] is V18() set
{z,c₁₁} is non empty set
{z} is non empty trivial 1 -element set
{{z,c₁₁},{z}} is non empty set
D . [z,c₁₁] is set
[z,c₁₁] is V18() Element of [:L,L:]
L is set
{L} is non empty trivial 1 -element set
{{L}} is non empty trivial 1 -element set
{{{L}}} is non empty trivial 1 -element set
{{L},{{L}},{{{L}}}} is non empty set
L \/ {{L},{{L}},{{{L}}}} is non empty set
L is set
(L) is set
{L} is non empty trivial 1 -element set
{{L}} is non empty trivial 1 -element set
{{{L}}} is non empty trivial 1 -element set
{{L},{{L}},{{{L}}}} is non empty set
L \/ {{L},{{L}},{{{L}}}} is non empty set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 1 -element set
{{L}} is non empty trivial 1 -element set
{{{L}}} is non empty trivial 1 -element set
{{L},{{L}},{{{L}}}} is non empty set
L \/ {{L},{{L}},{{{L}}}} is non empty set
[:(L),(L):] is non empty Relation-like set
[:[:(L),(L):], the carrier of A:] is non empty Relation-like set
bool [:[:(L),(L):], the carrier of A:] is non empty non empty-membered 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
S is Element of [:L,L, the carrier of A, the carrier of A:]
S `3_4 is Element of the carrier of A
S `1 is set
(S `1) `2 is set
S `4_4 is Element of the carrier of A
(S `3_4) "\/" (S `4_4) is Element of the carrier of A
S `1_4 is Element of L
(S `1) `1 is set
((S `1) `1) `1 is set
S `2_4 is Element of L
((S `1) `1) `2 is set
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
w is Element of (L)
z is Element of (L)
D . (w,z) is set
[w,z] is V18() set
{w,z} is non empty set
{w} is non empty trivial 1 -element set
{{w,z},{w}} is non empty set
D . [w,z] is set
c<sub>11</sub> is Element of L
dq9 is Element of L
(L,A,D,c<sub>11</sub>,dq9) is Element of the carrier of A
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
D . [c<sub>11</sub>,dq9] is set
c<sub>11</sub> is Element of L
(L,A,D,c<sub>11</sub>,(S `1_4)) is Element of the carrier of A
[c₁₁,(S `1_4)] is V18() set
{c<sub>11</sub>,(S `1_4)} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,(S `1_4)},{c<sub>11</sub>}} is non empty set
D . [c<sub>11</sub>,(S `1_4)] is set
(L,A,D,c₁₁,(S `1_4)) "\/" FS is Element of the carrier of A
c<sub>11</sub> is Element of L
(L,A,D,c<sub>11</sub>,(S `1_4)) is Element of the carrier of A
[c₁₁,(S `1_4)] is V18() set
{c<sub>11</sub>,(S `1_4)} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,(S `1_4)},{c<sub>11</sub>}} is non empty set
D . [c<sub>11</sub>,(S `1_4)] is set
(L,A,D,c₁₁,(S `1_4)) "\/" FS is Element of the carrier of A
((L,A,D,c<sub>11</sub>,(S `1_4)) "\/" FS) "\/" FS is Element of the carrier of A
c₁₁ is Element of L
(L,A,D,c₁₁,(S `2_4)) is Element of the carrier of A
[c<sub>11</sub>,(S `2_4)] is V18() set
{c₁₁,(S `2_4)} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,(S `2_4)},{c₁₁}} is non empty set
D . [c₁₁,(S `2_4)] is set
(L,A,D,c<sub>11</sub>,(S `2_4)) "\/" FS is Element of the carrier of A
c₁₁ is Element of L
(L,A,D,c₁₁,(S `1_4)) is Element of the carrier of A
[c<sub>11</sub>,(S `1_4)] is V18() set
{c₁₁,(S `1_4)} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,(S `1_4)},{c₁₁}} is non empty set
D . [c₁₁,(S `1_4)] is set
(L,A,D,c<sub>11</sub>,(S `1_4)) "\/" FS is Element of the carrier of A
c₁₁ is Element of L
(L,A,D,c₁₁,(S `1_4)) is Element of the carrier of A
[c<sub>11</sub>,(S `1_4)] is V18() set
{c₁₁,(S `1_4)} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,(S `1_4)},{c₁₁}} is non empty set
D . [c₁₁,(S `1_4)] is set
(L,A,D,c<sub>11</sub>,(S `1_4)) "\/" FS is Element of the carrier of A
((L,A,D,c₁₁,(S `1_4)) "\/" FS) "\/" FS is Element of the carrier of A
c<sub>11</sub> is Element of L
(L,A,D,c<sub>11</sub>,(S `2_4)) is Element of the carrier of A
[c₁₁,(S `2_4)] is V18() set
{c<sub>11</sub>,(S `2_4)} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,(S `2_4)},{c<sub>11</sub>}} is non empty set
D . [c<sub>11</sub>,(S `2_4)] is set
(L,A,D,c₁₁,(S `2_4)) "\/" FS is Element of the carrier of A
w is Relation-like [:(L),(L):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L),(L):], the carrier of A:]
z is Relation-like [:(L),(L):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L),(L):], the carrier of A:]
c<sub>11</sub> is Element of L
z . ({L},c<sub>11</sub>) is set
[{L},c<sub>11</sub>] is V18() set
{{L},c<sub>11</sub>} is non empty set
{{{L},c<sub>11</sub>},{{L}}} is non empty set
z . [{L},c<sub>11</sub>] is set
(L,A,D,c<sub>11</sub>,(S `1_4)) is Element of the carrier of A
[c₁₁,(S `1_4)] is V18() set
{c<sub>11</sub>,(S `1_4)} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,(S `1_4)},{c<sub>11</sub>}} is non empty set
D . [c<sub>11</sub>,(S `1_4)] is set
(L,A,D,c₁₁,(S `1_4)) "\/" FS is Element of the carrier of A
z . ({{L}},c<sub>11</sub>) is set
[{{L}},c<sub>11</sub>] is V18() set
{{{L}},c<sub>11</sub>} is non empty set
{{{{L}},c<sub>11</sub>},{{{L}}}} is non empty set
z . [{{L}},c<sub>11</sub>] is set
((L,A,D,c<sub>11</sub>,(S `1_4)) "\/" FS) "\/" FS is Element of the carrier of A
z . ({{{L}}},c₁₁) is set
[{{{L}}},c₁₁] is V18() set
{{{{L}}},c₁₁} is non empty set
{{{{L}}}} is non empty trivial 1 -element set
{{{{{L}}},c₁₁},{{{{L}}}}} is non empty set
z . [{{{L}}},c₁₁] is set
(L,A,D,c₁₁,(S `2_4)) is Element of the carrier of A
[c<sub>11</sub>,(S `2_4)] is V18() set
{c₁₁,(S `2_4)} is non empty set
{{c<sub>11</sub>,(S `2_4)},{c₁₁}} is non empty set
D . [c₁₁,(S `2_4)] is set
(L,A,D,c<sub>11</sub>,(S `2_4)) "\/" FS is Element of the carrier of A
dq9 is Element of (L)
z . ({L},dq9) is set
[{L},dq9] is V18() set
{{L},dq9} is non empty set
{{{L},dq9},{{L}}} is non empty set
z . [{L},dq9] is set
q is Element of L
(L,A,D,q,(S `1_4)) is Element of the carrier of A
[q,(S `1_4)] is V18() set
{q,(S `1_4)} is non empty set
{q} is non empty trivial 1 -element set
{{q,(S `1_4)},{q}} is non empty set
D . [q,(S `1_4)] is set
(L,A,D,q,(S `1_4)) "\/" FS is Element of the carrier of A
z . ({{L}},dq9) is set
[{{L}},dq9] is V18() set
{{{L}},dq9} is non empty set
{{{{L}},dq9},{{{L}}}} is non empty set
z . [{{L}},dq9] is set
q is Element of L
(L,A,D,q,(S `1_4)) is Element of the carrier of A
[q,(S `1_4)] is V18() set
{q,(S `1_4)} is non empty set
{q} is non empty trivial 1 -element set
{{q,(S `1_4)},{q}} is non empty set
D . [q,(S `1_4)] is set
(L,A,D,q,(S `1_4)) "\/" FS is Element of the carrier of A
((L,A,D,q,(S `1_4)) "\/" FS) "\/" FS is Element of the carrier of A
z . ({{{L}}},dq9) is set
[{{{L}}},dq9] is V18() set
{{{{L}}},dq9} is non empty set
{{{{{L}}},dq9},{{{{L}}}}} is non empty set
z . [{{{L}}},dq9] is set
q is Element of L
(L,A,D,q,(S `2_4)) is Element of the carrier of A
[q,(S `2_4)] is V18() set
{q,(S `2_4)} is non empty set
{q} is non empty trivial 1 -element set
{{q,(S `2_4)},{q}} is non empty set
D . [q,(S `2_4)] is set
(L,A,D,q,(S `2_4)) "\/" FS is Element of the carrier of A
z . ({L},{L}) is set
[{L},{L}] is V18() set
{{L},{L}} is non empty set
{{{L},{L}},{{L}}} is non empty set
z . [{L},{L}] is set
z . ({{L}},{{L}}) is set
[{{L}},{{L}}] is V18() set
{{{L}},{{L}}} is non empty set
{{{{L}},{{L}}},{{{L}}}} is non empty set
z . [{{L}},{{L}}] is set
z . ({{{L}}},{{{L}}}) is set
[{{{L}}},{{{L}}}] is V18() set
{{{{L}}},{{{L}}}} is non empty set
{{{{L}}}} is non empty trivial 1 -element set
{{{{{L}}},{{{L}}}},{{{{L}}}}} is non empty set
z . [{{{L}}},{{{L}}}] is set
z . ({{L}},{{{L}}}) is set
[{{L}},{{{L}}}] is V18() set
{{{L}},{{{L}}}} is non empty set
{{{{L}},{{{L}}}},{{{L}}}} is non empty set
z . [{{L}},{{{L}}}] is set
z . ({{{L}}},{{L}}) is set
[{{{L}}},{{L}}] is V18() set
{{{{L}}},{{L}}} is non empty set
{{{{{L}}},{{L}}},{{{{L}}}}} is non empty set
z . [{{{L}}},{{L}}] is set
z . ({L},{{L}}) is set
[{L},{{L}}] is V18() set
{{L},{{L}}} is non empty set
{{{L},{{L}}},{{L}}} is non empty set
z . [{L},{{L}}] is set
z . ({{L}},{L}) is set
[{{L}},{L}] is V18() set
{{{L}},{L}} is non empty set
{{{{L}},{L}},{{{L}}}} is non empty set
z . [{{L}},{L}] is set
z . ({L},{{{L}}}) is set
[{L},{{{L}}}] is V18() set
{{L},{{{L}}}} is non empty set
{{{L},{{{L}}}},{{L}}} is non empty set
z . [{L},{{{L}}}] is set
z . ({{{L}}},{L}) is set
[{{{L}}},{L}] is V18() set
{{{{L}}},{L}} is non empty set
{{{{{L}}},{L}},{{{{L}}}}} is non empty set
z . [{{{L}}},{L}] is set
c<sub>11</sub> is Element of L
dq9 is Element of L
z . (c<sub>11</sub>,dq9) is set
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
z . [c<sub>11</sub>,dq9] is set
(L,A,D,c<sub>11</sub>,dq9) is Element of the carrier of A
D . [c<sub>11</sub>,dq9] is set
q is Element of (L)
Q is Element of (L)
((L),A,z,q,Q) is Element of the carrier of A
[q,Q] is V18() set
{q,Q} is non empty set
{q} is non empty trivial 1 -element set
{{q,Q},{q}} is non empty set
z . [q,Q] is set
c<sub>11</sub> is Element of L
z . (c<sub>11</sub>,{L}) is set
[c<sub>11</sub>,{L}] is V18() set
{c<sub>11</sub>,{L}} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,{L}},{c<sub>11</sub>}} is non empty set
z . [c<sub>11</sub>,{L}] is set
(L,A,D,c<sub>11</sub>,(S `1_4)) is Element of the carrier of A
[c₁₁,(S `1_4)] is V18() set
{c<sub>11</sub>,(S `1_4)} is non empty set
{{c₁₁,(S `1_4)},{c<sub>11</sub>}} is non empty set
D . [c<sub>11</sub>,(S `1_4)] is set
(L,A,D,c₁₁,(S `1_4)) "\/" FS is Element of the carrier of A
z . (c<sub>11</sub>,{{L}}) is set
[c<sub>11</sub>,{{L}}] is V18() set
{c<sub>11</sub>,{{L}}} is non empty set
{{c<sub>11</sub>,{{L}}},{c<sub>11</sub>}} is non empty set
z . [c<sub>11</sub>,{{L}}] is set
((L,A,D,c<sub>11</sub>,(S `1_4)) "\/" FS) "\/" FS is Element of the carrier of A
z . (c₁₁,{{{L}}}) is set
[c₁₁,{{{L}}}] is V18() set
{c₁₁,{{{L}}}} is non empty set
{{c₁₁,{{{L}}}},{c₁₁}} is non empty set
z . [c₁₁,{{{L}}}] is set
(L,A,D,c₁₁,(S `2_4)) is Element of the carrier of A
[c<sub>11</sub>,(S `2_4)] is V18() set
{c₁₁,(S `2_4)} is non empty set
{{c<sub>11</sub>,(S `2_4)},{c₁₁}} is non empty set
D . [c₁₁,(S `2_4)] is set
(L,A,D,c<sub>11</sub>,(S `2_4)) "\/" FS is Element of the carrier of A
dq9 is Element of (L)
z . (dq9,{L}) is set
[dq9,{L}] is V18() set
{dq9,{L}} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,{L}},{dq9}} is non empty set
z . [dq9,{L}] is set
q is Element of L
(L,A,D,q,(S `1_4)) is Element of the carrier of A
[q,(S `1_4)] is V18() set
{q,(S `1_4)} is non empty set
{q} is non empty trivial 1 -element set
{{q,(S `1_4)},{q}} is non empty set
D . [q,(S `1_4)] is set
(L,A,D,q,(S `1_4)) "\/" FS is Element of the carrier of A
z . (dq9,{{L}}) is set
[dq9,{{L}}] is V18() set
{dq9,{{L}}} is non empty set
{{dq9,{{L}}},{dq9}} is non empty set
z . [dq9,{{L}}] is set
q is Element of L
(L,A,D,q,(S `1_4)) is Element of the carrier of A
[q,(S `1_4)] is V18() set
{q,(S `1_4)} is non empty set
{q} is non empty trivial 1 -element set
{{q,(S `1_4)},{q}} is non empty set
D . [q,(S `1_4)] is set
(L,A,D,q,(S `1_4)) "\/" FS is Element of the carrier of A
((L,A,D,q,(S `1_4)) "\/" FS) "\/" FS is Element of the carrier of A
z . (dq9,{{{L}}}) is set
[dq9,{{{L}}}] is V18() set
{dq9,{{{L}}}} is non empty set
{{dq9,{{{L}}}},{dq9}} is non empty set
z . [dq9,{{{L}}}] is set
q is Element of L
(L,A,D,q,(S `2_4)) is Element of the carrier of A
[q,(S `2_4)] is V18() set
{q,(S `2_4)} is non empty set
{q} is non empty trivial 1 -element set
{{q,(S `2_4)},{q}} is non empty set
D . [q,(S `2_4)] is set
(L,A,D,q,(S `2_4)) "\/" FS is Element of the carrier of A
c<sub>11</sub> is Element of L
dq9 is Element of L
z . (c<sub>11</sub>,dq9) is set
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
z . [c<sub>11</sub>,dq9] is set
(L,A,D,c<sub>11</sub>,dq9) is Element of the carrier of A
D . [c<sub>11</sub>,dq9] is set
q is Element of L
z . (q,{L}) is set
[q,{L}] is V18() set
{q,{L}} is non empty set
{q} is non empty trivial 1 -element set
{{q,{L}},{q}} is non empty set
z . [q,{L}] is set
(L,A,D,q,(S `1_4)) is Element of the carrier of A
[q,(S `1_4)] is V18() set
{q,(S `1_4)} is non empty set
{{q,(S `1_4)},{q}} is non empty set
D . [q,(S `1_4)] is set
(L,A,D,q,(S `1_4)) "\/" (S `3_4) is Element of the carrier of A
Q is Element of L
z . ({L},Q) is set
[{L},Q] is V18() set
{{L},Q} is non empty set
{{{L},Q},{{L}}} is non empty set
z . [{L},Q] is set
(L,A,D,Q,(S `1_4)) is Element of the carrier of A
[Q,(S `1_4)] is V18() set
{Q,(S `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(S `1_4)},{Q}} is non empty set
D . [Q,(S `1_4)] is set
(L,A,D,Q,(S `1_4)) "\/" (S `3_4) is Element of the carrier of A
u is Element of L
z . (u,{{L}}) is set
[u,{{L}}] is V18() set
{u,{{L}}} is non empty set
{u} is non empty trivial 1 -element set
{{u,{{L}}},{u}} is non empty set
z . [u,{{L}}] is set
(L,A,D,u,(S `1_4)) is Element of the carrier of A
[u,(S `1_4)] is V18() set
{u,(S `1_4)} is non empty set
{{u,(S `1_4)},{u}} is non empty set
D . [u,(S `1_4)] is set
(L,A,D,u,(S `1_4)) "\/" (S `3_4) is Element of the carrier of A
((L,A,D,u,(S `1_4)) "\/" (S `3_4)) "\/" (S `4_4) is Element of the carrier of A
v is Element of L
z . ({{L}},v) is set
[{{L}},v] is V18() set
{{{L}},v} is non empty set
{{{{L}},v},{{{L}}}} is non empty set
z . [{{L}},v] is set
(L,A,D,v,(S `1_4)) is Element of the carrier of A
[v,(S `1_4)] is V18() set
{v,(S `1_4)} is non empty set
{v} is non empty trivial 1 -element set
{{v,(S `1_4)},{v}} is non empty set
D . [v,(S `1_4)] is set
(L,A,D,v,(S `1_4)) "\/" (S `3_4) is Element of the carrier of A
((L,A,D,v,(S `1_4)) "\/" (S `3_4)) "\/" (S `4_4) is Element of the carrier of A
a is Element of L
z . (a,{{{L}}}) is set
[a,{{{L}}}] is V18() set
{a,{{{L}}}} is non empty set
{a} is non empty trivial 1 -element set
{{a,{{{L}}}},{a}} is non empty set
z . [a,{{{L}}}] is set
(L,A,D,a,(S `2_4)) is Element of the carrier of A
[a,(S `2_4)] is V18() set
{a,(S `2_4)} is non empty set
{{a,(S `2_4)},{a}} is non empty set
D . [a,(S `2_4)] is set
(L,A,D,a,(S `2_4)) "\/" (S `4_4) is Element of the carrier of A
b is Element of L
z . ({{{L}}},b) is set
[{{{L}}},b] is V18() set
{{{{L}}},b} is non empty set
{{{{{L}}},b},{{{{L}}}}} is non empty set
z . [{{{L}}},b] is set
(L,A,D,b,(S `2_4)) is Element of the carrier of A
[b,(S `2_4)] is V18() set
{b,(S `2_4)} is non empty set
{b} is non empty trivial 1 -element set
{{b,(S `2_4)},{b}} is non empty set
D . [b,(S `2_4)] is set
(L,A,D,b,(S `2_4)) "\/" (S `4_4) is Element of the carrier of A
w is Relation-like [:(L),(L):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L),(L):], the carrier of A:]
w . ({L},{L}) is set
[{L},{L}] is V18() set
{{L},{L}} is non empty set
{{{L},{L}},{{L}}} is non empty set
w . [{L},{L}] is set
w . ({{L}},{{L}}) is set
[{{L}},{{L}}] is V18() set
{{{L}},{{L}}} is non empty set
{{{{L}},{{L}}},{{{L}}}} is non empty set
w . [{{L}},{{L}}] is set
w . ({{{L}}},{{{L}}}) is set
[{{{L}}},{{{L}}}] is V18() set
{{{{L}}},{{{L}}}} is non empty set
{{{{L}}}} is non empty trivial 1 -element set
{{{{{L}}},{{{L}}}},{{{{L}}}}} is non empty set
w . [{{{L}}},{{{L}}}] is set
w . ({{L}},{{{L}}}) is set
[{{L}},{{{L}}}] is V18() set
{{{L}},{{{L}}}} is non empty set
{{{{L}},{{{L}}}},{{{L}}}} is non empty set
w . [{{L}},{{{L}}}] is set
w . ({{{L}}},{{L}}) is set
[{{{L}}},{{L}}] is V18() set
{{{{L}}},{{L}}} is non empty set
{{{{{L}}},{{L}}},{{{{L}}}}} is non empty set
w . [{{{L}}},{{L}}] is set
w . ({L},{{L}}) is set
[{L},{{L}}] is V18() set
{{L},{{L}}} is non empty set
{{{L},{{L}}},{{L}}} is non empty set
w . [{L},{{L}}] is set
w . ({{L}},{L}) is set
[{{L}},{L}] is V18() set
{{{L}},{L}} is non empty set
{{{{L}},{L}},{{{L}}}} is non empty set
w . [{{L}},{L}] is set
w . ({L},{{{L}}}) is set
[{L},{{{L}}}] is V18() set
{{L},{{{L}}}} is non empty set
{{{L},{{{L}}}},{{L}}} is non empty set
w . [{L},{{{L}}}] is set
w . ({{{L}}},{L}) is set
[{{{L}}},{L}] is V18() set
{{{{L}}},{L}} is non empty set
{{{{{L}}},{L}},{{{{L}}}}} is non empty set
w . [{{{L}}},{L}] is set
z is Relation-like [:(L),(L):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L),(L):], the carrier of A:]
z . ({L},{L}) is set
z . [{L},{L}] is set
z . ({{L}},{{L}}) is set
z . [{{L}},{{L}}] is set
z . ({{{L}}},{{{L}}}) is set
z . [{{{L}}},{{{L}}}] is set
z . ({{L}},{{{L}}}) is set
z . [{{L}},{{{L}}}] is set
z . ({{{L}}},{{L}}) is set
z . [{{{L}}},{{L}}] is set
z . ({L},{{L}}) is set
z . [{L},{{L}}] is set
z . ({{L}},{L}) is set
z . [{{L}},{L}] is set
z . ({L},{{{L}}}) is set
z . [{L},{{{L}}}] is set
z . ({{{L}}},{L}) is set
z . [{{{L}}},{L}] is set
c<sub>11</sub> is Element of (L)
dq9 is Element of (L)
((L),A,w,c<sub>11</sub>,dq9) is Element of the carrier of A
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
w . [c<sub>11</sub>,dq9] is set
D . (c<sub>11</sub>,dq9) is set
D . [c<sub>11</sub>,dq9] is set
((L),A,z,c<sub>11</sub>,dq9) is Element of the carrier of A
z . [c<sub>11</sub>,dq9] is set
((L),A,w,c<sub>11</sub>,dq9) is Element of the carrier of A
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
w . [c<sub>11</sub>,dq9] is set
q is Element of L
(L,A,D,q,(S `1_4)) is Element of the carrier of A
[q,(S `1_4)] is V18() set
{q,(S `1_4)} is non empty set
{q} is non empty trivial 1 -element set
{{q,(S `1_4)},{q}} is non empty set
D . [q,(S `1_4)] is set
(L,A,D,q,(S `1_4)) "\/" (S `3_4) is Element of the carrier of A
((L),A,z,c₁₁,dq9) is Element of the carrier of A
z . [c₁₁,dq9] is set
((L),A,w,c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
w . [c₁₁,dq9] is set
q is Element of L
(L,A,D,q,(S `1_4)) is Element of the carrier of A
[q,(S `1_4)] is V18() set
{q,(S `1_4)} is non empty set
{q} is non empty trivial 1 -element set
{{q,(S `1_4)},{q}} is non empty set
D . [q,(S `1_4)] is set
(L,A,D,q,(S `1_4)) "\/" (S `3_4) is Element of the carrier of A
((L,A,D,q,(S `1_4)) "\/" (S `3_4)) "\/" (S `4_4) is Element of the carrier of A
((L),A,z,c₁₁,dq9) is Element of the carrier of A
z . [c₁₁,dq9] is set
((L),A,w,c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
w . [c₁₁,dq9] is set
q is Element of L
(L,A,D,q,(S `2_4)) is Element of the carrier of A
[q,(S `2_4)] is V18() set
{q,(S `2_4)} is non empty set
{q} is non empty trivial 1 -element set
{{q,(S `2_4)},{q}} is non empty set
D . [q,(S `2_4)] is set
(L,A,D,q,(S `2_4)) "\/" (S `4_4) is Element of the carrier of A
((L),A,z,c<sub>11</sub>,dq9) is Element of the carrier of A
z . [c<sub>11</sub>,dq9] is set
((L),A,w,c<sub>11</sub>,dq9) is Element of the carrier of A
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
w . [c<sub>11</sub>,dq9] is set
q is Element of L
(L,A,D,q,(S `1_4)) is Element of the carrier of A
[q,(S `1_4)] is V18() set
{q,(S `1_4)} is non empty set
{q} is non empty trivial 1 -element set
{{q,(S `1_4)},{q}} is non empty set
D . [q,(S `1_4)] is set
(L,A,D,q,(S `1_4)) "\/" (S `3_4) is Element of the carrier of A
((L),A,z,c₁₁,dq9) is Element of the carrier of A
z . [c₁₁,dq9] is set
((L),A,w,c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
w . [c₁₁,dq9] is set
((L),A,z,c₁₁,dq9) is Element of the carrier of A
z . [c₁₁,dq9] is set
((L),A,w,c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
w . [c₁₁,dq9] is set
((L),A,z,c₁₁,dq9) is Element of the carrier of A
z . [c₁₁,dq9] is set
((L),A,w,c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
w . [c₁₁,dq9] is set
((L),A,z,c₁₁,dq9) is Element of the carrier of A
z . [c₁₁,dq9] is set
((L),A,w,c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
w . [c₁₁,dq9] is set
q is Element of L
(L,A,D,q,(S `1_4)) is Element of the carrier of A
[q,(S `1_4)] is V18() set
{q,(S `1_4)} is non empty set
{q} is non empty trivial 1 -element set
{{q,(S `1_4)},{q}} is non empty set
D . [q,(S `1_4)] is set
(L,A,D,q,(S `1_4)) "\/" (S `3_4) is Element of the carrier of A
((L,A,D,q,(S `1_4)) "\/" (S `3_4)) "\/" (S `4_4) is Element of the carrier of A
((L),A,z,c₁₁,dq9) is Element of the carrier of A
z . [c₁₁,dq9] is set
((L),A,w,c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
w . [c₁₁,dq9] is set
((L),A,z,c₁₁,dq9) is Element of the carrier of A
z . [c₁₁,dq9] is set
((L),A,w,c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
w . [c₁₁,dq9] is set
((L),A,z,c₁₁,dq9) is Element of the carrier of A
z . [c₁₁,dq9] is set
((L),A,w,c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
w . [c₁₁,dq9] is set
((L),A,z,c₁₁,dq9) is Element of the carrier of A
z . [c₁₁,dq9] is set
((L),A,w,c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
w . [c₁₁,dq9] is set
q is Element of L
(L,A,D,q,(S `2_4)) is Element of the carrier of A
[q,(S `2_4)] is V18() set
{q,(S `2_4)} is non empty set
{q} is non empty trivial 1 -element set
{{q,(S `2_4)},{q}} is non empty set
D . [q,(S `2_4)] is set
(L,A,D,q,(S `2_4)) "\/" (S `4_4) is Element of the carrier of A
((L),A,z,c<sub>11</sub>,dq9) is Element of the carrier of A
z . [c<sub>11</sub>,dq9] is set
((L),A,w,c<sub>11</sub>,dq9) is Element of the carrier of A
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
w . [c<sub>11</sub>,dq9] is set
((L),A,z,c<sub>11</sub>,dq9) is Element of the carrier of A
z . [c<sub>11</sub>,dq9] is set
((L),A,w,c<sub>11</sub>,dq9) is Element of the carrier of A
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
w . [c<sub>11</sub>,dq9] is set
((L),A,z,c<sub>11</sub>,dq9) is Element of the carrier of A
z . [c<sub>11</sub>,dq9] is set
((L),A,w,c<sub>11</sub>,dq9) is Element of the carrier of A
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
w . [c<sub>11</sub>,dq9] is set
((L),A,z,c<sub>11</sub>,dq9) is Element of the carrier of A
z . [c<sub>11</sub>,dq9] is set
L is non empty set
[:L,L:] is non empty Relation-like set
(L) is non empty set
{L} is non empty trivial 1 -element set
{{L}} is non empty trivial 1 -element set
{{{L}}} is non empty trivial 1 -element set
{{L},{{L}},{{{L}}}} is non empty set
L \/ {{L},{{L}},{{{L}}}} is non empty set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 Relation-like set
[:[:(L),(L):], the carrier of A:] is non empty Relation-like set
bool [:[:(L),(L):], the carrier of A:] is non empty non empty-membered set
Bottom A is Element of the carrier of A
FS is Element of (L)
((L),A,(L,A,D,S),FS,FS) is Element of the carrier of A
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
(L,A,D,S) . [FS,FS] is set
FD is Element of L
(L,A,D,FD,FD) is Element of the carrier of A
[FD,FD] is V18() set
{FD,FD} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,FD},{FD}} is non empty set
D . [FD,FD] is set
L is non empty set
[:L,L:] is non empty Relation-like set
(L) is non empty set
{L} is non empty trivial 1 -element set
{{L}} is non empty trivial 1 -element set
{{{L}}} is non empty trivial 1 -element set
{{L},{{L}},{{{L}}}} is non empty set
L \/ {{L},{{L}},{{{L}}}} is non empty set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 Relation-like set
[:[:(L),(L):], the carrier of A:] is non empty Relation-like set
bool [:[:(L),(L):], the carrier of A:] is non empty non empty-membered 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
z is Element of (L)
c₁₁ is Element of (L)
((L),A,(L,A,D,S),z,c₁₁) is Element of the carrier of A
[z,c₁₁] is V18() set
{z,c₁₁} is non empty set
{z} is non empty trivial 1 -element set
{{z,c₁₁},{z}} is non empty set
(L,A,D,S) . [z,c₁₁] is set
((L),A,(L,A,D,S),c₁₁,z) is Element of the carrier of A
[c₁₁,z] is V18() set
{c₁₁,z} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,z},{c₁₁}} is non empty set
(L,A,D,S) . [c₁₁,z] is set
dq9 is Element of L
q is Element of L
(L,A,D,dq9,q) is Element of the carrier of A
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
D . [dq9,q] is set
(L,A,D,q,dq9) is Element of the carrier of A
[q,dq9] is V18() set
{q,dq9} is non empty set
{q} is non empty trivial 1 -element set
{{q,dq9},{q}} is non empty set
D . [q,dq9] is set
dq9 is Element of L
(L,A,D,dq9,(S `1_4)) is Element of the carrier of A
[dq9,(S `1_4)] is V18() set
{dq9,(S `1_4)} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,(S `1_4)},{dq9}} is non empty set
D . [dq9,(S `1_4)] is set
(L,A,D,dq9,(S `1_4)) "\/" (S `3_4) is Element of the carrier of A
dq9 is Element of L
(L,A,D,dq9,(S `1_4)) is Element of the carrier of A
[dq9,(S `1_4)] is V18() set
{dq9,(S `1_4)} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,(S `1_4)},{dq9}} is non empty set
D . [dq9,(S `1_4)] is set
(L,A,D,dq9,(S `1_4)) "\/" (S `3_4) is Element of the carrier of A
((L,A,D,dq9,(S `1_4)) "\/" (S `3_4)) "\/" (S `4_4) is Element of the carrier of A
dq9 is Element of L
(L,A,D,dq9,(S `2_4)) is Element of the carrier of A
[dq9,(S `2_4)] is V18() set
{dq9,(S `2_4)} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,(S `2_4)},{dq9}} is non empty set
D . [dq9,(S `2_4)] is set
(L,A,D,dq9,(S `2_4)) "\/" (S `4_4) is Element of the carrier of A
dq9 is Element of L
(L,A,D,dq9,(S `1_4)) is Element of the carrier of A
[dq9,(S `1_4)] is V18() set
{dq9,(S `1_4)} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,(S `1_4)},{dq9}} is non empty set
D . [dq9,(S `1_4)] is set
(L,A,D,dq9,(S `1_4)) "\/" (S `3_4) is Element of the carrier of A
(S `3_4) "\/" (S `4_4) is Element of the carrier of A
dq9 is Element of L
(L,A,D,dq9,(S `1_4)) is Element of the carrier of A
[dq9,(S `1_4)] is V18() set
{dq9,(S `1_4)} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,(S `1_4)},{dq9}} is non empty set
D . [dq9,(S `1_4)] is set
(L,A,D,dq9,(S `1_4)) "\/" (S `3_4) is Element of the carrier of A
((L,A,D,dq9,(S `1_4)) "\/" (S `3_4)) "\/" (S `4_4) is Element of the carrier of A
dq9 is Element of L
(L,A,D,dq9,(S `2_4)) is Element of the carrier of A
[dq9,(S `2_4)] is V18() set
{dq9,(S `2_4)} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,(S `2_4)},{dq9}} is non empty set
D . [dq9,(S `2_4)] is set
(L,A,D,dq9,(S `2_4)) "\/" (S `4_4) is Element of the carrier of A
(S `3_4) "\/" (S `4_4) is Element of the carrier of A
L is non empty set
[:L,L:] is non empty Relation-like set
(L) is non empty set
{L} is non empty trivial 1 -element set
{{L}} is non empty trivial 1 -element set
{{{L}}} is non empty trivial 1 -element set
{{L},{{L}},{{{L}}}} is non empty set
L \/ {{L},{{L}},{{{L}}}} is non empty set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 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
(L,A,D,(FS `1_4),(FS `2_4)) is Element of the carrier of A
[(FS `1_4),(FS `2_4)] is V18() set
{(FS `1_4),(FS `2_4)} is non empty set
{(FS `1_4)} is non empty trivial 1 -element set
{{(FS `1_4),(FS `2_4)},{(FS `1_4)}} is non empty set
D . [(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,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 Relation-like set
[:[:(L),(L):], the carrier of A:] is non empty Relation-like set
bool [:[:(L),(L):], the carrier of A:] is non empty non empty-membered set
S is non empty set
c<sub>11</sub> is Element of (L)
dq9 is Element of (L)
q is Element of (L)
((L),A,(L,A,D,FS),c<sub>11</sub>,q) is Element of the carrier of A
[c<sub>11</sub>,q] is V18() set
{c<sub>11</sub>,q} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,q},{c<sub>11</sub>}} is non empty set
(L,A,D,FS) . [c<sub>11</sub>,q] is set
((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) is Element of the carrier of A
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
(L,A,D,FS) . [c<sub>11</sub>,dq9] is set
((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
(L,A,D,FS) . [dq9,q] is set
((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Q is Element of L
u is Element of L
(L,A,D,Q,u) is Element of the carrier of A
[Q,u] is V18() set
{Q,u} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,u},{Q}} is non empty set
D . [Q,u] is set
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,(FS `1_4),u) is Element of the carrier of A
[(FS `1_4),u] is V18() set
{(FS `1_4),u} is non empty set
{{(FS `1_4),u},{(FS `1_4)}} is non empty set
D . [(FS `1_4),u] is set
(L,A,D,Q,(FS `1_4)) "\/" (L,A,D,(FS `1_4),u) is Element of the carrier of A
(L,A,D,u,(FS `1_4)) is Element of the carrier of A
[u,(FS `1_4)] is V18() set
{u,(FS `1_4)} is non empty set
{u} is non empty trivial 1 -element set
{{u,(FS `1_4)},{u}} is non empty set
D . [u,(FS `1_4)] is set
(L,A,D,Q,(FS `1_4)) "\/" (L,A,D,u,(FS `1_4)) is Element of the carrier of A
w is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (L,A,D,u,(FS `1_4))) "\/" w is Element of the carrier of A
(L,A,D,u,(FS `1_4)) "\/" w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" ((L,A,D,u,(FS `1_4)) "\/" w) is Element of the carrier of A
w "\/" w is Element of the carrier of A
(L,A,D,u,(FS `1_4)) "\/" (w "\/" w) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" ((L,A,D,u,(FS `1_4)) "\/" (w "\/" w)) is Element of the carrier of A
((L,A,D,u,(FS `1_4)) "\/" w) "\/" w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (((L,A,D,u,(FS `1_4)) "\/" w) "\/" w) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" ((L,A,D,u,(FS `1_4)) "\/" w) is Element of the carrier of A
Q is Element of L
u is Element of L
(L,A,D,Q,u) is Element of the carrier of A
[Q,u] is V18() set
{Q,u} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,u},{Q}} is non empty set
D . [Q,u] is set
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,(FS `1_4),u) is Element of the carrier of A
[(FS `1_4),u] is V18() set
{(FS `1_4),u} is non empty set
{{(FS `1_4),u},{(FS `1_4)}} is non empty set
D . [(FS `1_4),u] is set
(L,A,D,Q,(FS `1_4)) "\/" (L,A,D,(FS `1_4),u) is Element of the carrier of A
(L,A,D,u,(FS `1_4)) is Element of the carrier of A
[u,(FS `1_4)] is V18() set
{u,(FS `1_4)} is non empty set
{u} is non empty trivial 1 -element set
{{u,(FS `1_4)},{u}} is non empty set
D . [u,(FS `1_4)] is set
(L,A,D,Q,(FS `1_4)) "\/" (L,A,D,u,(FS `1_4)) is Element of the carrier of A
w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (L,A,D,u,(FS `1_4))) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,u,(FS `1_4)) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" ((L,A,D,u,(FS `1_4)) "\/" (w "\/" z)) is Element of the carrier of A
(w "\/" z) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,u,(FS `1_4)) "\/" ((w "\/" z) "\/" (w "\/" z)) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" ((L,A,D,u,(FS `1_4)) "\/" ((w "\/" z) "\/" (w "\/" z))) is Element of the carrier of A
((L,A,D,u,(FS `1_4)) "\/" (w "\/" z)) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (((L,A,D,u,(FS `1_4)) "\/" (w "\/" z)) "\/" (w "\/" z)) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" z) is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (w "\/" z)) "\/" ((L,A,D,u,(FS `1_4)) "\/" (w "\/" z)) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
(((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z) "\/" ((L,A,D,u,(FS `1_4)) "\/" (w "\/" z)) is Element of the carrier of A
(L,A,D,u,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,u,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
(((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z) "\/" (((L,A,D,u,(FS `1_4)) "\/" w) "\/" z) is Element of the carrier of A
Q is Element of L
u is Element of L
(L,A,D,Q,u) is Element of the carrier of A
[Q,u] is V18() set
{Q,u} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,u},{Q}} is non empty set
D . [Q,u] is set
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
(L,A,D,(FS `2_4),u) is Element of the carrier of A
[(FS `2_4),u] is V18() set
{(FS `2_4),u} is non empty set
{(FS `2_4)} is non empty trivial 1 -element set
{{(FS `2_4),u},{(FS `2_4)}} is non empty set
D . [(FS `2_4),u] is set
(L,A,D,Q,(FS `2_4)) "\/" (L,A,D,(FS `2_4),u) is Element of the carrier of A
(L,A,D,u,(FS `2_4)) is Element of the carrier of A
[u,(FS `2_4)] is V18() set
{u,(FS `2_4)} is non empty set
{u} is non empty trivial 1 -element set
{{u,(FS `2_4)},{u}} is non empty set
D . [u,(FS `2_4)] is set
(L,A,D,Q,(FS `2_4)) "\/" (L,A,D,u,(FS `2_4)) is Element of the carrier of A
z is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" (L,A,D,u,(FS `2_4))) "\/" z is Element of the carrier of A
(L,A,D,u,(FS `2_4)) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" ((L,A,D,u,(FS `2_4)) "\/" z) is Element of the carrier of A
z "\/" z is Element of the carrier of A
(L,A,D,u,(FS `2_4)) "\/" (z "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" ((L,A,D,u,(FS `2_4)) "\/" (z "\/" z)) is Element of the carrier of A
((L,A,D,u,(FS `2_4)) "\/" z) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (((L,A,D,u,(FS `2_4)) "\/" z) "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" z) "\/" ((L,A,D,u,(FS `2_4)) "\/" z) is Element of the carrier of A
c₁₁ is Element of (L)
dq9 is Element of (L)
q is Element of (L)
((L),A,(L,A,D,FS),c₁₁,q) is Element of the carrier of A
[c₁₁,q] is V18() set
{c₁₁,q} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,q},{c₁₁}} is non empty set
(L,A,D,FS) . [c₁₁,q] is set
((L),A,(L,A,D,FS),c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{{c₁₁,dq9},{c₁₁}} is non empty set
(L,A,D,FS) . [c₁₁,dq9] is set
((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
(L,A,D,FS) . [dq9,q] is set
((L),A,(L,A,D,FS),c₁₁,dq9) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
z is Element of the carrier of A
z "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
z is Element of the carrier of A
w is Element of the carrier of A
w "\/" z is Element of the carrier of A
z "\/" (w "\/" z) is Element of the carrier of A
z "\/" z is Element of the carrier of A
(z "\/" z) "\/" w is Element of the carrier of A
z "\/" w is Element of the carrier of A
w "\/" w is Element of the carrier of A
z "\/" (w "\/" w) is Element of the carrier of A
w "\/" (w "\/" z) is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,Q,(FS `1_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" z) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" (w "\/" z)) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
(w "\/" z) "\/" ((L,A,D,Q,(FS `1_4)) "\/" w) is Element of the carrier of A
((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) "\/" ((L,A,D,Q,(FS `1_4)) "\/" w) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
(L,A,D,Q,(FS `1_4)) "\/" (L,A,D,(FS `1_4),(FS `2_4)) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (L,A,D,(FS `1_4),(FS `2_4))) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" z) "\/" (L,A,D,(FS `1_4),(FS `2_4)) is Element of the carrier of A
z is Element of the carrier of A
z "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
z "\/" (((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z) is Element of the carrier of A
z "\/" ((L),A,(L,A,D,FS),c<sub>11</sub>,q) is Element of the carrier of A
z "\/" (z "\/" ((L),A,(L,A,D,FS),c<sub>11</sub>,q)) is Element of the carrier of A
z "\/" z is Element of the carrier of A
(z "\/" z) "\/" ((L),A,(L,A,D,FS),c<sub>11</sub>,q) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
z is Element of the carrier of A
w is Element of the carrier of A
w "\/" z is Element of the carrier of A
z "\/" (w "\/" z) is Element of the carrier of A
z "\/" z is Element of the carrier of A
(z "\/" z) "\/" w is Element of the carrier of A
z "\/" w is Element of the carrier of A
w "\/" w is Element of the carrier of A
z "\/" (w "\/" w) is Element of the carrier of A
(w "\/" z) "\/" w is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,Q,(FS `1_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" z) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" ((w "\/" z) "\/" w) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" z) is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (w "\/" z)) "\/" w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
(((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z) "\/" w is Element of the carrier of A
((L),A,(L,A,D,FS),c₁₁,dq9) "\/" (((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (L,A,D,(FS `1_4),(FS `2_4)) is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (L,A,D,(FS `1_4),(FS `2_4))) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" z) "\/" (L,A,D,(FS `1_4),(FS `2_4)) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
(L,A,D,Q,(FS `2_4)) "\/" z is Element of the carrier of A
w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
w "\/" (w "\/" z) is Element of the carrier of A
w "\/" w is Element of the carrier of A
(w "\/" w) "\/" z is Element of the carrier of A
z "\/" z is Element of the carrier of A
w "\/" (z "\/" z) is Element of the carrier of A
z "\/" (w "\/" z) is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
w "\/" (L,A,D,Q,(FS `2_4)) is Element of the carrier of A
(w "\/" (L,A,D,Q,(FS `2_4))) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (w "\/" (w "\/" z)) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" z) "\/" (w "\/" z) is Element of the carrier of A
((L),A,(L,A,D,FS),c₁₁,dq9) "\/" ((L,A,D,Q,(FS `2_4)) "\/" z) is Element of the carrier of A
(w "\/" (L,A,D,Q,(FS `2_4))) "\/" (L,A,D,(FS `1_4),(FS `2_4)) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,(FS `2_4),(FS `1_4)) is Element of the carrier of A
[(FS `2_4),(FS `1_4)] is V18() set
{(FS `2_4),(FS `1_4)} is non empty set
{(FS `2_4)} is non empty trivial 1 -element set
{{(FS `2_4),(FS `1_4)},{(FS `2_4)}} is non empty set
D . [(FS `2_4),(FS `1_4)] is set
(L,A,D,Q,(FS `2_4)) "\/" (L,A,D,(FS `2_4),(FS `1_4)) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" (L,A,D,(FS `2_4),(FS `1_4))) "\/" w is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" w is Element of the carrier of A
(L,A,D,(FS `2_4),(FS `1_4)) "\/" ((L,A,D,Q,(FS `2_4)) "\/" w) is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
w "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
(w "\/" z) "\/" (L,A,D,Q,(FS `2_4)) is Element of the carrier of A
((w "\/" z) "\/" (L,A,D,Q,(FS `2_4))) "\/" (L,A,D,(FS `1_4),(FS `2_4)) is Element of the carrier of A
((w "\/" z) "\/" (L,A,D,Q,(FS `2_4))) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,(FS `2_4),(FS `1_4)) is Element of the carrier of A
[(FS `2_4),(FS `1_4)] is V18() set
{(FS `2_4),(FS `1_4)} is non empty set
{(FS `2_4)} is non empty trivial 1 -element set
{{(FS `2_4),(FS `1_4)},{(FS `2_4)}} is non empty set
D . [(FS `2_4),(FS `1_4)] is set
(L,A,D,Q,(FS `2_4)) "\/" (L,A,D,(FS `2_4),(FS `1_4)) is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" (L,A,D,(FS `2_4),(FS `1_4))) "\/" (w "\/" z) is Element of the carrier of A
((w "\/" z) "\/" (L,A,D,Q,(FS `2_4))) "\/" (L,A,D,(FS `2_4),(FS `1_4)) is Element of the carrier of A
w "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
z "\/" (L,A,D,Q,(FS `2_4)) is Element of the carrier of A
w "\/" (z "\/" (L,A,D,Q,(FS `2_4))) is Element of the carrier of A
(w "\/" z) "\/" (w "\/" z) is Element of the carrier of A
((w "\/" z) "\/" (w "\/" z)) "\/" (L,A,D,Q,(FS `2_4)) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (w "\/" z) is Element of the carrier of A
(w "\/" z) "\/" ((L,A,D,Q,(FS `2_4)) "\/" (w "\/" z)) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
c₁₁ is Element of (L)
dq9 is Element of (L)
q is Element of (L)
((L),A,(L,A,D,FS),c₁₁,q) is Element of the carrier of A
[c₁₁,q] is V18() set
{c₁₁,q} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,q},{c₁₁}} is non empty set
(L,A,D,FS) . [c₁₁,q] is set
((L),A,(L,A,D,FS),c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{{c₁₁,dq9},{c₁₁}} is non empty set
(L,A,D,FS) . [c₁₁,dq9] is set
((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
(L,A,D,FS) . [dq9,q] is set
((L),A,(L,A,D,FS),c₁₁,dq9) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
u is Element of L
(L,A,D,u,(FS `1_4)) is Element of the carrier of A
[u,(FS `1_4)] is V18() set
{u,(FS `1_4)} is non empty set
{u} is non empty trivial 1 -element set
{{u,(FS `1_4)},{u}} is non empty set
D . [u,(FS `1_4)] is set
Q is Element of L
(L,A,D,u,Q) is Element of the carrier of A
[u,Q] is V18() set
{u,Q} is non empty set
{{u,Q},{u}} is non empty set
D . [u,Q] is set
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,u,Q) "\/" (L,A,D,Q,(FS `1_4)) is Element of the carrier of A
(L,A,D,Q,u) is Element of the carrier of A
[Q,u] is V18() set
{Q,u} is non empty set
{{Q,u},{Q}} is non empty set
D . [Q,u] is set
(L,A,D,Q,u) "\/" (L,A,D,Q,(FS `1_4)) is Element of the carrier of A
w is Element of the carrier of A
(L,A,D,u,(FS `1_4)) "\/" w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (L,A,D,Q,u) is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (L,A,D,Q,u)) "\/" w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" (L,A,D,Q,u) is Element of the carrier of A
u is Element of L
(L,A,D,u,(FS `1_4)) is Element of the carrier of A
[u,(FS `1_4)] is V18() set
{u,(FS `1_4)} is non empty set
{u} is non empty trivial 1 -element set
{{u,(FS `1_4)},{u}} is non empty set
D . [u,(FS `1_4)] is set
Q is Element of L
(L,A,D,u,Q) is Element of the carrier of A
[u,Q] is V18() set
{u,Q} is non empty set
{{u,Q},{u}} is non empty set
D . [u,Q] is set
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,u,Q) "\/" (L,A,D,Q,(FS `1_4)) is Element of the carrier of A
(L,A,D,Q,u) is Element of the carrier of A
[Q,u] is V18() set
{Q,u} is non empty set
{{Q,u},{Q}} is non empty set
D . [Q,u] is set
(L,A,D,Q,u) "\/" (L,A,D,Q,(FS `1_4)) is Element of the carrier of A
w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
(L,A,D,u,(FS `1_4)) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (L,A,D,Q,u) is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (L,A,D,Q,u)) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,u,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,u,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" z) is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (w "\/" z)) "\/" (L,A,D,Q,u) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
(((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z) "\/" (L,A,D,Q,u) is Element of the carrier of A
u is Element of L
(L,A,D,u,(FS `2_4)) is Element of the carrier of A
[u,(FS `2_4)] is V18() set
{u,(FS `2_4)} is non empty set
{u} is non empty trivial 1 -element set
{{u,(FS `2_4)},{u}} is non empty set
D . [u,(FS `2_4)] is set
Q is Element of L
(L,A,D,u,Q) is Element of the carrier of A
[u,Q] is V18() set
{u,Q} is non empty set
{{u,Q},{u}} is non empty set
D . [u,Q] is set
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
(L,A,D,u,Q) "\/" (L,A,D,Q,(FS `2_4)) is Element of the carrier of A
(L,A,D,Q,u) is Element of the carrier of A
[Q,u] is V18() set
{Q,u} is non empty set
{{Q,u},{Q}} is non empty set
D . [Q,u] is set
(L,A,D,Q,u) "\/" (L,A,D,Q,(FS `2_4)) is Element of the carrier of A
z is Element of the carrier of A
(L,A,D,u,(FS `2_4)) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (L,A,D,Q,u) is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" (L,A,D,Q,u)) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" z) "\/" (L,A,D,Q,u) is Element of the carrier of A
c₁₁ is Element of (L)
dq9 is Element of (L)
q is Element of (L)
((L),A,(L,A,D,FS),c₁₁,q) is Element of the carrier of A
[c₁₁,q] is V18() set
{c₁₁,q} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,q},{c₁₁}} is non empty set
(L,A,D,FS) . [c₁₁,q] is set
((L),A,(L,A,D,FS),c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{{c₁₁,dq9},{c₁₁}} is non empty set
(L,A,D,FS) . [c₁₁,dq9] is set
((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
(L,A,D,FS) . [dq9,q] is set
((L),A,(L,A,D,FS),c₁₁,dq9) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Q is Element of L
u is Element of L
(L,A,D,Q,u) is Element of the carrier of A
[Q,u] is V18() set
{Q,u} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,u},{Q}} is non empty set
D . [Q,u] is set
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,u,(FS `1_4)) is Element of the carrier of A
[u,(FS `1_4)] is V18() set
{u,(FS `1_4)} is non empty set
{u} is non empty trivial 1 -element set
{{u,(FS `1_4)},{u}} is non empty set
D . [u,(FS `1_4)] is set
(L,A,D,Q,u) "\/" (L,A,D,u,(FS `1_4)) is Element of the carrier of A
w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,u) "\/" (L,A,D,u,(FS `1_4))) "\/" w is Element of the carrier of A
(L,A,D,u,(FS `1_4)) "\/" w is Element of the carrier of A
Q is Element of L
u is Element of L
(L,A,D,Q,u) is Element of the carrier of A
[Q,u] is V18() set
{Q,u} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,u},{Q}} is non empty set
D . [Q,u] is set
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,u,(FS `1_4)) is Element of the carrier of A
[u,(FS `1_4)] is V18() set
{u,(FS `1_4)} is non empty set
{u} is non empty trivial 1 -element set
{{u,(FS `1_4)},{u}} is non empty set
D . [u,(FS `1_4)] is set
(L,A,D,Q,u) "\/" (L,A,D,u,(FS `1_4)) is Element of the carrier of A
w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,u) "\/" (L,A,D,u,(FS `1_4))) "\/" w is Element of the carrier of A
z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
(((L,A,D,Q,u) "\/" (L,A,D,u,(FS `1_4))) "\/" w) "\/" z is Element of the carrier of A
(L,A,D,u,(FS `1_4)) "\/" w is Element of the carrier of A
(L,A,D,Q,u) "\/" ((L,A,D,u,(FS `1_4)) "\/" w) is Element of the carrier of A
((L,A,D,Q,u) "\/" ((L,A,D,u,(FS `1_4)) "\/" w)) "\/" z is Element of the carrier of A
((L,A,D,u,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
Q is Element of L
u is Element of L
(L,A,D,Q,u) is Element of the carrier of A
[Q,u] is V18() set
{Q,u} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,u},{Q}} is non empty set
D . [Q,u] is set
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
(L,A,D,u,(FS `2_4)) is Element of the carrier of A
[u,(FS `2_4)] is V18() set
{u,(FS `2_4)} is non empty set
{u} is non empty trivial 1 -element set
{{u,(FS `2_4)},{u}} is non empty set
D . [u,(FS `2_4)] is set
(L,A,D,Q,u) "\/" (L,A,D,u,(FS `2_4)) is Element of the carrier of A
z is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,u) "\/" (L,A,D,u,(FS `2_4))) "\/" z is Element of the carrier of A
(L,A,D,u,(FS `2_4)) "\/" z is Element of the carrier of A
c<sub>11</sub> is Element of (L)
dq9 is Element of (L)
q is Element of (L)
((L),A,(L,A,D,FS),c<sub>11</sub>,q) is Element of the carrier of A
[c<sub>11</sub>,q] is V18() set
{c<sub>11</sub>,q} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,q},{c<sub>11</sub>}} is non empty set
(L,A,D,FS) . [c<sub>11</sub>,q] is set
((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) is Element of the carrier of A
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
(L,A,D,FS) . [c<sub>11</sub>,dq9] is set
((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
(L,A,D,FS) . [dq9,q] is set
((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Bottom A is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" ((L),A,(L,A,D,FS),c<sub>11</sub>,q) is Element of the carrier of A
z is Element of the carrier of A
(Bottom A) "\/" z is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" ((L),A,(L,A,D,FS),c<sub>11</sub>,q) is Element of the carrier of A
w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
(Bottom A) "\/" (w "\/" z) is Element of the carrier of A
Bottom A is Element of the carrier of A
z is Element of the carrier of A
z "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" z is Element of the carrier of A
z is Element of the carrier of A
z "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
w is Element of the carrier of A
w "\/" z is Element of the carrier of A
Bottom A is Element of the carrier of A
z is Element of the carrier of A
w is Element of the carrier of A
w "\/" z is Element of the carrier of A
(w "\/" z) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
z "\/" w is Element of the carrier of A
(z "\/" w) "\/" w is Element of the carrier of A
w "\/" w is Element of the carrier of A
z "\/" (w "\/" w) is Element of the carrier of A
w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
(w "\/" z) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" (w "\/" z) is Element of the carrier of A
z is Element of the carrier of A
z "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" z is Element of the carrier of A
Bottom A is Element of the carrier of A
w is Element of the carrier of A
z is Element of the carrier of A
z "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
z "\/" w is Element of the carrier of A
z "\/" (z "\/" w) is Element of the carrier of A
z "\/" z is Element of the carrier of A
(z "\/" z) "\/" w is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" ((L),A,(L,A,D,FS),c<sub>11</sub>,q) is Element of the carrier of A
z is Element of the carrier of A
(Bottom A) "\/" z is Element of the carrier of A
Bottom A is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" ((L),A,(L,A,D,FS),c<sub>11</sub>,q) is Element of the carrier of A
w is Element of the carrier of A
(Bottom A) "\/" w is Element of the carrier of A
z is Element of the carrier of A
w is Element of the carrier of A
w "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
w "\/" z is Element of the carrier of A
w "\/" (w "\/" z) is Element of the carrier of A
w "\/" w is Element of the carrier of A
(w "\/" w) "\/" z is Element of the carrier of A
Bottom A is Element of the carrier of A
w is Element of the carrier of A
w "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" w is Element of the carrier of A
w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
(w "\/" z) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" (w "\/" z) is Element of the carrier of A
w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
(w "\/" z) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
(w "\/" z) "\/" z is Element of the carrier of A
z "\/" z is Element of the carrier of A
w "\/" (z "\/" z) is Element of the carrier of A
Bottom A is Element of the carrier of A
w is Element of the carrier of A
w "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
w is Element of the carrier of A
w "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" w is Element of the carrier of A
Bottom A is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" ((L),A,(L,A,D,FS),c<sub>11</sub>,q) is Element of the carrier of A
w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
(Bottom A) "\/" (w "\/" z) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" ((L),A,(L,A,D,FS),c<sub>11</sub>,q) is Element of the carrier of A
w is Element of the carrier of A
(Bottom A) "\/" w is Element of the carrier of A
Bottom A is Element of the carrier of A
c<sub>11</sub> is Element of (L)
dq9 is Element of (L)
q is Element of (L)
((L),A,(L,A,D,FS),c<sub>11</sub>,q) is Element of the carrier of A
[c<sub>11</sub>,q] is V18() set
{c<sub>11</sub>,q} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,q},{c<sub>11</sub>}} is non empty set
(L,A,D,FS) . [c<sub>11</sub>,q] is set
((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) is Element of the carrier of A
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
(L,A,D,FS) . [c<sub>11</sub>,dq9] is set
((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
(L,A,D,FS) . [dq9,q] is set
((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Bottom A is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
((L),A,(L,A,D,FS),c₁₁,dq9) "\/" (((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z) is Element of the carrier of A
w "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" z) is Element of the carrier of A
((L),A,(L,A,D,FS),c₁₁,dq9) "\/" ((L,A,D,Q,(FS `1_4)) "\/" (w "\/" z)) is Element of the carrier of A
((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) "\/" (L,A,D,Q,(FS `1_4)) is Element of the carrier of A
(((L),A,(L,A,D,FS),c₁₁,dq9) "\/" (L,A,D,Q,(FS `1_4))) "\/" (w "\/" z) is Element of the carrier of A
(((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) "\/" (L,A,D,Q,(FS `1_4))) "\/" w is Element of the carrier of A
((((L),A,(L,A,D,FS),c₁₁,dq9) "\/" (L,A,D,Q,(FS `1_4))) "\/" w) "\/" z is Element of the carrier of A
w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
(L,A,D,Q,(FS `2_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" ((L,A,D,Q,(FS `2_4)) "\/" z) is Element of the carrier of A
w "\/" ((L,A,D,Q,(FS `2_4)) "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" ((L,A,D,Q,(FS `2_4)) "\/" z)) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" ((L,A,D,Q,(FS `2_4)) "\/" (w "\/" z)) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (L,A,D,Q,(FS `2_4)) is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (L,A,D,Q,(FS `2_4))) "\/" (w "\/" z) is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
(((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
w "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" z) is Element of the carrier of A
((L),A,(L,A,D,FS),dq9,q) "\/" ((L,A,D,Q,(FS `1_4)) "\/" (w "\/" z)) is Element of the carrier of A
((L),A,(L,A,D,FS),dq9,q) "\/" (L,A,D,Q,(FS `1_4)) is Element of the carrier of A
(((L),A,(L,A,D,FS),dq9,q) "\/" (L,A,D,Q,(FS `1_4))) "\/" (w "\/" z) is Element of the carrier of A
(((L),A,(L,A,D,FS),dq9,q) "\/" (L,A,D,Q,(FS `1_4))) "\/" w is Element of the carrier of A
((((L),A,(L,A,D,FS),dq9,q) "\/" (L,A,D,Q,(FS `1_4))) "\/" w) "\/" z is Element of the carrier of A
Bottom A is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
(((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" z is Element of the carrier of A
w "\/" ((L,A,D,Q,(FS `1_4)) "\/" z) is Element of the carrier of A
(w "\/" ((L,A,D,Q,(FS `1_4)) "\/" z)) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" z) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
w "\/" (((L,A,D,Q,(FS `1_4)) "\/" z) "\/" ((L),A,(L,A,D,FS),dq9,q)) is Element of the carrier of A
w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
(L,A,D,Q,(FS `2_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" z) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" z) "\/" ((L,A,D,Q,(FS `1_4)) "\/" w) is Element of the carrier of A
z "\/" ((L,A,D,Q,(FS `1_4)) "\/" w) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (z "\/" ((L,A,D,Q,(FS `1_4)) "\/" w)) is Element of the carrier of A
z "\/" w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (z "\/" w) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" ((L,A,D,Q,(FS `1_4)) "\/" (z "\/" w)) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (L,A,D,Q,(FS `1_4)) is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" (L,A,D,Q,(FS `1_4))) "\/" (w "\/" z) is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) "\/" (((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z) is Element of the carrier of A
w "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" z) is Element of the carrier of A
((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) "\/" ((L,A,D,Q,(FS `1_4)) "\/" (w "\/" z)) is Element of the carrier of A
((L),A,(L,A,D,FS),c₁₁,dq9) "\/" (L,A,D,Q,(FS `1_4)) is Element of the carrier of A
(((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) "\/" (L,A,D,Q,(FS `1_4))) "\/" (w "\/" z) is Element of the carrier of A
(((L),A,(L,A,D,FS),c₁₁,dq9) "\/" (L,A,D,Q,(FS `1_4))) "\/" z is Element of the carrier of A
((((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) "\/" (L,A,D,Q,(FS `1_4))) "\/" z) "\/" w is Element of the carrier of A
Bottom A is Element of the carrier of A
c₁₁ is Element of (L)
dq9 is Element of (L)
q is Element of (L)
((L),A,(L,A,D,FS),c₁₁,q) is Element of the carrier of A
[c₁₁,q] is V18() set
{c₁₁,q} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,q},{c₁₁}} is non empty set
(L,A,D,FS) . [c₁₁,q] is set
((L),A,(L,A,D,FS),c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{{c₁₁,dq9},{c₁₁}} is non empty set
(L,A,D,FS) . [c₁₁,dq9] is set
((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
(L,A,D,FS) . [dq9,q] is set
((L),A,(L,A,D,FS),c₁₁,dq9) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" ((L),A,(L,A,D,FS),c₁₁,dq9) is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) "\/" z is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,Q,(FS `1_4)) "\/" (L,A,D,(FS `1_4),(FS `2_4)) is Element of the carrier of A
z is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (L,A,D,(FS `1_4),(FS `2_4))) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" z) "\/" (L,A,D,(FS `1_4),(FS `2_4)) is Element of the carrier of A
w is Element of the carrier of A
w "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" z) "\/" (w "\/" z) is Element of the carrier of A
z "\/" w is Element of the carrier of A
(z "\/" w) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" ((z "\/" w) "\/" z) is Element of the carrier of A
z "\/" z is Element of the carrier of A
w "\/" (z "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" (z "\/" z)) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" z) is Element of the carrier of A
w "\/" w is Element of the carrier of A
(w "\/" w) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" ((w "\/" w) "\/" z) is Element of the carrier of A
w "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" (w "\/" z)) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" (w "\/" z) is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
((L),A,(L,A,D,FS),c<sub>11</sub>,q) "\/" z is Element of the carrier of A
(((L),A,(L,A,D,FS),c<sub>11</sub>,q) "\/" z) "\/" z is Element of the carrier of A
z "\/" z is Element of the carrier of A
((L),A,(L,A,D,FS),c<sub>11</sub>,q) "\/" (z "\/" z) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" ((L),A,(L,A,D,FS),c<sub>11</sub>,dq9) is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,Q,(FS `1_4)) "\/" (L,A,D,(FS `1_4),(FS `2_4)) is Element of the carrier of A
z is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (L,A,D,(FS `1_4),(FS `2_4))) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" z) "\/" (L,A,D,(FS `1_4),(FS `2_4)) is Element of the carrier of A
w is Element of the carrier of A
w "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" z) "\/" (w "\/" z) is Element of the carrier of A
z "\/" w is Element of the carrier of A
(z "\/" w) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" ((z "\/" w) "\/" z) is Element of the carrier of A
z "\/" z is Element of the carrier of A
w "\/" (z "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" (z "\/" z)) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" z) is Element of the carrier of A
w "\/" w is Element of the carrier of A
(w "\/" w) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" ((w "\/" w) "\/" z) is Element of the carrier of A
w "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" (w "\/" z)) is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" (w "\/" z)) "\/" w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
(((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z) "\/" w is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
(L,A,D,(FS `2_4),(FS `1_4)) is Element of the carrier of A
[(FS `2_4),(FS `1_4)] is V18() set
{(FS `2_4),(FS `1_4)} is non empty set
{(FS `2_4)} is non empty trivial 1 -element set
{{(FS `2_4),(FS `1_4)},{(FS `2_4)}} is non empty set
D . [(FS `2_4),(FS `1_4)] is set
(L,A,D,Q,(FS `2_4)) "\/" (L,A,D,(FS `2_4),(FS `1_4)) is Element of the carrier of A
w is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" (L,A,D,(FS `2_4),(FS `1_4))) "\/" w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" w) "\/" (L,A,D,(FS `2_4),(FS `1_4)) is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" w) "\/" (w "\/" z) is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" w) "\/" w is Element of the carrier of A
(((L,A,D,Q,(FS `2_4)) "\/" w) "\/" w) "\/" z is Element of the carrier of A
w "\/" w is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (w "\/" w) is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" (w "\/" w)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" w) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (w "\/" z) is Element of the carrier of A
z "\/" z is Element of the carrier of A
w "\/" (z "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (w "\/" (z "\/" z)) is Element of the carrier of A
(w "\/" z) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" ((w "\/" z) "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" z) "\/" (w "\/" z) is Element of the carrier of A
Q is Element of L
(L,A,D,Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is V18() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,(FS `1_4)},{Q}} is non empty set
D . [Q,(FS `1_4)] is set
(L,A,D,Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is V18() set
{Q,(FS `2_4)} is non empty set
{{Q,(FS `2_4)},{Q}} is non empty set
D . [Q,(FS `2_4)] is set
(L,A,D,(FS `2_4),(FS `1_4)) is Element of the carrier of A
[(FS `2_4),(FS `1_4)] is V18() set
{(FS `2_4),(FS `1_4)} is non empty set
{(FS `2_4)} is non empty trivial 1 -element set
{{(FS `2_4),(FS `1_4)},{(FS `2_4)}} is non empty set
D . [(FS `2_4),(FS `1_4)] is set
(L,A,D,Q,(FS `2_4)) "\/" (L,A,D,(FS `2_4),(FS `1_4)) is Element of the carrier of A
w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" (w "\/" z) is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" (L,A,D,(FS `2_4),(FS `1_4))) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `1_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `1_4)) "\/" w) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" w is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" w) "\/" (w "\/" z) is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" w) "\/" w is Element of the carrier of A
(((L,A,D,Q,(FS `2_4)) "\/" w) "\/" w) "\/" z is Element of the carrier of A
w "\/" w is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (w "\/" w) is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" (w "\/" w)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" w) "\/" z is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" z is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" z) "\/" w is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (w "\/" z) is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" (w "\/" z)) "\/" (L,A,D,(FS `2_4),(FS `1_4)) is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" (w "\/" z)) "\/" (w "\/" z) is Element of the carrier of A
(w "\/" z) "\/" (w "\/" z) is Element of the carrier of A
((L,A,D,Q,(FS `2_4)) "\/" w) "\/" ((w "\/" z) "\/" (w "\/" z)) is Element of the carrier of A
w "\/" ((w "\/" z) "\/" (w "\/" z)) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (w "\/" ((w "\/" z) "\/" (w "\/" z))) is Element of the carrier of A
w "\/" (w "\/" z) is Element of the carrier of A
(w "\/" (w "\/" z)) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" ((w "\/" (w "\/" z)) "\/" (w "\/" z)) is Element of the carrier of A
(w "\/" w) "\/" z is Element of the carrier of A
((w "\/" w) "\/" z) "\/" (w "\/" z) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" (((w "\/" w) "\/" z) "\/" (w "\/" z)) is Element of the carrier of A
(L,A,D,Q,(FS `2_4)) "\/" ((w "\/" z) "\/" (w "\/" z)) is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" ((L),A,(L,A,D,FS),c₁₁,dq9) is Element of the carrier of A
c₁₁ is Element of (L)
dq9 is Element of (L)
q is Element of (L)
((L),A,(L,A,D,FS),c₁₁,q) is Element of the carrier of A
[c₁₁,q] is V18() set
{c₁₁,q} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,q},{c₁₁}} is non empty set
(L,A,D,FS) . [c₁₁,q] is set
((L),A,(L,A,D,FS),c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{{c₁₁,dq9},{c₁₁}} is non empty set
(L,A,D,FS) . [c₁₁,dq9] is set
((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
(L,A,D,FS) . [dq9,q] is set
((L),A,(L,A,D,FS),c₁₁,dq9) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
u is Element of L
v is Element of L
(L,A,D,u,v) is Element of the carrier of A
[u,v] is V18() set
{u,v} is non empty set
{u} is non empty trivial 1 -element set
{{u,v},{u}} is non empty set
D . [u,v] is set
Q is Element of L
(L,A,D,Q,v) is Element of the carrier of A
[Q,v] is V18() set
{Q,v} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,v},{Q}} is non empty set
D . [Q,v] is set
(L,A,D,Q,u) is Element of the carrier of A
[Q,u] is V18() set
{Q,u} is non empty set
{{Q,u},{Q}} is non empty set
D . [Q,u] is set
c₁₁ is Element of (L)
q is Element of (L)
((L),A,(L,A,D,FS),c₁₁,q) is Element of the carrier of A
[c₁₁,q] is V18() set
{c₁₁,q} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,q},{c₁₁}} is non empty set
(L,A,D,FS) . [c₁₁,q] is set
dq9 is Element of (L)
((L),A,(L,A,D,FS),c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{{c₁₁,dq9},{c₁₁}} is non empty set
(L,A,D,FS) . [c₁₁,dq9] is set
((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
(L,A,D,FS) . [dq9,q] is set
((L),A,(L,A,D,FS),c₁₁,dq9) "\/" ((L),A,(L,A,D,FS),dq9,q) is Element of the carrier of A
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 1 -element set
{{L}} is non empty trivial 1 -element set
{{{L}}} is non empty trivial 1 -element set
{{L},{{L}},{{{L}}}} is non empty set
L \/ {{L},{{L}},{{{L}}}} is non empty set
[:(L),(L):] is non empty Relation-like set
[:[:(L),(L):], the carrier of A:] is non empty Relation-like set
bool [:[:(L),(L):], the carrier of A:] is non empty non empty-membered set
dom D is Relation-like L -defined L -valued Element of bool [:L,L:]
bool [:L,L:] is non empty non empty-membered set
FS is set
D . FS is set
(L,A,D,S) . FS is set
FD is set
f is set
[FD,f] is V18() set
{FD,f} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,f},{FD}} is non empty set
D . [FD,f] is set
w is Element of L
z is Element of L
(L,A,D,w,z) is Element of the carrier of A
[w,z] is V18() set
{w,z} is non empty set
{w} is non empty trivial 1 -element set
{{w,z},{w}} is non empty set
D . [w,z] is set
(L,A,D,S) . (w,z) is set
(L,A,D,S) . [w,z] 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 non empty-membered set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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:]
{ [b₁,b₂,b₃,b₄] where b₁, b₂ is Element of L, b₃, b₄ is Element of the carrier of A : (L,A,D,b₁,b₂) <= b₃ "\/" b₄ } is set
card { [b₁,b₂,b₃,b₄] where b₁, b₂ is Element of L, b₃, b₄ is Element of the carrier of A : (L,A,D,b₁,b₂) <= b₃ "\/" b₄ } is epsilon-transitive epsilon-connected ordinal cardinal set
FS is epsilon-transitive epsilon-connected ordinal cardinal set
FS is epsilon-transitive epsilon-connected ordinal cardinal set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total (L,A) (L,A) (L,A) Element of bool [:[:L,L:], the carrier of A:]
(L,A,D) is epsilon-transitive epsilon-connected ordinal cardinal set
{ [b₁,b₂,b₃,b₄] where b₁, b₂ is Element of L, b₃, b₄ is Element of the carrier of A : (L,A,D,b₁,b₂) <= b₃ "\/" b₄ } is set
the Element of L is Element of L
Bottom A is Element of the carrier of A
[ the Element of L, the Element of L,(Bottom A),(Bottom A)] is V18() V19() V20() Element of [:L,L, the carrier of A, the carrier of A:]
[:L,L, the carrier of A, the carrier of A:] is non empty set
[ the Element of L, the Element of L,(Bottom A)] is V18() V19() set
[ the Element of L, the Element of L] is V18() set
{ the Element of L, the Element of L} is non empty set
{ the Element of L} is non empty trivial 1 -element set
{{ the Element of L, the Element of L},{ the Element of L}} is non empty set
[[ the Element of L, the Element of L],(Bottom A)] is V18() set
{[ the Element of L, the Element of L],(Bottom A)} is non empty set
{[ the Element of L, the Element of L]} is non empty trivial Relation-like Function-like constant 1 -element set
{{[ the Element of L, the Element of L],(Bottom A)},{[ the Element of L, the Element of L]}} is non empty set
[[ the Element of L, the Element of L,(Bottom A)],(Bottom A)] is V18() set
{[ the Element of L, the Element of L,(Bottom A)],(Bottom A)} is non empty set
{[ the Element of L, the Element of L,(Bottom A)]} is non empty trivial 1 -element set
{{[ the Element of L, the Element of L,(Bottom A)],(Bottom A)},{[ the Element of L, the Element of L,(Bottom A)]}} is non empty set
FS is set
(L,A,D, the Element of L, the Element of L) is Element of the carrier of A
D . [ the Element of L, the Element of L] is set
(Bottom A) "\/" (Bottom A) is Element of the carrier of A
A is epsilon-transitive epsilon-connected ordinal set
succ A is non empty epsilon-transitive epsilon-connected ordinal 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 non empty epsilon-transitive epsilon-connected ordinal set
FS is set
FS is Relation-like Function-like T-Sequence-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 non empty epsilon-transitive epsilon-connected ordinal set
FS . {} is set
(L,S) is set
L is non empty set
A is epsilon-transitive epsilon-connected ordinal set
succ A is non empty epsilon-transitive epsilon-connected ordinal set
(L,(succ A)) is set
(L,A) is set
((L,A)) is non empty set
{(L,A)} is non empty trivial 1 -element set
{{(L,A)}} is non empty trivial 1 -element set
{{{(L,A)}}} is non empty trivial 1 -element set
{{(L,A)},{{(L,A)}},{{{(L,A)}}}} is non empty set
(L,A) \/ {{(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 non empty epsilon-transitive epsilon-connected ordinal set
FS is set
FD is Relation-like Function-like T-Sequence-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 non empty epsilon-transitive epsilon-connected ordinal set
FD . {} is set
(L,FS) is set
L is non empty set
A is Relation-like Function-like T-Sequence-like set
proj1 A is epsilon-transitive epsilon-connected ordinal set
proj2 A is set
union (proj2 A) is set
D is epsilon-transitive epsilon-connected ordinal set
(L,D) is set
FS is set
S is epsilon-transitive epsilon-connected ordinal set
(L,S) is set
succ S is non empty epsilon-transitive epsilon-connected ordinal set
FD is set
f is Relation-like Function-like T-Sequence-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 non empty epsilon-transitive epsilon-connected ordinal 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 non empty epsilon-transitive epsilon-connected ordinal set
(L,(succ D)) is set
((L,D)) is non empty set
{(L,D)} is non empty trivial 1 -element set
{{(L,D)}} is non empty trivial 1 -element set
{{{(L,D)}}} is non empty trivial 1 -element set
{{(L,D)},{{(L,D)}},{{{(L,D)}}}} is non empty set
(L,D) \/ {{(L,D)},{{(L,D)}},{{{(L,D)}}}} is non empty set
D is epsilon-transitive epsilon-connected ordinal set
(L,D) is set
S is Relation-like Function-like T-Sequence-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 non empty epsilon-transitive epsilon-connected ordinal set
(L,(succ D)) is non empty set
((L,D)) is non empty set
{(L,D)} is non empty trivial 1 -element set
{{(L,D)}} is non empty trivial 1 -element set
{{{(L,D)}}} is non empty trivial 1 -element set
{{(L,D)},{{(L,D)}},{{{(L,D)}}}} is non empty set
(L,D) \/ {{(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 Relation-like Function-like T-Sequence-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 Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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:]
{ [b₁,b₂,b₃,b₄] where b₁, b₂ is Element of L, b₃, b₄ is Element of the carrier of A : (L,A,D,b₁,b₂) <= b₃ "\/" b₄ } is set
card { [b₁,b₂,b₃,b₄] where b₁, b₂ is Element of L, b₃, b₄ is Element of the carrier of A : (L,A,D,b₁,b₂) <= b₃ "\/" b₄ } is epsilon-transitive epsilon-connected ordinal cardinal set
FS is Relation-like Function-like set
proj1 FS is set
proj2 FS is set
FS is Relation-like Function-like T-Sequence-like set
proj2 FS is set
FD is set
f is Element of L
w is Element of L
z is Element of the carrier of A
c₁₁ is Element of the carrier of A
[f,w,z,c₁₁] is V18() V19() V20() Element of [:L,L, the carrier of A, the carrier of A:]
[f,w,z] is V18() V19() set
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
[[f,w],z] is V18() set
{[f,w],z} is non empty set
{[f,w]} is non empty trivial Relation-like Function-like constant 1 -element set
{{[f,w],z},{[f,w]}} is non empty set
[[f,w,z],c₁₁] is V18() set
{[f,w,z],c₁₁} is non empty set
{[f,w,z]} is non empty trivial 1 -element set
{{[f,w,z],c₁₁},{[f,w,z]}} is non empty set
(L,A,D,f,w) is Element of the carrier of A
D . [f,w] is set
z "\/" c₁₁ is Element of the carrier of A
FD is Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like set
proj1 FD is epsilon-transitive epsilon-connected ordinal set
rng FD 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 non empty-membered set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,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 non empty-membered set
{ [b₁,b₂,b₃,b₄] where b₁, b₂ is Element of L, b₃, b₄ is Element of the carrier of A : (L,A,D,b₁,b₂) <= b₃ "\/" b₄ } is set
FS is Element of L
FD is Element of L
f is Element of the carrier of A
w is Element of the carrier of A
[FS,FD,f,w] is V18() V19() V20() Element of [:L,L, the carrier of A, the carrier of A:]
[FS,FD,f] is V18() V19() set
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
[[FS,FD],f] is V18() set
{[FS,FD],f} is non empty set
{[FS,FD]} is non empty trivial Relation-like Function-like constant 1 -element set
{{[FS,FD],f},{[FS,FD]}} is non empty set
[[FS,FD,f],w] is V18() set
{[FS,FD,f],w} is non empty set
{[FS,FD,f]} is non empty trivial 1 -element set
{{[FS,FD,f],w},{[FS,FD,f]}} is non empty set
(L,A,D,FS,FD) is Element of the carrier of A
D . [FS,FD] is set
f "\/" w is Element of the carrier of A
dq9 is Element of (L,FS)
q is Element of (L,FS)
z is Element of the carrier of A
c₁₁ is Element of the carrier of A
[dq9,q,z,c₁₁] is V18() V19() V20() Element of [:(L,FS),(L,FS), the carrier of A, the carrier of A:]
[dq9,q,z] is V18() V19() set
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
[[dq9,q],z] is V18() set
{[dq9,q],z} is non empty set
{[dq9,q]} is non empty trivial Relation-like Function-like constant 1 -element set
{{[dq9,q],z},{[dq9,q]}} is non empty set
[[dq9,q,z],c₁₁] is V18() set
{[dq9,q,z],c₁₁} is non empty set
{[dq9,q,z]} is non empty trivial 1 -element set
{{[dq9,q,z],c₁₁},{[dq9,q,z]}} is non empty set
Q 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 Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is epsilon-transitive epsilon-connected ordinal 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:]
(L,A,S) is epsilon-transitive epsilon-connected ordinal cardinal set
FS is Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,S)
proj1 FS is epsilon-transitive epsilon-connected ordinal 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 non empty-membered set
{ [b₁,b₂,b₃,b₄] where b₁, b₂ is Element of L, b₃, b₄ is Element of the carrier of A : (L,A,S,b₁,b₂) <= b₃ "\/" b₄ } is set
FD is epsilon-transitive epsilon-connected ordinal cardinal set
FS is epsilon-transitive epsilon-connected ordinal cardinal set
D is set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 non empty epsilon-transitive epsilon-connected ordinal set
S is Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,D)
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,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 non empty epsilon-transitive epsilon-connected ordinal set
f is set
w is Relation-like Function-like T-Sequence-like set
last w is set
proj1 w is epsilon-transitive epsilon-connected ordinal set
FD is epsilon-transitive epsilon-connected ordinal set
succ FD is non empty epsilon-transitive epsilon-connected ordinal set
w . {} is set
(L,A,D,S,FD) is set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is epsilon-transitive epsilon-connected ordinal set
succ D is non empty epsilon-transitive epsilon-connected ordinal set
(L,D) 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 Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,S)
(L,A,S,FS,(succ D)) is set
(L,A,S,FS,D) is set
((L,D),A,(L,A,S,FS,D)) is Relation-like [:(L,D),(L,D):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,D),(L,D):], the carrier of A:]
[:(L,D),(L,D):] is non empty Relation-like set
[:[:(L,D),(L,D):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,D),(L,D):], the carrier of A:] is non empty non empty-membered set
(L,A,S,FS,D) is Element of [:(L,D),(L,D), the carrier of A, the carrier of A:]
[:(L,D),(L,D), the carrier of A, the carrier of A:] is non empty set
((L,D),A,((L,D),A,(L,A,S,FS,D)),(L,A,S,FS,D)) is Relation-like [:((L,D)),((L,D)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,D)),((L,D)):], the carrier of A:]
((L,D)) is non empty set
{(L,D)} is non empty trivial 1 -element set
{{(L,D)}} is non empty trivial 1 -element set
{{{(L,D)}}} is non empty trivial 1 -element set
{{(L,D)},{{(L,D)}},{{{(L,D)}}}} is non empty set
(L,D) \/ {{(L,D)},{{(L,D)}},{{{(L,D)}}}} is non empty set
[:((L,D)),((L,D)):] is non empty Relation-like set
[:[:((L,D)),((L,D)):], the carrier of A:] is non empty Relation-like set
bool [:[:((L,D)),((L,D)):], the carrier of A:] is non empty non empty-membered set
FD is set
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,S,FS,FS) is set
succ FS is non empty epsilon-transitive epsilon-connected ordinal set
w is set
z is Relation-like Function-like T-Sequence-like set
last z is set
proj1 z is epsilon-transitive epsilon-connected ordinal set
f is epsilon-transitive epsilon-connected ordinal set
succ f is non empty epsilon-transitive epsilon-connected ordinal set
z . {} is set
(L,A,S,FS,f) is set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like Function-like T-Sequence-like set
proj1 D is epsilon-transitive epsilon-connected ordinal set
proj2 D is set
union (proj2 D) is set
S is epsilon-transitive epsilon-connected ordinal 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 is Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,FS)
(L,A,FS,FS,S) is set
f is set
FD is epsilon-transitive epsilon-connected ordinal set
(L,A,FS,FS,FD) is set
succ FD is non empty epsilon-transitive epsilon-connected ordinal set
z is set
c₁₁ is Relation-like Function-like T-Sequence-like set
last c₁₁ is set
proj1 c₁₁ is epsilon-transitive epsilon-connected ordinal set
w is epsilon-transitive epsilon-connected ordinal set
succ w is non empty epsilon-transitive epsilon-connected ordinal set
c₁₁ . {} is set
(L,A,FS,FS,w) 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
S is epsilon-transitive epsilon-connected ordinal set
(L,S) is non empty set
succ S is non empty epsilon-transitive epsilon-connected ordinal set
(L,(succ S)) is non empty set
((L,S)) is non empty set
{(L,S)} is non empty trivial 1 -element set
{{(L,S)}} is non empty trivial 1 -element set
{{{(L,S)}}} is non empty trivial 1 -element set
{{(L,S)},{{(L,S)}},{{{(L,S)}}}} is non empty set
(L,S) \/ {{(L,S)},{{(L,S)}},{{{(L,S)}}}} is non empty set
S is epsilon-transitive epsilon-connected ordinal set
(L,S) is non empty set
FS is Relation-like Function-like T-Sequence-like set
proj1 FS is epsilon-transitive epsilon-connected ordinal set
proj2 FS is set
union (proj2 FS) is set
FS . A is set
(L,{}) is non empty set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is epsilon-transitive epsilon-connected ordinal set
(L,D) is non empty set
[:(L,D),(L,D):] is non empty Relation-like set
[:[:(L,D),(L,D):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,D),(L,D):], the carrier of A:] is non empty non empty-membered 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 Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,S)
(L,A,S,FS,D) is set
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,S,FS,FS) is set
(L,FS) is non empty set
[:(L,FS),(L,FS):] is non empty Relation-like set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty non empty-membered set
succ FS is non empty epsilon-transitive epsilon-connected ordinal set
(L,A,S,FS,(succ FS)) is set
(L,(succ FS)) is non empty set
[:(L,(succ FS)),(L,(succ FS)):] is non empty Relation-like set
[:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty non empty-membered set
((L,FS)) is non empty set
{(L,FS)} is non empty trivial 1 -element set
{{(L,FS)}} is non empty trivial 1 -element set
{{{(L,FS)}}} is non empty trivial 1 -element set
{{(L,FS)},{{(L,FS)}},{{{(L,FS)}}}} is non empty set
(L,FS) \/ {{(L,FS)},{{(L,FS)}},{{{(L,FS)}}}} is non empty set
((L,FS),A,(L,A,S,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,A,S,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,FS),A,(L,A,S,FS,FS)),(L,A,S,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 Relation-like set
[:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty Relation-like set
bool [:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty non empty-membered 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,S,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,A,S,FS,FS) is set
(L,FS) is non empty set
[:(L,FS),(L,FS):] is non empty Relation-like set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty non empty-membered set
FD is Relation-like Function-like T-Sequence-like set
proj1 FD is epsilon-transitive epsilon-connected ordinal set
f is epsilon-transitive epsilon-connected ordinal set
FD . f is set
w is epsilon-transitive epsilon-connected ordinal set
FD . w is set
z is Relation-like Function-like T-Sequence-like set
proj1 z is epsilon-transitive epsilon-connected ordinal set
(L,A,S,FS,w) is set
proj2 z is set
union (proj2 z) is set
(L,A,S,FS,f) is set
z . f is set
w is epsilon-transitive epsilon-connected ordinal set
FD . w is set
succ w is non empty epsilon-transitive epsilon-connected ordinal set
FD . (succ w) is set
(L,w) is non empty set
[:(L,w),(L,w):] is non empty Relation-like set
[:[:(L,w),(L,w):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,w),(L,w):], the carrier of A:] is non empty non empty-membered set
(L,A,S,FS,w) is set
(L,A,S,FS,(succ w)) is set
((L,w),A,(L,A,S,FS,w)) is Relation-like [:(L,w),(L,w):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,w),(L,w):], the carrier of A:]
(L,A,S,FS,w) is Element of [:(L,w),(L,w), the carrier of A, the carrier of A:]
[:(L,w),(L,w), the carrier of A, the carrier of A:] is non empty set
((L,w),A,((L,w),A,(L,A,S,FS,w)),(L,A,S,FS,w)) is Relation-like [:((L,w)),((L,w)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,w)),((L,w)):], the carrier of A:]
((L,w)) is non empty set
{(L,w)} is non empty trivial 1 -element set
{{(L,w)}} is non empty trivial 1 -element set
{{{(L,w)}}} is non empty trivial 1 -element set
{{(L,w)},{{(L,w)}},{{{(L,w)}}}} is non empty set
(L,w) \/ {{(L,w)},{{(L,w)}},{{{(L,w)}}}} is non empty set
[:((L,w)),((L,w)):] is non empty Relation-like set
[:[:((L,w)),((L,w)):], the carrier of A:] is non empty Relation-like set
bool [:[:((L,w)),((L,w)):], the carrier of A:] is non empty non empty-membered set
z is Relation-like [:(L,w),(L,w):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,w),(L,w):], the carrier of A:]
((L,w),A,z,(L,A,S,FS,w)) is Relation-like [:((L,w)),((L,w)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,w)),((L,w)):], the carrier of A:]
FD . {} is set
proj2 FD is set
f is set
w is set
z is set
FD . z is set
c₁₁ is set
FD . c₁₁ is set
dq9 is epsilon-transitive epsilon-connected ordinal set
q is epsilon-transitive epsilon-connected ordinal set
union (proj2 FD) is set
PFuncs ([:(L,FS),(L,FS):], the carrier of A) is non empty functional set
c₁₁ is set
dq9 is set
FD . dq9 is set
q is epsilon-transitive epsilon-connected ordinal set
FD . q is set
(L,A,S,FS,q) is set
(L,q) is non empty set
[:(L,q),(L,q):] is non empty Relation-like set
[:[:(L,q),(L,q):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,q),(L,q):], the carrier of A:] is non empty non empty-membered 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 non empty-membered set
rng Q is Element of bool the carrier of A
bool the carrier of A is non empty non empty-membered set
c₁₁ is non empty epsilon-transitive epsilon-connected ordinal set
{ [:(L,b₁),(L,b₁):] where b₁ is epsilon-transitive epsilon-connected ordinal Element of c₁₁ : verum } is set
q is Relation-like Function-like T-Sequence-like set
proj1 q is epsilon-transitive epsilon-connected ordinal set
Q is set
FD . Q is set
u is epsilon-transitive epsilon-connected ordinal set
FD . u is set
(L,A,S,FS,u) is set
doms FD is Relation-like Function-like set
proj2 (doms FD) is set
u is set
proj1 (doms FD) is set
v is set
(doms FD) . v is set
Q is Relation-like Function-like Function-yielding V91() set
proj1 Q is set
a is epsilon-transitive epsilon-connected ordinal Element of c₁₁
FD . a is set
(L,A,S,FS,a) is set
(L,a) is non empty set
[:(L,a),(L,a):] is non empty Relation-like set
[:[:(L,a),(L,a):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,a),(L,a):], the carrier of A:] is non empty non empty-membered set
b 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:]
dom b is Relation-like (L,a) -defined (L,a) -valued Element of bool [:(L,a),(L,a):]
bool [:(L,a),(L,a):] is non empty non empty-membered set
u is set
v is epsilon-transitive epsilon-connected ordinal Element of c₁₁
(L,v) is non empty set
[:(L,v),(L,v):] is non empty Relation-like set
FD . v is set
(L,A,S,FS,v) is set
[:[:(L,v),(L,v):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,v),(L,v):], the carrier of A:] is non empty non empty-membered set
Q is Relation-like Function-like Function-yielding V91() set
proj1 Q is set
doms Q is Relation-like Function-like set
proj1 (doms Q) is set
a is Relation-like [:(L,v),(L,v):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,v),(L,v):], the carrier of A:]
dom a is Relation-like (L,v) -defined (L,v) -valued Element of bool [:(L,v),(L,v):]
bool [:(L,v),(L,v):] is non empty non empty-membered set
(doms FD) . v is set
proj2 q is set
a is Relation-like Function-like set
proj1 a is set
proj2 a is set
v is Relation-like Function-like set
proj1 v is set
Q is Relation-like Function-like Function-yielding V91() set
doms Q is Relation-like Function-like set
proj2 (doms Q) is set
union (proj2 (doms Q)) is set
u is non empty set
{ [:b₁,b₁:] where b₁ is Element of u : b₁ in u } is set
b is set
e is epsilon-transitive epsilon-connected ordinal Element of c₁₁
(L,e) is non empty set
[:(L,e),(L,e):] is non empty Relation-like set
q . e is set
W is Element of u
[:W,W:] is Relation-like set
b is set
e is Element of u
[:e,e:] is Relation-like set
W is set
q . W is set
V is epsilon-transitive epsilon-connected ordinal set
(L,V) is non empty set
a is set
b is set
e is set
q . e is set
W is set
q . W is set
j is epsilon-transitive epsilon-connected ordinal set
q . j is set
(L,j) is non empty set
V is epsilon-transitive epsilon-connected ordinal set
q . V is set
(L,V) is non empty set
union (proj2 q) is set
[:(union (proj2 q)),(L,FS):] is Relation-like set
union u is set
[:(union u),(union u):] is Relation-like set
a is Relation-like Function-like set
proj1 a is set
proj2 a is set
(L,{}) is non empty set
(L,A,S,FS,{}) is set
[:(L,{}),(L,{}):] is non empty Relation-like set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty non empty-membered set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,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 Relation-like set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty non empty-membered set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is epsilon-transitive epsilon-connected ordinal 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 Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,S)
(L,A,S,FS,D) is Relation-like [:(L,D),(L,D):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,D),(L,D):], the carrier of A:]
(L,D) is non empty set
[:(L,D),(L,D):] is non empty Relation-like set
[:[:(L,D),(L,D):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,D),(L,D):], the carrier of A:] is non empty non empty-membered set
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,S,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 Relation-like set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty non empty-membered set
FD is Relation-like Function-like T-Sequence-like set
proj1 FD is epsilon-transitive epsilon-connected ordinal set
FD . {} is set
(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,{}) is non empty set
[:(L,{}),(L,{}):] is non empty Relation-like set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty non empty-membered set
proj2 FD is set
union (proj2 FD) is set
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,S,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 Relation-like set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty non empty-membered set
succ FS is non empty epsilon-transitive epsilon-connected ordinal set
(L,A,S,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)) is non empty set
[:(L,(succ FS)),(L,(succ FS)):] is non empty Relation-like set
[:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty non empty-membered set
((L,FS),A,(L,A,S,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,A,S,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,FS),A,(L,A,S,FS,FS)),(L,A,S,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)} is non empty trivial 1 -element set
{{(L,FS)}} is non empty trivial 1 -element set
{{{(L,FS)}}} is non empty trivial 1 -element set
{{(L,FS)},{{(L,FS)}},{{{(L,FS)}}}} is non empty set
(L,FS) \/ {{(L,FS)},{{(L,FS)}},{{{(L,FS)}}}} is non empty set
[:((L,FS)),((L,FS)):] is non empty Relation-like set
[:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty Relation-like set
bool [:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty non empty-membered set
((L,FS),A,(L,A,S,FS,FS),(L,A,S,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,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,{}) is non empty set
[:(L,{}),(L,{}):] is non empty Relation-like set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty non empty-membered set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is epsilon-transitive epsilon-connected ordinal set
(L,D) is non empty set
[:(L,D),(L,D):] is non empty Relation-like set
S is epsilon-transitive epsilon-connected ordinal 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 is Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,FS)
(L,A,FS,FS,D) is Relation-like [:(L,D),(L,D):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,D),(L,D):], the carrier of A:]
[:[:(L,D),(L,D):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,D),(L,D):], the carrier of A:] is non empty non empty-membered set
(L,A,FS,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 Relation-like set
[:[:(L,S),(L,S):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,S),(L,S):], the carrier of A:] is non empty non empty-membered set
FD is epsilon-transitive epsilon-connected ordinal set
(L,A,FS,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 Relation-like set
[:[:(L,FD),(L,FD):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FD),(L,FD):], the carrier of A:] is non empty non empty-membered set
f is Relation-like Function-like T-Sequence-like set
proj1 f is epsilon-transitive epsilon-connected ordinal set
proj2 f is set
union (proj2 f) is set
f . D is set
FD is epsilon-transitive epsilon-connected ordinal set
(L,A,FS,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 Relation-like set
[:[:(L,FD),(L,FD):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FD),(L,FD):], the carrier of A:] is non empty non empty-membered set
succ FD is non empty epsilon-transitive epsilon-connected ordinal set
(L,A,FS,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 Relation-like set
[:[:(L,(succ FD)),(L,(succ FD)):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,(succ FD)),(L,(succ FD)):], the carrier of A:] is non empty non empty-membered set
((L,FD),A,(L,A,FS,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,FS,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,((L,FD),A,(L,A,FS,FS,FD)),(L,A,FS,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 1 -element set
{{(L,FD)}} is non empty trivial 1 -element set
{{{(L,FD)}}} is non empty trivial 1 -element set
{{(L,FD)},{{(L,FD)}},{{{(L,FD)}}}} is non empty set
(L,FD) \/ {{(L,FD)},{{(L,FD)}},{{{(L,FD)}}}} is non empty set
[:((L,FD)),((L,FD)):] is non empty Relation-like set
[:[:((L,FD)),((L,FD)):], the carrier of A:] is non empty Relation-like set
bool [:[:((L,FD)),((L,FD)):], the carrier of A:] is non empty non empty-membered set
((L,FD),A,(L,A,FS,FS,FD),(L,A,FS,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,FS,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 Relation-like set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty non empty-membered set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is epsilon-transitive epsilon-connected ordinal set
(L,D) 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 Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,S)
(L,A,S,FS,D) is Relation-like [:(L,D),(L,D):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,D),(L,D):], the carrier of A:]
[:(L,D),(L,D):] is non empty Relation-like set
[:[:(L,D),(L,D):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,D),(L,D):], the carrier of A:] is non empty non empty-membered set
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,S,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 Relation-like set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty non empty-membered set
succ FS is non empty epsilon-transitive epsilon-connected ordinal set
(L,(succ FS)) is non empty set
(L,A,S,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 Relation-like set
[:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty non empty-membered set
((L,FS)) is non empty set
{(L,FS)} is non empty trivial 1 -element set
{{(L,FS)}} is non empty trivial 1 -element set
{{{(L,FS)}}} is non empty trivial 1 -element set
{{(L,FS)},{{(L,FS)}},{{{(L,FS)}}}} is non empty set
(L,FS) \/ {{(L,FS)},{{(L,FS)}},{{{(L,FS)}}}} is non empty set
(L,A,S,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,S,FS,FS),(L,A,S,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 Relation-like set
[:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty Relation-like set
bool [:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty non empty-membered set
FD is Element of (L,(succ FS))
((L,(succ FS)),A,(L,A,S,FS,(succ FS)),FD,FD) is Element of the carrier of A
[FD,FD] is V18() set
{FD,FD} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,FD},{FD}} is non empty set
(L,A,S,FS,(succ FS)) . [FD,FD] is set
Bottom A is Element of the carrier of A
((L,FS),A,(L,A,S,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),A,((L,FS),A,(L,A,S,FS,FS)),(L,A,S,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:]
f is Element of ((L,FS))
(((L,FS)),A,((L,FS),A,(L,A,S,FS,FS),(L,A,S,FS,FS)),f,f) is Element of the carrier of A
[f,f] is V18() set
{f,f} is non empty set
{f} is non empty trivial 1 -element set
{{f,f},{f}} is non empty set
((L,FS),A,(L,A,S,FS,FS),(L,A,S,FS,FS)) . [f,f] is set
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,S,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 Relation-like set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty non empty-membered set
f is Relation-like Function-like T-Sequence-like set
proj1 f is epsilon-transitive epsilon-connected ordinal set
proj2 f is set
union (proj2 f) is set
z is Relation-like Function-like T-Sequence-like set
proj1 z is epsilon-transitive epsilon-connected ordinal set
proj2 z is set
union (proj2 z) is set
w 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:]
c₁₁ is Element of (L,FS)
((L,FS),A,w,c₁₁,c₁₁) is Element of the carrier of A
[c₁₁,c₁₁] is V18() set
{c₁₁,c₁₁} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,c₁₁},{c₁₁}} is non empty set
w . [c₁₁,c₁₁] is set
Bottom A is Element of the carrier of A
dq9 is set
q is set
z . q is set
Q is epsilon-transitive epsilon-connected ordinal set
f . Q is set
(L,A,S,FS,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) is non empty set
[:(L,Q),(L,Q):] is non empty Relation-like set
[:[:(L,Q),(L,Q):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,Q),(L,Q):], the carrier of A:] is non empty non empty-membered set
u 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 u is Relation-like (L,Q) -defined (L,Q) -valued Element of bool [:(L,Q),(L,Q):]
bool [:(L,Q),(L,Q):] is non empty non empty-membered set
a is Element of (L,Q)
((L,Q),A,u,a,a) is Element of the carrier of A
[a,a] is V18() set
{a,a} is non empty set
{a} is non empty trivial 1 -element set
{{a,a},{a}} is non empty set
u . [a,a] is set
((L,Q),A,(L,A,S,FS,Q),a,a) is Element of the carrier of A
(L,A,S,FS,Q) . [a,a] is set
[c₁₁,c₁₁] is V18() Element of [:(L,FS),(L,FS):]
v is Element of (L,Q)
((L,Q),A,u,v,v) is Element of the carrier of A
[v,v] is V18() set
{v,v} is non empty set
{v} is non empty trivial 1 -element set
{{v,v},{v}} is non empty set
u . [v,v] is set
(L,{}) is non empty set
(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 Relation-like set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty non empty-membered set
FS is Element of (L,{})
((L,{}),A,(L,A,S,FS,{}),FS,FS) is Element of the carrier of A
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
(L,A,S,FS,{}) . [FS,FS] is set
Bottom A is Element of the carrier of A
FD is Element of L
(L,A,S,FD,FD) is Element of the carrier of A
[FD,FD] is V18() set
{FD,FD} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,FD},{FD}} is non empty set
S . [FD,FD] is set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is epsilon-transitive epsilon-connected ordinal set
(L,D) 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 Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,S)
(L,A,S,FS,D) is Relation-like [:(L,D),(L,D):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,D),(L,D):], the carrier of A:]
[:(L,D),(L,D):] is non empty Relation-like set
[:[:(L,D),(L,D):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,D),(L,D):], the carrier of A:] is non empty non empty-membered set
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,S,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 Relation-like set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty non empty-membered set
succ FS is non empty epsilon-transitive epsilon-connected ordinal set
(L,(succ FS)) is non empty set
(L,A,S,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 Relation-like set
[:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty non empty-membered set
((L,FS)) is non empty set
{(L,FS)} is non empty trivial 1 -element set
{{(L,FS)}} is non empty trivial 1 -element set
{{{(L,FS)}}} is non empty trivial 1 -element set
{{(L,FS)},{{(L,FS)}},{{{(L,FS)}}}} is non empty set
(L,FS) \/ {{(L,FS)},{{(L,FS)}},{{{(L,FS)}}}} is non empty set
(L,A,S,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,S,FS,FS),(L,A,S,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 Relation-like set
[:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty Relation-like set
bool [:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty non empty-membered set
FD is Element of (L,(succ FS))
f is Element of (L,(succ FS))
((L,(succ FS)),A,(L,A,S,FS,(succ FS)),FD,f) is Element of the carrier of A
[FD,f] is V18() set
{FD,f} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,f},{FD}} is non empty set
(L,A,S,FS,(succ FS)) . [FD,f] is set
((L,(succ FS)),A,(L,A,S,FS,(succ FS)),f,FD) is Element of the carrier of A
[f,FD] is V18() set
{f,FD} is non empty set
{f} is non empty trivial 1 -element set
{{f,FD},{f}} is non empty set
(L,A,S,FS,(succ FS)) . [f,FD] is set
((L,FS),A,(L,A,S,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),A,((L,FS),A,(L,A,S,FS,FS)),(L,A,S,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:]
z is Element of ((L,FS))
w is Element of ((L,FS))
(((L,FS)),A,((L,FS),A,(L,A,S,FS,FS),(L,A,S,FS,FS)),z,w) is Element of the carrier of A
[z,w] is V18() set
{z,w} is non empty set
{z} is non empty trivial 1 -element set
{{z,w},{z}} is non empty set
((L,FS),A,(L,A,S,FS,FS),(L,A,S,FS,FS)) . [z,w] is set
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,S,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 Relation-like set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty non empty-membered set
f is Relation-like Function-like T-Sequence-like set
proj1 f is epsilon-transitive epsilon-connected ordinal set
proj2 f is set
union (proj2 f) is set
z is Relation-like Function-like T-Sequence-like set
proj1 z is epsilon-transitive epsilon-connected ordinal set
proj2 z is set
union (proj2 z) is set
w 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:]
c₁₁ is Element of (L,FS)
dq9 is Element of (L,FS)
((L,FS),A,w,c₁₁,dq9) is Element of the carrier of A
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
w . [c₁₁,dq9] is set
((L,FS),A,w,dq9,c₁₁) is Element of the carrier of A
[dq9,c₁₁] is V18() set
{dq9,c₁₁} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,c₁₁},{dq9}} is non empty set
w . [dq9,c₁₁] is set
q is set
Q is set
z . Q is set
u is set
v is set
z . v is set
a is epsilon-transitive epsilon-connected ordinal set
(L,a) is non empty set
f . a is set
(L,A,S,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 Relation-like set
[:[:(L,a),(L,a):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,a),(L,a):], the carrier of A:] is non empty non empty-membered set
e 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:]
W is Element of (L,a)
V is Element of (L,a)
((L,a),A,e,W,V) is Element of the carrier of A
[W,V] is V18() set
{W,V} is non empty set
{W} is non empty trivial 1 -element set
{{W,V},{W}} is non empty set
e . [W,V] is set
((L,a),A,e,V,W) is Element of the carrier of A
[V,W] is V18() set
{V,W} is non empty set
{V} is non empty trivial 1 -element set
{{V,W},{V}} is non empty set
e . [V,W] is set
((L,a),A,(L,A,S,FS,a),W,V) is Element of the carrier of A
(L,A,S,FS,a) . [W,V] is set
((L,a),A,(L,A,S,FS,a),V,W) is Element of the carrier of A
(L,A,S,FS,a) . [V,W] is set
dom e is Relation-like (L,a) -defined (L,a) -valued Element of bool [:(L,a),(L,a):]
bool [:(L,a),(L,a):] is non empty non empty-membered set
b is epsilon-transitive epsilon-connected ordinal set
(L,b) is non empty set
f . b is set
(L,A,S,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),(L,b):] is non empty Relation-like set
[:[:(L,b),(L,b):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,b),(L,b):], the carrier of A:] is non empty non empty-membered set
W 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:]
V is Element of (L,b)
j is Element of (L,b)
((L,b),A,W,V,j) is Element of the carrier of A
[V,j] is V18() set
{V,j} is non empty set
{V} is non empty trivial 1 -element set
{{V,j},{V}} is non empty set
W . [V,j] is set
((L,b),A,W,j,V) is Element of the carrier of A
[j,V] is V18() set
{j,V} is non empty set
{j} is non empty trivial 1 -element set
{{j,V},{j}} is non empty set
W . [j,V] is set
((L,b),A,(L,A,S,FS,b),V,j) is Element of the carrier of A
(L,A,S,FS,b) . [V,j] is set
((L,b),A,(L,A,S,FS,b),j,V) is Element of the carrier of A
(L,A,S,FS,b) . [j,V] is set
dom W is Relation-like (L,b) -defined (L,b) -valued Element of bool [:(L,b),(L,b):]
bool [:(L,b),(L,b):] is non empty non empty-membered set
[dq9,c₁₁] is V18() Element of [:(L,FS),(L,FS):]
[c₁₁,dq9] is V18() Element of [:(L,FS),(L,FS):]
V is Element of (L,b)
j is Element of (L,b)
((L,b),A,W,V,j) is Element of the carrier of A
[V,j] is V18() set
{V,j} is non empty set
{V} is non empty trivial 1 -element set
{{V,j},{V}} is non empty set
W . [V,j] is set
((L,b),A,W,j,V) is Element of the carrier of A
[j,V] is V18() set
{j,V} is non empty set
{j} is non empty trivial 1 -element set
{{j,V},{j}} is non empty set
W . [j,V] is set
[dq9,c₁₁] is V18() Element of [:(L,FS),(L,FS):]
[c₁₁,dq9] is V18() Element of [:(L,FS),(L,FS):]
V is Element of (L,a)
j is Element of (L,a)
((L,a),A,e,V,j) is Element of the carrier of A
[V,j] is V18() set
{V,j} is non empty set
{V} is non empty trivial 1 -element set
{{V,j},{V}} is non empty set
e . [V,j] is set
((L,a),A,e,j,V) is Element of the carrier of A
[j,V] is V18() set
{j,V} is non empty set
{j} is non empty trivial 1 -element set
{{j,V},{j}} is non empty set
e . [j,V] is set
(L,{}) is non empty set
(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 Relation-like set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty non empty-membered set
FS is Element of (L,{})
FD is Element of (L,{})
((L,{}),A,(L,A,S,FS,{}),FS,FD) is Element of the carrier of A
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
(L,A,S,FS,{}) . [FS,FD] is set
((L,{}),A,(L,A,S,FS,{}),FD,FS) is Element of the carrier of A
[FD,FS] is V18() set
{FD,FS} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,FS},{FD}} is non empty set
(L,A,S,FS,{}) . [FD,FS] is set
f is Element of L
w is Element of L
(L,A,S,f,w) is Element of the carrier of A
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
S . [f,w] is set
(L,A,S,w,f) is Element of the carrier of A
[w,f] is V18() set
{w,f} is non empty set
{w} is non empty trivial 1 -element set
{{w,f},{w}} is non empty set
S . [w,f] is set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is epsilon-transitive epsilon-connected ordinal set
(L,D) 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:]
(L,A,S) is epsilon-transitive epsilon-connected ordinal cardinal set
FS is Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,S)
(L,A,S,FS,D) is Relation-like [:(L,D),(L,D):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,D),(L,D):], the carrier of A:]
[:(L,D),(L,D):] is non empty Relation-like set
[:[:(L,D),(L,D):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,D),(L,D):], the carrier of A:] is non empty non empty-membered set
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,S,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 Relation-like set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty non empty-membered set
succ FS is non empty epsilon-transitive epsilon-connected ordinal set
(L,(succ FS)) is non empty set
(L,A,S,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 Relation-like set
[:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty non empty-membered 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 non empty-membered set
{ [b₁,b₂,b₃,b₄] where b₁, b₂ is Element of L, b₃, b₄ is Element of the carrier of A : (L,A,S,b₁,b₂) <= b₃ "\/" b₄ } is set
FD is Element of (L,(succ FS))
w is Element of (L,(succ FS))
((L,(succ FS)),A,(L,A,S,FS,(succ FS)),FD,w) is Element of the carrier of A
[FD,w] is V18() set
{FD,w} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,w},{FD}} is non empty set
(L,A,S,FS,(succ FS)) . [FD,w] is set
f is Element of (L,(succ FS))
((L,(succ FS)),A,(L,A,S,FS,(succ FS)),FD,f) is Element of the carrier of A
[FD,f] is V18() set
{FD,f} is non empty set
{{FD,f},{FD}} is non empty set
(L,A,S,FS,(succ FS)) . [FD,f] is set
((L,(succ FS)),A,(L,A,S,FS,(succ FS)),f,w) is Element of the carrier of A
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
(L,A,S,FS,(succ FS)) . [f,w] is set
((L,(succ FS)),A,(L,A,S,FS,(succ FS)),FD,f) "\/" ((L,(succ FS)),A,(L,A,S,FS,(succ FS)),f,w) is Element of the carrier of A
((L,FS)) is non empty set
{(L,FS)} is non empty trivial 1 -element set
{{(L,FS)}} is non empty trivial 1 -element set
{{{(L,FS)}}} is non empty trivial 1 -element set
{{(L,FS)},{{(L,FS)}},{{{(L,FS)}}}} is non empty set
(L,FS) \/ {{(L,FS)},{{(L,FS)}},{{{(L,FS)}}}} is non empty set
(L,A,S,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,S,FS,FS),(L,A,S,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 Relation-like set
[:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty Relation-like set
bool [:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty non empty-membered set
(L,A,S,FS,FS) `1_4 is Element of (L,FS)
(L,A,S,FS,FS) `1 is set
((L,A,S,FS,FS) `1) `1 is set
(((L,A,S,FS,FS) `1) `1) `1 is set
(L,A,S,FS,FS) `2_4 is Element of (L,FS)
(((L,A,S,FS,FS) `1) `1) `2 is set
(L,A,S,FS,FS) `3_4 is Element of the carrier of A
((L,A,S,FS,FS) `1) `2 is set
(L,A,S,FS,FS) `4_4 is Element of the carrier of A
dom S is Relation-like L -defined L -valued Element of bool [:L,L:]
bool [:L,L:] is non empty non empty-membered set
b is Element of L
e is Element of L
W is Element of the carrier of A
V is Element of the carrier of A
[b,e,W,V] is V18() V19() V20() Element of [:L,L, the carrier of A, the carrier of A:]
[b,e,W] is V18() V19() set
[b,e] is V18() set
{b,e} is non empty set
{b} is non empty trivial 1 -element set
{{b,e},{b}} is non empty set
[[b,e],W] is V18() set
{[b,e],W} is non empty set
{[b,e]} is non empty trivial Relation-like Function-like constant 1 -element set
{{[b,e],W},{[b,e]}} is non empty set
[[b,e,W],V] is V18() set
{[b,e,W],V} is non empty set
{[b,e,W]} is non empty trivial 1 -element set
{{[b,e,W],V},{[b,e,W]}} is non empty set
(L,A,S,b,e) is Element of the carrier of A
S . [b,e] is set
W "\/" V is Element of the carrier of A
v is Element of the carrier of A
a is Element of the carrier of A
[b,e] is V18() Element of [:L,L:]
S . [b,e] is Element of the carrier of A
((L,FS),A,(L,A,S,FS,FS),((L,A,S,FS,FS) `1_4),((L,A,S,FS,FS) `2_4)) is Element of the carrier of A
[((L,A,S,FS,FS) `1_4),((L,A,S,FS,FS) `2_4)] is V18() set
{((L,A,S,FS,FS) `1_4),((L,A,S,FS,FS) `2_4)} is non empty set
{((L,A,S,FS,FS) `1_4)} is non empty trivial 1 -element set
{{((L,A,S,FS,FS) `1_4),((L,A,S,FS,FS) `2_4)},{((L,A,S,FS,FS) `1_4)}} is non empty set
(L,A,S,FS,FS) . [((L,A,S,FS,FS) `1_4),((L,A,S,FS,FS) `2_4)] is set
z is Element of ((L,FS))
dq9 is Element of ((L,FS))
(((L,FS)),A,((L,FS),A,(L,A,S,FS,FS),(L,A,S,FS,FS)),z,dq9) is Element of the carrier of A
[z,dq9] is V18() set
{z,dq9} is non empty set
{z} is non empty trivial 1 -element set
{{z,dq9},{z}} is non empty set
((L,FS),A,(L,A,S,FS,FS),(L,A,S,FS,FS)) . [z,dq9] is set
c<sub>11</sub> is Element of ((L,FS))
(((L,FS)),A,((L,FS),A,(L,A,S,FS,FS),(L,A,S,FS,FS)),z,c<sub>11</sub>) is Element of the carrier of A
[z,c<sub>11</sub>] is V18() set
{z,c<sub>11</sub>} is non empty set
{{z,c<sub>11</sub>},{z}} is non empty set
((L,FS),A,(L,A,S,FS,FS),(L,A,S,FS,FS)) . [z,c<sub>11</sub>] is set
(((L,FS)),A,((L,FS),A,(L,A,S,FS,FS),(L,A,S,FS,FS)),c<sub>11</sub>,dq9) is Element of the carrier of A
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
((L,FS),A,(L,A,S,FS,FS),(L,A,S,FS,FS)) . [c<sub>11</sub>,dq9] is set
(((L,FS)),A,((L,FS),A,(L,A,S,FS,FS),(L,A,S,FS,FS)),z,c<sub>11</sub>) "\/" (((L,FS)),A,((L,FS),A,(L,A,S,FS,FS),(L,A,S,FS,FS)),c<sub>11</sub>,dq9) is Element of the carrier of A
((L,FS),A,(L,A,S,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),A,((L,FS),A,(L,A,S,FS,FS)),(L,A,S,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,S,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 Relation-like set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty non empty-membered set
f is Relation-like Function-like T-Sequence-like set
proj1 f is epsilon-transitive epsilon-connected ordinal set
proj2 f is set
union (proj2 f) is set
z is Relation-like Function-like T-Sequence-like set
proj1 z is epsilon-transitive epsilon-connected ordinal set
proj2 z is set
union (proj2 z) is set
w 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:]
c<sub>11</sub> is Element of (L,FS)
q is Element of (L,FS)
((L,FS),A,w,c<sub>11</sub>,q) is Element of the carrier of A
[c<sub>11</sub>,q] is V18() set
{c<sub>11</sub>,q} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,q},{c<sub>11</sub>}} is non empty set
w . [c<sub>11</sub>,q] is set
dq9 is Element of (L,FS)
((L,FS),A,w,c<sub>11</sub>,dq9) is Element of the carrier of A
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
w . [c<sub>11</sub>,dq9] is set
((L,FS),A,w,dq9,q) is Element of the carrier of A
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
w . [dq9,q] is set
((L,FS),A,w,c<sub>11</sub>,dq9) "\/" ((L,FS),A,w,dq9,q) is Element of the carrier of A
Q is set
u is set
z . u is set
v is set
a is set
z . a is set
b is set
e is set
z . e is set
W is epsilon-transitive epsilon-connected ordinal set
(L,W) is non empty set
j is epsilon-transitive epsilon-connected ordinal set
f . j is set
(L,A,S,FS,j) is Relation-like [:(L,j),(L,j):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,j),(L,j):], the carrier of A:]
(L,j) is non empty set
[:(L,j),(L,j):] is non empty Relation-like set
[:[:(L,j),(L,j):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,j),(L,j):], the carrier of A:] is non empty non empty-membered set
z1 is Relation-like [:(L,j),(L,j):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,j),(L,j):], the carrier of A:]
z2 is Element of (L,j)
h is Element of (L,j)
((L,j),A,z1,z2,h) is Element of the carrier of A
[z2,h] is V18() set
{z2,h} is non empty set
{z2} is non empty trivial 1 -element set
{{z2,h},{z2}} is non empty set
z1 . [z2,h] is set
z3 is Element of (L,j)
((L,j),A,z1,z2,z3) is Element of the carrier of A
[z2,z3] is V18() set
{z2,z3} is non empty set
{{z2,z3},{z2}} is non empty set
z1 . [z2,z3] is set
((L,j),A,z1,z3,h) is Element of the carrier of A
[z3,h] is V18() set
{z3,h} is non empty set
{z3} is non empty trivial 1 -element set
{{z3,h},{z3}} is non empty set
z1 . [z3,h] is set
((L,j),A,z1,z2,z3) "\/" ((L,j),A,z1,z3,h) is Element of the carrier of A
dom z1 is Relation-like (L,j) -defined (L,j) -valued Element of bool [:(L,j),(L,j):]
bool [:(L,j),(L,j):] is non empty non empty-membered set
V is epsilon-transitive epsilon-connected ordinal set
f . V is set
(L,A,S,FS,V) is Relation-like [:(L,V),(L,V):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,V),(L,V):], the carrier of A:]
(L,V) is non empty set
[:(L,V),(L,V):] is non empty Relation-like set
[:[:(L,V),(L,V):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,V),(L,V):], the carrier of A:] is non empty non empty-membered set
z2 is Relation-like [:(L,V),(L,V):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,V),(L,V):], the carrier of A:]
z3 is Element of (L,V)
h is Element of (L,V)
((L,V),A,z2,z3,h) is Element of the carrier of A
[z3,h] is V18() set
{z3,h} is non empty set
{z3} is non empty trivial 1 -element set
{{z3,h},{z3}} is non empty set
z2 . [z3,h] is set
h is Element of (L,V)
((L,V),A,z2,z3,h) is Element of the carrier of A
[z3,h] is V18() set
{z3,h} is non empty set
{{z3,h},{z3}} is non empty set
z2 . [z3,h] is set
((L,V),A,z2,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
z2 . [h,h] is set
((L,V),A,z2,z3,h) "\/" ((L,V),A,z2,h,h) is Element of the carrier of A
dom z2 is Relation-like (L,V) -defined (L,V) -valued Element of bool [:(L,V),(L,V):]
bool [:(L,V),(L,V):] is non empty non empty-membered set
f . W is set
(L,A,S,FS,W) is Relation-like [:(L,W),(L,W):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,W),(L,W):], the carrier of A:]
[:(L,W),(L,W):] is non empty Relation-like set
[:[:(L,W),(L,W):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,W),(L,W):], the carrier of A:] is non empty non empty-membered set
z3 is Relation-like [:(L,W),(L,W):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,W),(L,W):], the carrier of A:]
h is Element of (L,W)
h is Element of (L,W)
((L,W),A,z3,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
z3 . [h,h] is set
h is Element of (L,W)
((L,W),A,z3,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{{h,h},{h}} is non empty set
z3 . [h,h] is set
((L,W),A,z3,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
z3 . [h,h] is set
((L,W),A,z3,h,h) "\/" ((L,W),A,z3,h,h) is Element of the carrier of A
dom z3 is Relation-like (L,W) -defined (L,W) -valued Element of bool [:(L,W),(L,W):]
bool [:(L,W),(L,W):] is non empty non empty-membered set
[dq9,q] is V18() Element of [:(L,FS),(L,FS):]
h is Element of (L,j)
h is Element of (L,j)
((L,j),A,z1,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
z1 . [h,h] is set
[c<sub>11</sub>,q] is V18() Element of [:(L,FS),(L,FS):]
h is Element of (L,j)
((L,j),A,z1,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
z1 . [h,h] is set
[c<sub>11</sub>,dq9] is V18() Element of [:(L,FS),(L,FS):]
((L,j),A,z1,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{{h,h},{h}} is non empty set
z1 . [h,h] is set
[dq9,q] is V18() Element of [:(L,FS),(L,FS):]
h is Element of (L,V)
h is Element of (L,V)
((L,V),A,z2,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
z2 . [h,h] is set
[c<sub>11</sub>,dq9] is V18() Element of [:(L,FS),(L,FS):]
h is Element of (L,V)
((L,V),A,z2,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
z2 . [h,h] is set
[c<sub>11</sub>,q] is V18() Element of [:(L,FS),(L,FS):]
((L,V),A,z2,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{{h,h},{h}} is non empty set
z2 . [h,h] is set
[c<sub>11</sub>,dq9] is V18() Element of [:(L,FS),(L,FS):]
h is Element of (L,V)
h is Element of (L,V)
((L,V),A,z2,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
z2 . [h,h] is set
[dq9,q] is V18() Element of [:(L,FS),(L,FS):]
h is Element of (L,V)
((L,V),A,z2,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
z2 . [h,h] is set
[c<sub>11</sub>,q] is V18() Element of [:(L,FS),(L,FS):]
((L,V),A,z2,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{{h,h},{h}} is non empty set
z2 . [h,h] is set
[c<sub>11</sub>,dq9] is V18() Element of [:(L,FS),(L,FS):]
h is Element of (L,W)
h is Element of (L,W)
((L,W),A,z3,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
z3 . [h,h] is set
[c<sub>11</sub>,q] is V18() Element of [:(L,FS),(L,FS):]
h is Element of (L,W)
((L,W),A,z3,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{{h,h},{h}} is non empty set
z3 . [h,h] is set
[dq9,q] is V18() Element of [:(L,FS),(L,FS):]
((L,W),A,z3,h,h) is Element of the carrier of A
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
z3 . [h,h] is set
(L,{}) is non empty set
(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 Relation-like set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty non empty-membered set
FS is Element of (L,{})
f is Element of (L,{})
((L,{}),A,(L,A,S,FS,{}),FS,f) is Element of the carrier of A
[FS,f] is V18() set
{FS,f} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,f},{FS}} is non empty set
(L,A,S,FS,{}) . [FS,f] is set
FD is Element of (L,{})
((L,{}),A,(L,A,S,FS,{}),FS,FD) is Element of the carrier of A
[FS,FD] is V18() set
{FS,FD} is non empty set
{{FS,FD},{FS}} is non empty set
(L,A,S,FS,{}) . [FS,FD] is set
((L,{}),A,(L,A,S,FS,{}),FD,f) is Element of the carrier of A
[FD,f] is V18() set
{FD,f} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,f},{FD}} is non empty set
(L,A,S,FS,{}) . [FD,f] is set
((L,{}),A,(L,A,S,FS,{}),FS,FD) "\/" ((L,{}),A,(L,A,S,FS,{}),FD,f) is Element of the carrier of A
w is Element of L
c<sub>11</sub> is Element of L
(L,A,S,w,c<sub>11</sub>) is Element of the carrier of A
[w,c<sub>11</sub>] is V18() set
{w,c<sub>11</sub>} is non empty set
{w} is non empty trivial 1 -element set
{{w,c<sub>11</sub>},{w}} is non empty set
S . [w,c<sub>11</sub>] is set
z is Element of L
(L,A,S,w,z) is Element of the carrier of A
[w,z] is V18() set
{w,z} is non empty set
{{w,z},{w}} is non empty set
S . [w,z] is set
(L,A,S,z,c<sub>11</sub>) is Element of the carrier of A
[z,c<sub>11</sub>] is V18() set
{z,c<sub>11</sub>} is non empty set
{z} is non empty trivial 1 -element set
{{z,c<sub>11</sub>},{z}} is non empty set
S . [z,c<sub>11</sub>] is set
(L,A,S,w,z) "\/" (L,A,S,z,c<sub>11</sub>) is Element of the carrier of A
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 (L,A) (L,A) (L,A) Element of bool [:[:L,L:], the carrier of A:]
D is epsilon-transitive epsilon-connected ordinal set
(L,A,S) is epsilon-transitive epsilon-connected ordinal cardinal set
FS is Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,S)
(L,A,S,FS,D) is Relation-like [:(L,D),(L,D):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,D),(L,D):], the carrier of A:]
(L,D) is non empty set
[:(L,D),(L,D):] is non empty Relation-like set
[:[:(L,D),(L,D):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,D),(L,D):], the carrier of A:] is non empty non empty-membered set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 epsilon-transitive epsilon-connected ordinal cardinal set
(L,(L,A,D)) is non empty set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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
(L,A,D) is epsilon-transitive epsilon-connected ordinal cardinal set
(L,(L,A,D)) is non empty set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,D)
(L,A,D) is epsilon-transitive epsilon-connected ordinal cardinal set
(L,A,D,S,(L,A,D)) is Relation-like [:(L,(L,A,D)),(L,(L,A,D)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(L,A,D)),(L,(L,A,D)):], the carrier of A:]
(L,(L,A,D)) is non empty set
[:(L,(L,A,D)),(L,(L,A,D)):] is non empty Relation-like set
[:[:(L,(L,A,D)),(L,(L,A,D)):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,(L,A,D)),(L,(L,A,D)):], the carrier of A:] is non empty non empty-membered set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered 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 (L,A) (L,A) (L,A) Element of bool [:[:L,L:], the carrier of A:]
S is Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,D)
(L,A,D,S) is set
(L,A,D) is epsilon-transitive epsilon-connected ordinal cardinal set
(L,A,D,S,(L,A,D)) is Relation-like [:(L,(L,A,D)),(L,(L,A,D)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(L,A,D)),(L,(L,A,D)):], the carrier of A:]
(L,(L,A,D)) is non empty set
[:(L,(L,A,D)),(L,(L,A,D)):] is non empty Relation-like set
[:[:(L,(L,A,D)),(L,(L,A,D)):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,(L,A,D)),(L,(L,A,D)):], the carrier of A:] is non empty non empty-membered set
(L,A,D) is non empty set
[:(L,A,D),(L,A,D):] is non empty Relation-like set
[:[:(L,A,D),(L,A,D):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,A,D),(L,A,D):], the carrier of A:] is non empty non empty-membered set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
S is non empty set
[:S,S:] is non empty Relation-like set
[:[:S,S:], the carrier of A:] is non empty Relation-like set
bool [:[:S,S:], the carrier of A:] is non empty non empty-membered set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total (L,A) (L,A) (L,A) Element of bool [:[:L,L:], the carrier of A:]
S is non empty set
[:S,S:] is non empty Relation-like set
[:[:S,S:], the carrier of A:] is non empty Relation-like set
bool [:[:S,S:], the carrier of A:] is non empty non empty-membered set
FS is Relation-like [:S,S:] -defined the carrier of A -valued Function-like quasi_total (S,A) (S,A) (S,A) 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
(L,A,D) is epsilon-transitive epsilon-connected ordinal cardinal set
(L,(L,A,D)) is non empty set
[:(L,A,D),(L,A,D):] is non empty Relation-like set
FS is Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,D)
(L,A,D,FS) is Relation-like [:(L,A,D),(L,A,D):] -defined the carrier of A -valued Function-like quasi_total ((L,A,D),A) ((L,A,D),A) ((L,A,D),A) Element of bool [:[:(L,A,D),(L,A,D):], the carrier of A:]
[:[:(L,A,D),(L,A,D):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,A,D),(L,A,D):], the carrier of A:] is non empty non empty-membered set
(L,A,D,FS,(L,A,D)) is Relation-like [:(L,(L,A,D)),(L,(L,A,D)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(L,A,D)),(L,(L,A,D)):], the carrier of A:]
[:(L,(L,A,D)),(L,(L,A,D)):] is non empty Relation-like set
[:[:(L,(L,A,D)),(L,(L,A,D)):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,(L,A,D)),(L,(L,A,D)):], the carrier of A:] is non empty non empty-membered set
FD is Element of L
f is Element of L
(L,A,D,FD,f) is Element of the carrier of A
[FD,f] is V18() set
{FD,f} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,f},{FD}} is non empty set
D . [FD,f] is set
w is Element of the carrier of A
z is Element of the carrier of A
w "\/" z 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 non empty-membered 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 : (L,A,D,b<sub>1</sub>,b<sub>2</sub>) <= b<sub>3</sub> "\/" b<sub>4</sub> } is set
[FD,f,w,z] is V18() V19() V20() Element of [:L,L, the carrier of A, the carrier of A:]
[FD,f,w] is V18() V19() set
[[FD,f],w] is V18() set
{[FD,f],w} is non empty set
{[FD,f]} is non empty trivial Relation-like Function-like constant 1 -element set
{{[FD,f],w},{[FD,f]}} is non empty set
[[FD,f,w],z] is V18() set
{[FD,f,w],z} is non empty set
{[FD,f,w]} is non empty trivial 1 -element set
{{[FD,f,w],z},{[FD,f,w]}} is non empty set
proj1 FS is epsilon-transitive epsilon-connected ordinal set
c<sub>11</sub> is set
FS . c<sub>11</sub> is set
dq9 is epsilon-transitive epsilon-connected ordinal set
FS . dq9 is set
(L,A,D,FS,dq9) is Element of [:(L,dq9),(L,dq9), the carrier of A, the carrier of A:]
(L,dq9) is non empty set
[:(L,dq9),(L,dq9), the carrier of A, the carrier of A:] is non empty set
(L,A,D,FS,dq9) `1_4 is Element of (L,dq9)
(L,A,D,FS,dq9) `1 is set
((L,A,D,FS,dq9) `1) `1 is set
(((L,A,D,FS,dq9) `1) `1) `1 is set
(L,A,D,FS,dq9) `4_4 is Element of the carrier of A
(L,A,D,FS,dq9) `2_4 is Element of (L,dq9)
(((L,A,D,FS,dq9) `1) `1) `2 is set
(L,A,D,FS,dq9) `3_4 is Element of the carrier of A
((L,A,D,FS,dq9) `1) `2 is set
q is non empty set
{q} is non empty trivial 1 -element set
{{q}} is non empty trivial 1 -element set
{{{q}}} is non empty trivial 1 -element set
{{q},{{q}},{{{q}}}} is non empty set
q \/ {{q},{{q}},{{{q}}}} is non empty set
[:q,q:] is non empty Relation-like set
[:[:q,q:], the carrier of A:] is non empty Relation-like set
bool [:[:q,q:], the carrier of A:] is non empty non empty-membered set
(L,A,D,FS,dq9) 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:]
[:(L,dq9),(L,dq9):] is non empty Relation-like set
[:[:(L,dq9),(L,dq9):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,dq9),(L,dq9):], the carrier of A:] is non empty non empty-membered set
[:q,q, the carrier of A, the carrier of A:] is non empty set
(q) is non empty set
v is Element of q
a is Element of q
Q is Relation-like [:q,q:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:q,q:], the carrier of A:]
succ dq9 is non empty epsilon-transitive epsilon-connected ordinal set
(L,(succ dq9)) is non empty set
[:(L,(succ dq9)),(L,(succ dq9)):] is non empty Relation-like set
(L,A,D,FS,(succ dq9)) is Relation-like [:(L,(succ dq9)),(L,(succ dq9)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(succ dq9)),(L,(succ dq9)):], the carrier of A:]
[:[:(L,(succ dq9)),(L,(succ dq9)):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,(succ dq9)),(L,(succ dq9)):], the carrier of A:] is non empty non empty-membered set
W is Element of S
FS . (FD,W) is set
[FD,W] is V18() set
{FD,W} is non empty set
{{FD,W},{FD}} is non empty set
FS . [FD,W] is set
V is Element of S
(S,A,FS,W,V) is Element of the carrier of A
[W,V] is V18() set
{W,V} is non empty set
{W} is non empty trivial 1 -element set
{{W,V},{W}} is non empty set
FS . [W,V] is set
j is Element of S
(S,A,FS,V,j) is Element of the carrier of A
[V,j] is V18() set
{V,j} is non empty set
{V} is non empty trivial 1 -element set
{{V,j},{V}} is non empty set
FS . [V,j] is set
FS . (j,f) is set
[j,f] is V18() set
{j,f} is non empty set
{j} is non empty trivial 1 -element set
{{j,f},{j}} is non empty set
FS . [j,f] is set
((L,dq9),A,(L,A,D,FS,dq9)) 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:]
((L,dq9),A,((L,dq9),A,(L,A,D,FS,dq9)),(L,A,D,FS,dq9)) 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:]
((L,dq9)) is non empty set
{(L,dq9)} is non empty trivial 1 -element set
{{(L,dq9)}} is non empty trivial 1 -element set
{{{(L,dq9)}}} is non empty trivial 1 -element set
{{(L,dq9)},{{(L,dq9)}},{{{(L,dq9)}}}} is non empty set
(L,dq9) \/ {{(L,dq9)},{{(L,dq9)}},{{{(L,dq9)}}}} is non empty set
[:((L,dq9)),((L,dq9)):] is non empty Relation-like set
[:[:((L,dq9)),((L,dq9)):], the carrier of A:] is non empty Relation-like set
bool [:[:((L,dq9)),((L,dq9)):], the carrier of A:] is non empty non empty-membered set
u is Element of [:q,q, the carrier of A, the carrier of A:]
(q,A,Q,u) is Relation-like [:(q),(q):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(q),(q):], the carrier of A:]
[:(q),(q):] is non empty Relation-like set
[:[:(q),(q):], the carrier of A:] is non empty Relation-like set
bool [:[:(q),(q):], the carrier of A:] is non empty non empty-membered set
dom (q,A,Q,u) is Relation-like (q) -defined (q) -valued Element of bool [:(q),(q):]
bool [:(q),(q):] is non empty non empty-membered set
b is Element of (q)
[b,{q}] is V18() set
{b,{q}} is non empty set
{b} is non empty trivial 1 -element set
{{b,{q}},{b}} is non empty set
(q,A,Q,u) . (b,{q}) is set
(q,A,Q,u) . [b,{q}] is set
(q,A,Q,v,v) is Element of the carrier of A
[v,v] is V18() set
{v,v} is non empty set
{v} is non empty trivial 1 -element set
{{v,v},{v}} is non empty set
Q . [v,v] is set
(q,A,Q,v,v) "\/" w is Element of the carrier of A
Bottom A is Element of the carrier of A
(Bottom A) "\/" w is Element of the carrier of A
[{{q}},{{{q}}}] is V18() set
{{{q}},{{{q}}}} is non empty set
{{{{q}},{{{q}}}},{{{q}}}} is non empty set
(q,A,Q,u) . ({{q}},{{{q}}}) is set
(q,A,Q,u) . [{{q}},{{{q}}}] is set
[{q},{{q}}] is V18() set
{{q},{{q}}} is non empty set
{{{q},{{q}}},{{q}}} is non empty set
(q,A,Q,u) . ({q},{{q}}) is set
(q,A,Q,u) . [{q},{{q}}] is set
e is Element of (q)
[{{{q}}},e] is V18() set
{{{{q}}},e} is non empty set
{{{{q}}}} is non empty trivial 1 -element set
{{{{{q}}},e},{{{{q}}}}} is non empty set
(q,A,Q,u) . ({{{q}}},e) is set
(q,A,Q,u) . [{{{q}}},e] is set
(q,A,Q,a,a) is Element of the carrier of A
[a,a] is V18() set
{a,a} is non empty set
{a} is non empty trivial 1 -element set
{{a,a},{a}} is non empty set
Q . [a,a] is set
(q,A,Q,a,a) "\/" z is Element of the carrier of A
(Bottom A) "\/" z is Element of the carrier of A
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total (L,A) (L,A) (L,A) Element of bool [:[:L,L:], the carrier of A:]
[L,D] is V18() set
{L,D} is non empty set
{L} is non empty trivial 1 -element set
{{L,D},{L}} is non empty set
S is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
FS is set
FS is non empty set
[:FS,FS:] is non empty Relation-like set
[:[:FS,FS:], the carrier of A:] is non empty Relation-like set
bool [:[:FS,FS:], the carrier of A:] is non empty non empty-membered set
f is non empty set
[:f,f:] is non empty Relation-like set
[:[:f,f:], the carrier of A:] is non empty Relation-like set
bool [:[:f,f:], the carrier of A:] is non empty non empty-membered set
FD is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total (FS,A) (FS,A) (FS,A) Element of bool [:[:FS,FS:], the carrier of A:]
w is Relation-like [:f,f:] -defined the carrier of A -valued Function-like quasi_total (f,A) (f,A) (f,A) Element of bool [:[:f,f:], the carrier of A:]
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
FS is non empty set
[:FS,FS:] is non empty Relation-like set
[:[:FS,FS:], the carrier of A:] is non empty Relation-like set
bool [:[:FS,FS:], the carrier of A:] is non empty non empty-membered set
f is non empty set
[:f,f:] is non empty Relation-like set
[:[:f,f:], the carrier of A:] is non empty Relation-like set
bool [:[:f,f:], the carrier of A:] is non empty non empty-membered set
FD is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total (FS,A) (FS,A) (FS,A) Element of bool [:[:FS,FS:], the carrier of A:]
w is Relation-like [:f,f:] -defined the carrier of A -valued Function-like quasi_total (f,A) (f,A) (f,A) Element of bool [:[:f,f:], the carrier of A:]
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
z is non empty set
[:z,z:] is non empty Relation-like set
[:[:z,z:], the carrier of A:] is non empty Relation-like set
bool [:[:z,z:], the carrier of A:] is non empty non empty-membered set
dq9 is non empty set
[:dq9,dq9:] is non empty Relation-like set
[:[:dq9,dq9:], the carrier of A:] is non empty Relation-like set
bool [:[:dq9,dq9:], the carrier of A:] is non empty non empty-membered set
c₁₁ is Relation-like [:z,z:] -defined the carrier of A -valued Function-like quasi_total (z,A) (z,A) (z,A) Element of bool [:[:z,z:], the carrier of A:]
q is Relation-like [:dq9,dq9:] -defined the carrier of A -valued Function-like quasi_total (dq9,A) (dq9,A) (dq9,A) Element of bool [:[:dq9,dq9:], the carrier of A:]
[z,c₁₁] is V18() set
{z,c₁₁} is non empty set
{z} is non empty trivial 1 -element set
{{z,c₁₁},{z}} is non empty set
FS is non empty set
[:FS,FS:] is non empty Relation-like set
[:[:FS,FS:], the carrier of A:] is non empty Relation-like set
bool [:[:FS,FS:], the carrier of A:] is non empty non empty-membered set
f is non empty set
[:f,f:] is non empty Relation-like set
[:[:f,f:], the carrier of A:] is non empty Relation-like set
bool [:[:f,f:], the carrier of A:] is non empty non empty-membered set
FD is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total (FS,A) (FS,A) (FS,A) Element of bool [:[:FS,FS:], the carrier of A:]
w is Relation-like [:f,f:] -defined the carrier of A -valued Function-like quasi_total (f,A) (f,A) (f,A) Element of bool [:[:f,f:], the carrier of A:]
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
FS is non empty set
[:FS,FS:] is non empty Relation-like set
[:[:FS,FS:], the carrier of A:] is non empty Relation-like set
bool [:[:FS,FS:], the carrier of A:] is non empty non empty-membered set
f is non empty set
[:f,f:] is non empty Relation-like set
[:[:f,f:], the carrier of A:] is non empty Relation-like set
bool [:[:f,f:], the carrier of A:] is non empty non empty-membered set
FD is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total (FS,A) (FS,A) (FS,A) Element of bool [:[:FS,FS:], the carrier of A:]
w is Relation-like [:f,f:] -defined the carrier of A -valued Function-like quasi_total (f,A) (f,A) (f,A) Element of bool [:[:f,f:], the carrier of A:]
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element 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 V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
S . FS is set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
S . (FS + 1) is set
(FS + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
S . ((FS + 1) + 1) is set
FS is non empty set
[:FS,FS:] is non empty Relation-like set
[:[:FS,FS:], the carrier of A:] is non empty Relation-like set
bool [:[:FS,FS:], the carrier of A:] is non empty non empty-membered set
f is non empty set
[:f,f:] is non empty Relation-like set
[:[:f,f:], the carrier of A:] is non empty Relation-like set
bool [:[:f,f:], the carrier of A:] is non empty non empty-membered set
FD is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total (FS,A) (FS,A) (FS,A) Element of bool [:[:FS,FS:], the carrier of A:]
w is Relation-like [:f,f:] -defined the carrier of A -valued Function-like quasi_total (f,A) (f,A) (f,A) Element of bool [:[:f,f:], the carrier of A:]
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
[:f,f, the carrier of A, the carrier of A:] is non empty set
the Relation-like [:f,f, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (f,A,w) is Relation-like [:f,f, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (f,A,w)
(f,A,w) is non empty set
(f,A,w) is epsilon-transitive epsilon-connected ordinal cardinal set
(f,(f,A,w)) is non empty set
(f,A,w, the Relation-like [:f,f, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (f,A,w)) is Relation-like [:(f,A,w),(f,A,w):] -defined the carrier of A -valued Function-like quasi_total ((f,A,w),A) ((f,A,w),A) ((f,A,w),A) Element of bool [:[:(f,A,w),(f,A,w):], the carrier of A:]
[:(f,A,w),(f,A,w):] is non empty Relation-like set
[:[:(f,A,w),(f,A,w):], the carrier of A:] is non empty Relation-like set
bool [:[:(f,A,w),(f,A,w):], the carrier of A:] is non empty non empty-membered set
(f,A,w, the Relation-like [:f,f, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (f,A,w),(f,A,w)) is Relation-like [:(f,(f,A,w)),(f,(f,A,w)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(f,(f,A,w)),(f,(f,A,w)):], the carrier of A:]
[:(f,(f,A,w)),(f,(f,A,w)):] is non empty Relation-like set
[:[:(f,(f,A,w)),(f,(f,A,w)):], the carrier of A:] is non empty Relation-like set
bool [:[:(f,(f,A,w)),(f,(f,A,w)):], the carrier of A:] is non empty non empty-membered set
z is non empty set
[:z,z:] is non empty Relation-like set
[:[:z,z:], the carrier of A:] is non empty Relation-like set
bool [:[:z,z:], the carrier of A:] is non empty non empty-membered set
dq9 is non empty set
[:dq9,dq9:] is non empty Relation-like set
[:[:dq9,dq9:], the carrier of A:] is non empty Relation-like set
bool [:[:dq9,dq9:], the carrier of A:] is non empty non empty-membered set
c₁₁ is Relation-like [:z,z:] -defined the carrier of A -valued Function-like quasi_total (z,A) (z,A) (z,A) Element of bool [:[:z,z:], the carrier of A:]
q is Relation-like [:dq9,dq9:] -defined the carrier of A -valued Function-like quasi_total (dq9,A) (dq9,A) (dq9,A) Element of bool [:[:dq9,dq9:], the carrier of A:]
[z,c₁₁] is V18() set
{z,c₁₁} is non empty set
{z} is non empty trivial 1 -element set
{{z,c₁₁},{z}} is non empty set
(L,A,D) is non empty set
(L,A,D) is epsilon-transitive epsilon-connected ordinal cardinal set
(L,(L,A,D)) is non empty set
[:L,L, the carrier of A, the carrier of A:] is non empty set
the Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,D) is Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,D)
[:(L,A,D),(L,A,D):] is non empty Relation-like set
[:[:(L,A,D),(L,A,D):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,A,D),(L,A,D):], the carrier of A:] is non empty non empty-membered set
(L,A,D, the Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,D)) is Relation-like [:(L,A,D),(L,A,D):] -defined the carrier of A -valued Function-like quasi_total ((L,A,D),A) ((L,A,D),A) ((L,A,D),A) Element of bool [:[:(L,A,D),(L,A,D):], the carrier of A:]
(L,A,D, the Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (L,A,D),(L,A,D)) is Relation-like [:(L,(L,A,D)),(L,(L,A,D)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(L,A,D)),(L,(L,A,D)):], the carrier of A:]
[:(L,(L,A,D)),(L,(L,A,D)):] is non empty Relation-like set
[:[:(L,(L,A,D)),(L,(L,A,D)):], the carrier of A:] is non empty Relation-like set
bool [:[:(L,(L,A,D)),(L,(L,A,D)):], the carrier of A:] is non empty non empty-membered set
FD is Relation-like [:(L,A,D),(L,A,D):] -defined the carrier of A -valued Function-like quasi_total ((L,A,D),A) ((L,A,D),A) ((L,A,D),A) Element of bool [:[:(L,A,D),(L,A,D):], the carrier of A:]
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
S . (0 + 1) is set
FS is non empty set
[:FS,FS:] is non empty Relation-like set
[:[:FS,FS:], the carrier of A:] is non empty Relation-like set
bool [:[:FS,FS:], the carrier of A:] is non empty non empty-membered set
FD is non empty set
[:FD,FD:] is non empty Relation-like set
[:[:FD,FD:], the carrier of A:] is non empty Relation-like set
bool [:[:FD,FD:], the carrier of A:] is non empty non empty-membered set
FS is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total (FS,A) (FS,A) (FS,A) 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 (FD,A) (FD,A) (FD,A) Element of bool [:[:FD,FD:], the carrier of A:]
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total (L,A) (L,A) (L,A) 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 V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
S . FS is set
(S . FS) `1 is set
FS is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
S . FS is set
(S . FS) `1 is set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
S . (FS + 1) is set
(S . (FS + 1)) `1 is set
FD is non empty set
[:FD,FD:] is non empty Relation-like set
[:[:FD,FD:], the carrier of A:] is non empty Relation-like set
bool [:[:FD,FD:], the carrier of A:] is non empty non empty-membered set
w is non empty set
[:w,w:] is non empty Relation-like set
[:[:w,w:], the carrier of A:] is non empty Relation-like set
bool [:[:w,w:], the carrier of A:] is non empty non empty-membered set
f is Relation-like [:FD,FD:] -defined the carrier of A -valued Function-like quasi_total (FD,A) (FD,A) (FD,A) Element of bool [:[:FD,FD:], the carrier of A:]
z is Relation-like [:w,w:] -defined the carrier of A -valued Function-like quasi_total (w,A) (w,A) (w,A) Element of bool [:[:w,w:], the carrier of A:]
[FD,f] is V18() set
{FD,f} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,f},{FD}} is non empty set
[w,z] is V18() set
{w,z} is non empty set
{w} is non empty trivial 1 -element set
{{w,z},{w}} is non empty set
[FD,f] `1 is set
(FD,A,f) is epsilon-transitive epsilon-connected ordinal cardinal set
(FD,(FD,A,f)) is non empty set
[w,z] `1 is 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 Relation-like set
c<sub>11</sub> is Relation-like [:FD,FD, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (FD,A,f)
(FD,A,f,c<sub>11</sub>) is Relation-like [:(FD,A,f),(FD,A,f):] -defined the carrier of A -valued Function-like quasi_total ((FD,A,f),A) ((FD,A,f),A) ((FD,A,f),A) 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 Relation-like set
bool [:[:(FD,A,f),(FD,A,f):], the carrier of A:] is non empty non empty-membered set
(FD,A,f,c<sub>11</sub>,(FD,A,f)) is Relation-like [:(FD,(FD,A,f)),(FD,(FD,A,f)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(FD,(FD,A,f)),(FD,(FD,A,f)):], the carrier of A:]
[:(FD,(FD,A,f)),(FD,(FD,A,f)):] is non empty Relation-like set
[:[:(FD,(FD,A,f)),(FD,(FD,A,f)):], the carrier of A:] is non empty Relation-like set
bool [:[:(FD,(FD,A,f)),(FD,(FD,A,f)):], the carrier of A:] is non empty non empty-membered set
S . 0 is set
(S . 0) `1 is set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total (L,A) (L,A) (L,A) 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 V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
S . FS is set
(S . FS) `2 is set
FS is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
S . FS is set
(S . FS) `2 is set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
S . (FS + 1) is set
(S . (FS + 1)) `2 is set
FD is non empty set
[:FD,FD:] is non empty Relation-like set
[:[:FD,FD:], the carrier of A:] is non empty Relation-like set
bool [:[:FD,FD:], the carrier of A:] is non empty non empty-membered set
w is non empty set
[:w,w:] is non empty Relation-like set
[:[:w,w:], the carrier of A:] is non empty Relation-like set
bool [:[:w,w:], the carrier of A:] is non empty non empty-membered set
f is Relation-like [:FD,FD:] -defined the carrier of A -valued Function-like quasi_total (FD,A) (FD,A) (FD,A) Element of bool [:[:FD,FD:], the carrier of A:]
z is Relation-like [:w,w:] -defined the carrier of A -valued Function-like quasi_total (w,A) (w,A) (w,A) Element of bool [:[:w,w:], the carrier of A:]
[FD,f] is V18() set
{FD,f} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,f},{FD}} is non empty set
[w,z] is V18() set
{w,z} is non empty set
{w} is non empty trivial 1 -element set
{{w,z},{w}} 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) is epsilon-transitive epsilon-connected ordinal cardinal set
(FD,(FD,A,f)) is non empty set
[:(FD,A,f),(FD,A,f):] is non empty Relation-like set
c<sub>11</sub> is Relation-like [:FD,FD, the carrier of A, the carrier of A:] -valued Function-like T-Sequence-like (FD,A,f)
(FD,A,f,c<sub>11</sub>) is Relation-like [:(FD,A,f),(FD,A,f):] -defined the carrier of A -valued Function-like quasi_total ((FD,A,f),A) ((FD,A,f),A) ((FD,A,f),A) 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 Relation-like set
bool [:[:(FD,A,f),(FD,A,f):], the carrier of A:] is non empty non empty-membered set
(FD,A,f,c<sub>11</sub>,(FD,A,f)) is Relation-like [:(FD,(FD,A,f)),(FD,(FD,A,f)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(FD,(FD,A,f)),(FD,(FD,A,f)):], the carrier of A:]
[:(FD,(FD,A,f)),(FD,(FD,A,f)):] is non empty Relation-like set
[:[:(FD,(FD,A,f)),(FD,(FD,A,f)):], the carrier of A:] is non empty Relation-like set
bool [:[:(FD,(FD,A,f)),(FD,(FD,A,f)):], the carrier of A:] is non empty non empty-membered set
[FD,f] `2 is set
[w,z] `2 is set
S . 0 is set
(S . 0) `2 is set
L is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of L is non empty set
[: the carrier of L, the carrier of L:] is non empty Relation-like set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty Relation-like set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty non empty-membered set
Bottom L is Element of the carrier of L
D is Element of the carrier of L
S is Element of the carrier of L
D "\/" S is Element of the carrier of L
D 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:]
S 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:]
FS is Element of the carrier of L
( the carrier of L,L,S,FS,FS) is Element of the carrier of L
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
S . [FS,FS] is set
FS is Element of the carrier of L
FD is Element of the carrier of L
( the carrier of L,L,S,FS,FD) is Element of the carrier of L
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
S . [FS,FD] is set
FS is Element of the carrier of L
( the carrier of L,L,S,FS,FS) is Element of the carrier of L
[FS,FS] is V18() set
{FS,FS} is non empty set
{{FS,FS},{FS}} is non empty set
S . [FS,FS] is set
( the carrier of L,L,S,FS,FD) is Element of the carrier of L
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
S . [FS,FD] is set
( the carrier of L,L,S,FS,FS) "\/" ( the carrier of L,L,S,FS,FD) is Element of the carrier of L
f is Element of the carrier of L
z is Element of the carrier of L
f "\/" z is Element of the carrier of L
(Bottom L) "\/" ( the carrier of L,L,S,FS,FD) is Element of the carrier of L
f is Element of the carrier of L
z is Element of the carrier of L
f "\/" z is Element of the carrier of L
w is Element of the carrier of L
f "\/" w is Element of the carrier of L
(f "\/" w) "\/" ( the carrier of L,L,S,FS,FD) is Element of the carrier of L
(Bottom L) "\/" (f "\/" w) is Element of the carrier of L
(f "\/" z) "\/" w is Element of the carrier of L
w "\/" w is Element of the carrier of L
(f "\/" z) "\/" (w "\/" w) is Element of the carrier of L
z "\/" (w "\/" w) is Element of the carrier of L
f "\/" (z "\/" (w "\/" w)) is Element of the carrier of L
w "\/" z is Element of the carrier of L
w "\/" (w "\/" z) is Element of the carrier of L
f "\/" (w "\/" (w "\/" z)) is Element of the carrier of L
(f "\/" w) "\/" (w "\/" z) is Element of the carrier of L
FS is Element of the carrier of L
FS is Element of the carrier of L
( the carrier of L,L,S,FS,FS) is Element of the carrier of L
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
S . [FS,FS] is set
( the carrier of L,L,S,FS,FS) is Element of the carrier of L
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
S . [FS,FS] is set
f is Element of the carrier of L
FD is Element of the carrier of L
f "\/" FD is Element of the carrier of L
FS is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like quasi_total ( the carrier of L,L) ( the carrier of L,L) ( the carrier of L,L) Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
FS is Element of the carrier of L
FD is Element of the carrier of L
( the carrier of L,L,FS,FS,FD) is Element of the carrier of L
[FS,FD] is V18() set
{FS,FD} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FD},{FS}} is non empty set
FS . [FS,FD] is set
FS "\/" FD is Element of the carrier of L
f is Element of the carrier of L
w is Element of the carrier of L
( the carrier of L,L,FS,f,w) is Element of the carrier of L
[f,w] is V18() set
{f,w} is non empty set
{f} is non empty trivial 1 -element set
{{f,w},{f}} is non empty set
FS . [f,w] is set
A is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like quasi_total ( the carrier of L,L) ( the carrier of L,L) ( the carrier of L,L) Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
D is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like quasi_total ( the carrier of L,L) ( the carrier of L,L) ( the carrier of L,L) Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
dom A 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 non empty-membered set
S is set
A . S is set
D . S is set
FS is set
FS is set
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
FD is Element of the carrier of L
f is Element of the carrier of L
( the carrier of L,L,A,FD,f) is Element of the carrier of L
[FD,f] is V18() set
{FD,f} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,f},{FD}} is non empty set
A . [FD,f] is set
( the carrier of L,L,D,FD,f) is Element of the carrier of L
D . [FD,f] is set
FD is Element of the carrier of L
f is Element of the carrier of L
( the carrier of L,L,A,FD,f) is Element of the carrier of L
[FD,f] is V18() set
{FD,f} is non empty set
{FD} is non empty trivial 1 -element set
{{FD,f},{FD}} is non empty set
A . [FD,f] is set
FD "\/" f is Element of the carrier of L
( the carrier of L,L,D,FD,f) is Element of the carrier of L
D . [FD,f] is set
FD is Element of the carrier of L
f is Element of the carrier of L
dom D is Relation-like the carrier of L -defined the carrier of L -valued Element of bool [: the carrier of L, the carrier of L:]
L is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of L is non empty set
(L) is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like quasi_total ( the carrier of L,L) ( the carrier of L,L) ( the carrier of L,L) 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 Relation-like set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty Relation-like set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty non empty-membered set
S is set
Bottom L is Element of the carrier of L
[S,S] is V18() set
{S,S} is non empty set
{S} is non empty trivial 1 -element set
{{S,S},{S}} is non empty set
FD is V18() set
(L) . FD is set
FS is Element of the carrier of L
( the carrier of L,L,(L),FS,FS) is Element of the carrier of L
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element set
{{FS,FS},{FS}} is non empty set
(L) . [FS,FS] is set
Bottom L is Element of the carrier of L
[(Bottom L),S] is V18() set
{(Bottom L),S} is non empty set
{(Bottom L)} is non empty trivial 1 -element set
{{(Bottom L),S},{(Bottom L)}} is non empty set
FD is V18() set
(L) . FD is set
FS is Element of the carrier of L
( the carrier of L,L,(L),(Bottom L),FS) is Element of the carrier of L
[(Bottom L),FS] is V18() set
{(Bottom L),FS} is non empty set
{{(Bottom L),FS},{(Bottom L)}} is non empty set
(L) . [(Bottom L),FS] is set
FS is Element of the carrier of L
(Bottom L) "\/" FS is Element of the carrier of L
Bottom L is Element of the carrier of L
rng (L) is Element of bool the carrier of L
bool the carrier of L is non empty non empty-membered set
L is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
4 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
L is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
Seg 5 is non empty V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() 5 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= 5 ) } is set
L is non empty set
[:L,L:] is non empty Relation-like set
A is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty Relation-like set
bool [:[:L,L:], the carrier of A:] is non empty non empty-membered set
succ {} is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V63() cardinal set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total (L,A) (L,A) (L,A) Element of bool [:[:L,L:], the carrier of A:]
(L,A,D) is epsilon-transitive epsilon-connected ordinal cardinal set
L is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of L is non empty set
(L) is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like quasi_total ( the carrier of L,L) ( the carrier of L,L) ( the carrier of L,L) 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 Relation-like set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty Relation-like set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty non empty-membered set
A is Relation-like Function-like ( the carrier of L,L,(L))
{ ((A . b₁) `1) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
union { ((A . b<sub>1</sub>) `1) where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
{ ((A . b₁) `2) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
union { ((A . b<sub>1</sub>) `2) where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
D is non empty set
[:D,D:] is non empty Relation-like set
[:[:D,D:], the carrier of L:] is non empty Relation-like set
bool [:[:D,D:], the carrier of L:] is non empty non empty-membered set
FD is set
f is set
w is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . w is set
(A . w) `2 is set
z is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . z is set
(A . z) `2 is set
S is non empty set
[:S,S:] is non empty Relation-like set
PFuncs ([:S,S:], the carrier of L) is non empty functional set
FD is set
f is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . f is set
(A . f) `2 is set
f + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . (f + 1) is set
w is non empty set
[:w,w:] is non empty Relation-like set
[:[:w,w:], the carrier of L:] is non empty Relation-like set
bool [:[:w,w:], the carrier of L:] is non empty non empty-membered set
c<sub>11</sub> is non empty set
[:c<sub>11</sub>,c<sub>11</sub>:] is non empty Relation-like set
[:[:c<sub>11</sub>,c<sub>11</sub>:], the carrier of L:] is non empty Relation-like set
bool [:[:c<sub>11</sub>,c<sub>11</sub>:], the carrier of L:] is non empty non empty-membered set
z is Relation-like [:w,w:] -defined the carrier of L -valued Function-like quasi_total (w,L) (w,L) (w,L) Element of bool [:[:w,w:], the carrier of L:]
dq9 is Relation-like [:c<sub>11</sub>,c<sub>11</sub>:] -defined the carrier of L -valued Function-like quasi_total (c<sub>11</sub>,L) (c<sub>11</sub>,L) (c<sub>11</sub>,L) Element of bool [:[:c<sub>11</sub>,c<sub>11</sub>:], the carrier of L:]
[w,z] is V18() set
{w,z} is non empty set
{w} is non empty trivial 1 -element set
{{w,z},{w}} is non empty set
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} is non empty set
[w,z] `2 is set
[w,z] `1 is set
dom z is Relation-like w -defined w -valued Element of bool [:w,w:]
bool [:w,w:] is non empty non empty-membered set
rng z is Element of bool the carrier of L
bool the carrier of L is non empty non empty-membered set
A . 0 is set
(A . 0) `1 is set
FD is non empty set
{ [:b₁,b₁:] where b₁ is Element of FD : b₁ in FD } is set
{ [:((A . b₁) `1),((A . b<sub>1</sub>) `1):] where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
z is set
c₁₁ is Element of FD
[:c₁₁,c₁₁:] is Relation-like set
dq9 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . dq9 is set
(A . dq9) `1 is set
z is set
c<sub>11</sub> is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . c<sub>11</sub> is set
(A . c<sub>11</sub>) `1 is set
[:((A . c₁₁) `1),((A . c<sub>11</sub>) `1):] is Relation-like set
c₁₁ is Relation-like Function-like set
proj1 c₁₁ is set
proj2 c₁₁ is set
c₁₁ is set
A . c₁₁ is set
(A . c₁₁) `2 is set
c<sub>11</sub> is Relation-like Function-like set
proj1 c<sub>11</sub> is set
proj2 c<sub>11</sub> is set
dq9 is set
q is set
c<sub>11</sub> . q is set
Q is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . Q is set
(A . Q) `2 is set
dq9 is set
q is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . q is set
(A . q) `2 is set
c<sub>11</sub> . q is set
dq9 is set
c<sub>11</sub> . dq9 is set
q is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . q is set
q + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . (q + 1) is set
Q is non empty set
[:Q,Q:] is non empty Relation-like set
[:[:Q,Q:], the carrier of L:] is non empty Relation-like set
bool [:[:Q,Q:], the carrier of L:] is non empty non empty-membered set
v is non empty set
[:v,v:] is non empty Relation-like set
[:[:v,v:], the carrier of L:] is non empty Relation-like set
bool [:[:v,v:], the carrier of L:] is non empty non empty-membered set
u is Relation-like [:Q,Q:] -defined the carrier of L -valued Function-like quasi_total (Q,L) (Q,L) (Q,L) 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 (v,L) (v,L) (v,L) Element of bool [:[:v,v:], the carrier of L:]
[Q,u] is V18() set
{Q,u} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,u},{Q}} is non empty set
[v,a] is V18() set
{v,a} is non empty set
{v} is non empty trivial 1 -element set
{{v,a},{v}} is non empty set
[Q,u] `2 is set
dq9 is Relation-like Function-like Function-yielding V91() set
doms dq9 is Relation-like Function-like set
proj2 (doms dq9) is set
q is set
proj1 (doms dq9) is set
Q is set
(doms dq9) . Q is set
proj1 dq9 is set
u is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . u is set
u + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . (u + 1) is set
v is non empty set
[:v,v:] is non empty Relation-like set
[:[:v,v:], the carrier of L:] is non empty Relation-like set
bool [:[:v,v:], the carrier of L:] is non empty non empty-membered set
b is non empty set
[:b,b:] is non empty Relation-like set
[:[:b,b:], the carrier of L:] is non empty Relation-like set
bool [:[:b,b:], the carrier of L:] is non empty non empty-membered set
a is Relation-like [:v,v:] -defined the carrier of L -valued Function-like quasi_total (v,L) (v,L) (v,L) 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 (b,L) (b,L) (b,L) Element of bool [:[:b,b:], the carrier of L:]
[v,a] is V18() set
{v,a} is non empty set
{v} is non empty trivial 1 -element set
{{v,a},{v}} is non empty set
[b,e] is V18() set
{b,e} is non empty set
{b} is non empty trivial 1 -element set
{{b,e},{b}} is non empty set
[v,a] `2 is set
[v,a] `1 is set
dq9 . u is Relation-like Function-like set
proj1 (dq9 . u) is set
dom a is Relation-like v -defined v -valued Element of bool [:v,v:]
bool [:v,v:] is non empty non empty-membered set
(A . u) `1 is set
[:((A . u) `1),((A . u) `1):] is Relation-like set
q is set
Q is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . Q is set
(A . Q) `1 is set
[:((A . Q) `1),((A . Q) `1):] is Relation-like set
Q + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . (Q + 1) is set
u is non empty set
[:u,u:] is non empty Relation-like set
[:[:u,u:], the carrier of L:] is non empty Relation-like set
bool [:[:u,u:], the carrier of L:] is non empty non empty-membered set
a is non empty set
[:a,a:] is non empty Relation-like set
[:[:a,a:], the carrier of L:] is non empty Relation-like set
bool [:[:a,a:], the carrier of L:] is non empty non empty-membered set
v is Relation-like [:u,u:] -defined the carrier of L -valued Function-like quasi_total (u,L) (u,L) (u,L) 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 (a,L) (a,L) (a,L) Element of bool [:[:a,a:], the carrier of L:]
[u,v] is V18() set
{u,v} is non empty set
{u} is non empty trivial 1 -element set
{{u,v},{u}} is non empty set
[a,b] is V18() set
{a,b} is non empty set
{a} is non empty trivial 1 -element set
{{a,b},{a}} is non empty set
[u,v] `2 is set
proj1 (doms dq9) is set
[u,v] `1 is set
dom v is Relation-like u -defined u -valued Element of bool [:u,u:]
bool [:u,u:] is non empty non empty-membered set
dq9 . Q is Relation-like Function-like set
proj1 (dq9 . Q) is set
(doms dq9) . Q is set
q is set
Q is set
u is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . u is set
(A . u) `1 is set
v is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . v is set
(A . v) `1 is set
union (proj2 (doms dq9)) is set
z is Relation-like Function-like set
proj1 z is set
[:[:S,S:], the carrier of L:] is non empty Relation-like set
bool [:[:S,S:], the carrier of L:] is non empty non empty-membered set
Q is Relation-like Function-like set
proj1 Q is set
proj2 Q is set
q is Relation-like [:S,S:] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:S,S:], the carrier of L:]
Q is Element of S
u is Element of S
(S,L,q,Q,u) is Element of the carrier of L
[Q,u] is V18() set
{Q,u} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,u},{Q}} is non empty set
q . [Q,u] is set
(S,L,q,u,Q) is Element of the carrier of L
[u,Q] is V18() set
{u,Q} is non empty set
{u} is non empty trivial 1 -element set
{{u,Q},{u}} is non empty set
q . [u,Q] is set
v is set
a is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . a is set
(A . a) `1 is set
a + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . (a + 1) is set
b is non empty set
[:b,b:] is non empty Relation-like set
[:[:b,b:], the carrier of L:] is non empty Relation-like set
bool [:[:b,b:], the carrier of L:] is non empty non empty-membered set
W is non empty set
[:W,W:] is non empty Relation-like set
[:[:W,W:], the carrier of L:] is non empty Relation-like set
bool [:[:W,W:], the carrier of L:] is non empty non empty-membered set
e is Relation-like [:b,b:] -defined the carrier of L -valued Function-like quasi_total (b,L) (b,L) (b,L) Element of bool [:[:b,b:], the carrier of L:]
V is Relation-like [:W,W:] -defined the carrier of L -valued Function-like quasi_total (W,L) (W,L) (W,L) Element of bool [:[:W,W:], the carrier of L:]
[b,e] is V18() set
{b,e} is non empty set
{b} is non empty trivial 1 -element set
{{b,e},{b}} is non empty set
[W,V] is V18() set
{W,V} is non empty set
{W} is non empty trivial 1 -element set
{{W,V},{W}} is non empty set
[b,e] `1 is set
[b,e] `2 is set
j is set
z1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . z1 is set
(A . z1) `1 is set
z1 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . (z1 + 1) is set
z2 is non empty set
[:z2,z2:] is non empty Relation-like set
[:[:z2,z2:], the carrier of L:] is non empty Relation-like set
bool [:[:z2,z2:], the carrier of L:] is non empty non empty-membered set
h is non empty set
[:h,h:] is non empty Relation-like set
[:[:h,h:], the carrier of L:] is non empty Relation-like set
bool [:[:h,h:], the carrier of L:] is non empty non empty-membered set
z3 is Relation-like [:z2,z2:] -defined the carrier of L -valued Function-like quasi_total (z2,L) (z2,L) (z2,L) Element of bool [:[:z2,z2:], the carrier of L:]
h is Relation-like [:h,h:] -defined the carrier of L -valued Function-like quasi_total (h,L) (h,L) (h,L) Element of bool [:[:h,h:], the carrier of L:]
[z2,z3] is V18() set
{z2,z3} is non empty set
{z2} is non empty trivial 1 -element set
{{z2,z3},{z2}} is non empty set
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
[z2,z3] `1 is set
[z2,z3] `2 is set
dom z3 is Relation-like z2 -defined z2 -valued Element of bool [:z2,z2:]
bool [:z2,z2:] is non empty non empty-membered set
h is Element of z2
c₂₉ is Element of z2
[h,c₂₉] is V18() Element of [:z2,z2:]
{h,c₂₉} is non empty set
{h} is non empty trivial 1 -element set
{{h,c₂₉},{h}} is non empty set
z3 . [h,c₂₉] is Element of the carrier of L
(z2,L,z3,h,c₂₉) is Element of the carrier of L
[h,c₂₉] is V18() set
z3 . [h,c₂₉] is set
(z2,L,z3,c₂₉,h) is Element of the carrier of L
[c₂₉,h] is V18() set
{c₂₉,h} is non empty set
{c₂₉} is non empty trivial 1 -element set
{{c₂₉,h},{c₂₉}} is non empty set
z3 . [c₂₉,h] is set
[c₂₉,h] is V18() Element of [:z2,z2:]
q . [c₂₉,h] is set
dom e is Relation-like b -defined b -valued Element of bool [:b,b:]
bool [:b,b:] is non empty non empty-membered set
h is Element of b
c₂₉ is Element of b
[h,c₂₉] is V18() Element of [:b,b:]
{h,c₂₉} is non empty set
{h} is non empty trivial 1 -element set
{{h,c₂₉},{h}} is non empty set
e . [h,c₂₉] is Element of the carrier of L
(b,L,e,h,c₂₉) is Element of the carrier of L
[h,c₂₉] is V18() set
e . [h,c₂₉] is set
(b,L,e,c₂₉,h) is Element of the carrier of L
[c₂₉,h] is V18() set
{c₂₉,h} is non empty set
{c₂₉} is non empty trivial 1 -element set
{{c₂₉,h},{c₂₉}} is non empty set
e . [c₂₉,h] is set
[c₂₉,h] is V18() Element of [:b,b:]
q . [c₂₉,h] is set
Q is Element of S
v is Element of S
(S,L,q,Q,v) is Element of the carrier of L
[Q,v] is V18() set
{Q,v} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,v},{Q}} is non empty set
q . [Q,v] is set
u is Element of S
(S,L,q,Q,u) is Element of the carrier of L
[Q,u] is V18() set
{Q,u} is non empty set
{{Q,u},{Q}} is non empty set
q . [Q,u] is set
(S,L,q,u,v) is Element of the carrier of L
[u,v] is V18() set
{u,v} is non empty set
{u} is non empty trivial 1 -element set
{{u,v},{u}} is non empty set
q . [u,v] is set
(S,L,q,Q,u) "\/" (S,L,q,u,v) is Element of the carrier of L
a is set
b is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . b is set
(A . b) `1 is set
b + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . (b + 1) is set
e is non empty set
[:e,e:] is non empty Relation-like set
[:[:e,e:], the carrier of L:] is non empty Relation-like set
bool [:[:e,e:], the carrier of L:] is non empty non empty-membered set
V is non empty set
[:V,V:] is non empty Relation-like set
[:[:V,V:], the carrier of L:] is non empty Relation-like set
bool [:[:V,V:], the carrier of L:] is non empty non empty-membered set
W is Relation-like [:e,e:] -defined the carrier of L -valued Function-like quasi_total (e,L) (e,L) (e,L) Element of bool [:[:e,e:], the carrier of L:]
j is Relation-like [:V,V:] -defined the carrier of L -valued Function-like quasi_total (V,L) (V,L) (V,L) Element of bool [:[:V,V:], the carrier of L:]
[e,W] is V18() set
{e,W} is non empty set
{e} is non empty trivial 1 -element set
{{e,W},{e}} is non empty set
[V,j] is V18() set
{V,j} is non empty set
{V} is non empty trivial 1 -element set
{{V,j},{V}} is non empty set
[e,W] `1 is set
[e,W] `2 is set
dom W is Relation-like e -defined e -valued Element of bool [:e,e:]
bool [:e,e:] is non empty non empty-membered set
z1 is set
z2 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . z2 is set
(A . z2) `1 is set
z2 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . (z2 + 1) is set
z3 is non empty set
[:z3,z3:] is non empty Relation-like set
[:[:z3,z3:], the carrier of L:] is non empty Relation-like set
bool [:[:z3,z3:], the carrier of L:] is non empty non empty-membered set
h is non empty set
[:h,h:] is non empty Relation-like set
[:[:h,h:], the carrier of L:] is non empty Relation-like set
bool [:[:h,h:], the carrier of L:] is non empty non empty-membered set
h is Relation-like [:z3,z3:] -defined the carrier of L -valued Function-like quasi_total (z3,L) (z3,L) (z3,L) Element of bool [:[:z3,z3:], the carrier of L:]
h is Relation-like [:h,h:] -defined the carrier of L -valued Function-like quasi_total (h,L) (h,L) (h,L) Element of bool [:[:h,h:], the carrier of L:]
[z3,h] is V18() set
{z3,h} is non empty set
{z3} is non empty trivial 1 -element set
{{z3,h},{z3}} is non empty set
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
[z3,h] `1 is set
[z3,h] `2 is set
dom h is Relation-like z3 -defined z3 -valued Element of bool [:z3,z3:]
bool [:z3,z3:] is non empty non empty-membered set
c₂₉ is set
z29 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . z29 is set
(A . z29) `1 is set
z29 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . (z29 + 1) is set
z39 is non empty set
[:z39,z39:] is non empty Relation-like set
[:[:z39,z39:], the carrier of L:] is non empty Relation-like set
bool [:[:z39,z39:], the carrier of L:] is non empty non empty-membered set
Aq3 is non empty set
[:Aq3,Aq3:] is non empty Relation-like set
[:[:Aq3,Aq3:], the carrier of L:] is non empty Relation-like set
bool [:[:Aq3,Aq3:], the carrier of L:] is non empty non empty-membered set
c<sub>32</sub> is Relation-like [:z39,z39:] -defined the carrier of L -valued Function-like quasi_total (z39,L) (z39,L) (z39,L) Element of bool [:[:z39,z39:], the carrier of L:]
dq3 is Relation-like [:Aq3,Aq3:] -defined the carrier of L -valued Function-like quasi_total (Aq3,L) (Aq3,L) (Aq3,L) Element of bool [:[:Aq3,Aq3:], the carrier of L:]
[z39,c<sub>32</sub>] is V18() set
{z39,c<sub>32</sub>} is non empty set
{z39} is non empty trivial 1 -element set
{{z39,c<sub>32</sub>},{z39}} is non empty set
[Aq3,dq3] is V18() set
{Aq3,dq3} is non empty set
{Aq3} is non empty trivial 1 -element set
{{Aq3,dq3},{Aq3}} is non empty set
[z39,c<sub>32</sub>] `1 is set
[z39,c₃₂] `2 is set
dom c<sub>32</sub> is Relation-like z39 -defined z39 -valued Element of bool [:z39,z39:]
bool [:z39,z39:] is non empty non empty-membered set
y9 is Element of z39
z9 is Element of z39
[y9,z9] is V18() Element of [:z39,z39:]
{y9,z9} is non empty set
{y9} is non empty trivial 1 -element set
{{y9,z9},{y9}} is non empty set
c<sub>32</sub> . [y9,z9] is Element of the carrier of L
(z39,L,c<sub>32</sub>,y9,z9) is Element of the carrier of L
[y9,z9] is V18() set
c<sub>32</sub> . [y9,z9] is set
x9 is Element of z39
[x9,z9] is V18() Element of [:z39,z39:]
{x9,z9} is non empty set
{x9} is non empty trivial 1 -element set
{{x9,z9},{x9}} is non empty set
c<sub>32</sub> . [x9,z9] is Element of the carrier of L
(z39,L,c<sub>32</sub>,x9,z9) is Element of the carrier of L
[x9,z9] is V18() set
c<sub>32</sub> . [x9,z9] is set
[x9,y9] is V18() Element of [:z39,z39:]
{x9,y9} is non empty set
{{x9,y9},{x9}} is non empty set
c<sub>32</sub> . [x9,y9] is Element of the carrier of L
(z39,L,c<sub>32</sub>,x9,y9) is Element of the carrier of L
[x9,y9] is V18() set
c<sub>32</sub> . [x9,y9] is set
x9 is Element of z3
z9 is Element of z3
[x9,z9] is V18() Element of [:z3,z3:]
{x9,z9} is non empty set
{x9} is non empty trivial 1 -element set
{{x9,z9},{x9}} is non empty set
h . [x9,z9] is Element of the carrier of L
(z3,L,h,x9,z9) is Element of the carrier of L
[x9,z9] is V18() set
h . [x9,z9] is set
y9 is Element of z3
[y9,z9] is V18() Element of [:z3,z3:]
{y9,z9} is non empty set
{y9} is non empty trivial 1 -element set
{{y9,z9},{y9}} is non empty set
h . [y9,z9] is Element of the carrier of L
(z3,L,h,y9,z9) is Element of the carrier of L
[y9,z9] is V18() set
h . [y9,z9] is set
[y9,x9] is V18() Element of [:z3,z3:]
{y9,x9} is non empty set
{{y9,x9},{y9}} is non empty set
h . [y9,x9] is Element of the carrier of L
(z3,L,h,y9,x9) is Element of the carrier of L
[y9,x9] is V18() set
h . [y9,x9] is set
z9 is Element of z39
y9 is Element of z39
[z9,y9] is V18() Element of [:z39,z39:]
{z9,y9} is non empty set
{z9} is non empty trivial 1 -element set
{{z9,y9},{z9}} is non empty set
c<sub>32</sub> . [z9,y9] is Element of the carrier of L
(z39,L,c<sub>32</sub>,z9,y9) is Element of the carrier of L
[z9,y9] is V18() set
c<sub>32</sub> . [z9,y9] is set
x9 is Element of z39
[x9,y9] is V18() Element of [:z39,z39:]
{x9,y9} is non empty set
{x9} is non empty trivial 1 -element set
{{x9,y9},{x9}} is non empty set
c<sub>32</sub> . [x9,y9] is Element of the carrier of L
(z39,L,c<sub>32</sub>,x9,y9) is Element of the carrier of L
[x9,y9] is V18() set
c<sub>32</sub> . [x9,y9] is set
[x9,z9] is V18() Element of [:z39,z39:]
{x9,z9} is non empty set
{{x9,z9},{x9}} is non empty set
c<sub>32</sub> . [x9,z9] is Element of the carrier of L
(z39,L,c<sub>32</sub>,x9,z9) is Element of the carrier of L
[x9,z9] is V18() set
c<sub>32</sub> . [x9,z9] is set
y9 is Element of e
z9 is Element of e
[y9,z9] is V18() Element of [:e,e:]
{y9,z9} is non empty set
{y9} is non empty trivial 1 -element set
{{y9,z9},{y9}} is non empty set
W . [y9,z9] is Element of the carrier of L
(e,L,W,y9,z9) is Element of the carrier of L
[y9,z9] is V18() set
W . [y9,z9] is set
x9 is Element of e
[x9,z9] is V18() Element of [:e,e:]
{x9,z9} is non empty set
{x9} is non empty trivial 1 -element set
{{x9,z9},{x9}} is non empty set
W . [x9,z9] is Element of the carrier of L
(e,L,W,x9,z9) is Element of the carrier of L
[x9,z9] is V18() set
W . [x9,z9] is set
[x9,y9] is V18() Element of [:e,e:]
{x9,y9} is non empty set
{{x9,y9},{x9}} is non empty set
W . [x9,y9] is Element of the carrier of L
(e,L,W,x9,y9) is Element of the carrier of L
[x9,y9] is V18() set
W . [x9,y9] is set
Q is Element of S
(S,L,q,Q,Q) is Element of the carrier of L
[Q,Q] is V18() set
{Q,Q} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,Q},{Q}} is non empty set
q . [Q,Q] is set
Bottom L is Element of the carrier of L
u is set
v is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . v is set
(A . v) `1 is set
v + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . (v + 1) is set
a is non empty set
[:a,a:] is non empty Relation-like set
[:[:a,a:], the carrier of L:] is non empty Relation-like set
bool [:[:a,a:], the carrier of L:] is non empty non empty-membered set
e is non empty set
[:e,e:] is non empty Relation-like set
[:[:e,e:], the carrier of L:] is non empty Relation-like set
bool [:[:e,e:], the carrier of L:] is non empty non empty-membered set
b is Relation-like [:a,a:] -defined the carrier of L -valued Function-like quasi_total (a,L) (a,L) (a,L) Element of bool [:[:a,a:], the carrier of L:]
W is Relation-like [:e,e:] -defined the carrier of L -valued Function-like quasi_total (e,L) (e,L) (e,L) Element of bool [:[:e,e:], the carrier of L:]
[a,b] is V18() set
{a,b} is non empty set
{a} is non empty trivial 1 -element set
{{a,b},{a}} is non empty set
[e,W] is V18() set
{e,W} is non empty set
{e} is non empty trivial 1 -element set
{{e,W},{e}} is non empty set
[a,b] `1 is set
[a,b] `2 is set
dom b is Relation-like a -defined a -valued Element of bool [:a,a:]
bool [:a,a:] is non empty non empty-membered set
V is Element of a
[V,V] is V18() Element of [:a,a:]
{V,V} is non empty set
{V} is non empty trivial 1 -element set
{{V,V},{V}} is non empty set
b . [V,V] is Element of the carrier of L
(a,L,b,V,V) is Element of the carrier of L
[V,V] is V18() set
b . [V,V] is set
L is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of L is non empty set
(L) is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like quasi_total ( the carrier of L,L) ( the carrier of L,L) ( the carrier of L,L) 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 Relation-like set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty Relation-like set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty non empty-membered set
A is Relation-like Function-like ( the carrier of L,L,(L))
{ ((A . b₁) `1) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
union { ((A . b<sub>1</sub>) `1) where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
{ ((A . b₁) `2) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
union { ((A . b<sub>1</sub>) `2) where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
D is non empty set
[:D,D:] is non empty Relation-like set
[:[:D,D:], the carrier of L:] is non empty Relation-like set
bool [:[:D,D:], the carrier of L:] is non empty non empty-membered set
S is Relation-like [:D,D:] -defined the carrier of L -valued Function-like quasi_total (D,L) (D,L) (D,L) Element of bool [:[:D,D:], the carrier of L:]
FS is Element of D
FS is Element of D
(D,L,S,FS,FS) is Element of the carrier of L
[FS,FS] is V18() set
{FS,FS} is non empty set
{FS} is non empty trivial 1 -element 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
A . 0 is set
(A . 0) `1 is set
w is non empty set
z is set
c<sub>11</sub> is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . c<sub>11</sub> is set
(A . c<sub>11</sub>) `1 is set
c₁₁ + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . (c₁₁ + 1) is set
dq9 is non empty set
[:dq9,dq9:] is non empty Relation-like set
[:[:dq9,dq9:], the carrier of L:] is non empty Relation-like set
bool [:[:dq9,dq9:], the carrier of L:] is non empty non empty-membered set
Q is non empty set
[:Q,Q:] is non empty Relation-like set
[:[:Q,Q:], the carrier of L:] is non empty Relation-like set
bool [:[:Q,Q:], the carrier of L:] is non empty non empty-membered set
q is Relation-like [:dq9,dq9:] -defined the carrier of L -valued Function-like quasi_total (dq9,L) (dq9,L) (dq9,L) 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 (Q,L) (Q,L) (Q,L) Element of bool [:[:Q,Q:], the carrier of L:]
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
[Q,u] is V18() set
{Q,u} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,u},{Q}} is non empty set
[dq9,q] `1 is set
[dq9,q] `2 is set
[Q,u] `1 is set
[Q,u] `2 is set
v is set
a is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . a is set
(A . a) `1 is set
a + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
A . (a + 1) is set
b is non empty set
[:b,b:] is non empty Relation-like set
[:[:b,b:], the carrier of L:] is non empty Relation-like set
bool [:[:b,b:], the carrier of L:] is non empty non empty-membered set
W is non empty set
[:W,W:] is non empty Relation-like set
[:[:W,W:], the carrier of L:] is non empty Relation-like set
bool [:[:W,W:], the carrier of L:] is non empty non empty-membered set
e is Relation-like [:b,b:] -defined the carrier of L -valued Function-like quasi_total (b,L) (b,L) (b,L) Element of bool [:[:b,b:], the carrier of L:]
V is Relation-like [:W,W:] -defined the carrier of L -valued Function-like quasi_total (W,L) (W,L) (W,L) Element of bool [:[:W,W:], the carrier of L:]
[b,e] is V18() set
{b,e} is non empty set
{b} is non empty trivial 1 -element set
{{b,e},{b}} is non empty set
[W,V] is V18() set
{W,V} is non empty set
{W} is non empty trivial 1 -element set
{{W,V},{W}} is non empty set
[b,e] `1 is set
[b,e] `2 is set
[W,V] `1 is set
[W,V] `2 is set
j is Element of b
z1 is Element of b
dom e is Relation-like b -defined b -valued Element of bool [:b,b:]
bool [:b,b:] is non empty non empty-membered set
[j,z1] is V18() Element of [:b,b:]
{j,z1} is non empty set
{j} is non empty trivial 1 -element set
{{j,z1},{j}} is non empty set
e . [j,z1] is Element of the carrier of L
(b,L,e,j,z1) is Element of the carrier of L
[j,z1] is V18() set
e . [j,z1] is set
h is Element of W
V . (FS,h) is set
[FS,h] is V18() set
{FS,h} is non empty set
{{FS,h},{FS}} is non empty set
V . [FS,h] is set
h is Element of W
h is Element of W
(W,L,V,h,h) is Element of the carrier of L
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
V . [h,h] is set
(W,L,V,h,h) is Element of the carrier of L
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
V . [h,h] is set
V . (h,FS) is set
[h,FS] is V18() set
{h,FS} is non empty set
{h} is non empty trivial 1 -element set
{{h,FS},{h}} is non empty set
V . [h,FS] is set
c<sub>29</sub> is Element of D
(D,L,S,FS,c<sub>29</sub>) is Element of the carrier of L
[FS,c<sub>29</sub>] is V18() set
{FS,c<sub>29</sub>} is non empty set
{{FS,c<sub>29</sub>},{FS}} is non empty set
S . [FS,c<sub>29</sub>] is set
z29 is Element of D
(D,L,S,c<sub>29</sub>,z29) is Element of the carrier of L
[c<sub>29</sub>,z29] is V18() set
{c<sub>29</sub>,z29} is non empty set
{c<sub>29</sub>} is non empty trivial 1 -element set
{{c<sub>29</sub>,z29},{c<sub>29</sub>}} is non empty set
S . [c<sub>29</sub>,z29] is set
z39 is Element of D
(D,L,S,z29,z39) is Element of the carrier of L
[z29,z39] is V18() set
{z29,z39} is non empty set
{z29} is non empty trivial 1 -element set
{{z29,z39},{z29}} is non empty set
S . [z29,z39] is set
(D,L,S,z39,FS) is Element of the carrier of L
[z39,FS] is V18() set
{z39,FS} is non empty set
{z39} is non empty trivial 1 -element set
{{z39,FS},{z39}} is non empty set
S . [z39,FS] is set
dom V is Relation-like W -defined W -valued Element of bool [:W,W:]
bool [:W,W:] is non empty non empty-membered set
z2 is Element of W
[z2,h] is V18() Element of [:W,W:]
{z2,h} is non empty set
{z2} is non empty trivial 1 -element set
{{z2,h},{z2}} is non empty set
V . [z2,h] is Element of the carrier of L
[h,h] is V18() Element of [:W,W:]
V . [h,h] is Element of the carrier of L
[h,h] is V18() Element of [:W,W:]
V . [h,h] is Element of the carrier of L
z3 is Element of W
[h,z3] is V18() Element of [:W,W:]
{h,z3} is non empty set
{{h,z3},{h}} is non empty set
V . [h,z3] is Element of the carrier of L
j is Element of dq9
z1 is Element of dq9
dom q is Relation-like dq9 -defined dq9 -valued Element of bool [:dq9,dq9:]
bool [:dq9,dq9:] is non empty non empty-membered set
[j,z1] is V18() Element of [:dq9,dq9:]
{j,z1} is non empty set
{j} is non empty trivial 1 -element set
{{j,z1},{j}} is non empty set
q . [j,z1] is Element of the carrier of L
(dq9,L,q,j,z1) is Element of the carrier of L
[j,z1] is V18() set
q . [j,z1] is set
h is Element of Q
u . (FS,h) is set
[FS,h] is V18() set
{FS,h} is non empty set
{{FS,h},{FS}} is non empty set
u . [FS,h] is set
h is Element of Q
h is Element of Q
(Q,L,u,h,h) is Element of the carrier of L
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
u . [h,h] is set
(Q,L,u,h,h) is Element of the carrier of L
[h,h] is V18() set
{h,h} is non empty set
{h} is non empty trivial 1 -element set
{{h,h},{h}} is non empty set
u . [h,h] is set
u . (h,FS) is set
[h,FS] is V18() set
{h,FS} is non empty set
{h} is non empty trivial 1 -element set
{{h,FS},{h}} is non empty set
u . [h,FS] is set
c<sub>29</sub> is Element of D
(D,L,S,FS,c<sub>29</sub>) is Element of the carrier of L
[FS,c<sub>29</sub>] is V18() set
{FS,c<sub>29</sub>} is non empty set
{{FS,c<sub>29</sub>},{FS}} is non empty set
S . [FS,c<sub>29</sub>] is set
z29 is Element of D
(D,L,S,c<sub>29</sub>,z29) is Element of the carrier of L
[c<sub>29</sub>,z29] is V18() set
{c<sub>29</sub>,z29} is non empty set
{c<sub>29</sub>} is non empty trivial 1 -element set
{{c<sub>29</sub>,z29},{c<sub>29</sub>}} is non empty set
S . [c<sub>29</sub>,z29] is set
z39 is Element of D
(D,L,S,z29,z39) is Element of the carrier of L
[z29,z39] is V18() set
{z29,z39} is non empty set
{z29} is non empty trivial 1 -element set
{{z29,z39},{z29}} is non empty set
S . [z29,z39] is set
(D,L,S,z39,FS) is Element of the carrier of L
[z39,FS] is V18() set
{z39,FS} is non empty set
{z39} is non empty trivial 1 -element set
{{z39,FS},{z39}} is non empty set
S . [z39,FS] is set
dom u is Relation-like Q -defined Q -valued Element of bool [:Q,Q:]
bool [:Q,Q:] is non empty non empty-membered set
z2 is Element of Q
[z2,h] is V18() Element of [:Q,Q:]
{z2,h} is non empty set
{z2} is non empty trivial 1 -element set
{{z2,h},{z2}} is non empty set
u . [z2,h] is Element of the carrier of L
[h,h] is V18() Element of [:Q,Q:]
u . [h,h] is Element of the carrier of L
[h,h] is V18() Element of [:Q,Q:]
u . [h,h] is Element of the carrier of L
z3 is Element of Q
[h,z3] is V18() Element of [:Q,Q:]
{h,z3} is non empty set
{{h,z3},{h}} is non empty set
u . [h,z3] is Element of the carrier of L
3 + 2 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
L is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of L is non empty set
(L) is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like quasi_total ( the carrier of L,L) ( the carrier of L,L) ( the carrier of L,L) 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 Relation-like set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty Relation-like set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty non empty-membered set
A is Relation-like Function-like ( the carrier of L,L,(L))
{ ((A . b<sub>1</sub>) `1) where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
union { ((A . b₁) `1) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
{ ((A . b<sub>1</sub>) `2) where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
union { ((A . b₁) `2) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
D is non empty set
[:D,D:] is non empty Relation-like set
[:[:D,D:], the carrier of L:] is non empty Relation-like set
bool [:[:D,D:], the carrier of L:] is non empty non empty-membered set
(D) is non empty reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V183() RelStr
EqRelLatt D is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt D) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt D) is non empty set
K559((EqRelLatt D)) is Relation-like the carrier of (EqRelLatt D) -defined the carrier of (EqRelLatt D) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt D), the carrier of (EqRelLatt D):]
[: the carrier of (EqRelLatt D), the carrier of (EqRelLatt D):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt D), the carrier of (EqRelLatt D):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt D),K559((EqRelLatt D)) #) is strict RelStr
the carrier of (D) is non empty set
[: the carrier of L, the carrier of (D):] is non empty Relation-like set
bool [: the carrier of L, the carrier of (D):] is non empty non empty-membered set
bool [:D,D:] is non empty non empty-membered set
S is Relation-like [:D,D:] -defined the carrier of L -valued Function-like quasi_total (D,L) (D,L) (D,L) Element of bool [:[:D,D:], the carrier of L:]
(D,L,S) is Relation-like the carrier of L -defined the carrier of (D) -valued Function-like quasi_total Element of bool [: the carrier of L, the carrier of (D):]
FS is Relation-like the carrier of L -defined the carrier of (D) -valued Function-like quasi_total meet-preserving join-preserving Element of bool [: the carrier of L, the carrier of (D):]
Image FS is strict reflexive transitive antisymmetric V184((D)) meet-inheriting join-inheriting SubRelStr of (D)
the carrier of (Image FS) is set
f is Relation-like D -defined D -valued total reflexive symmetric transitive Element of bool [:D,D:]
w is Relation-like D -defined D -valued total reflexive symmetric transitive Element of bool [:D,D:]
f "\/" w is Relation-like D -defined D -valued total reflexive symmetric transitive Element of bool [:D,D:]
z is set
c<sub>11</sub> is set
[z,c<sub>11</sub>] is V18() set
{z,c<sub>11</sub>} is non empty set
{z} is non empty trivial 1 -element set
{{z,c<sub>11</sub>},{z}} is non empty set
field (f "\/" w) is set
rng FS is Element of bool the carrier of (D)
bool the carrier of (D) is non empty non empty-membered set
subrelstr (rng FS) is strict reflexive transitive antisymmetric V184((D)) SubRelStr of (D)
dom FS is Element of bool the carrier of L
bool the carrier of L is non empty non empty-membered set
Q is set
FS . Q is set
u is set
FS . u is set
v is Element of the carrier of L
a is Element of the carrier of L
b is Element of the carrier of L
e is Element of the carrier of L
b "\/" e is Element of the carrier of L
FS . (b "\/" e) is Element of the carrier of (D)
W is Relation-like D -defined D -valued total reflexive symmetric transitive Element of bool [:D,D:]
FS . b is Element of the carrier of (D)
V is Relation-like D -defined D -valued total reflexive symmetric transitive Element of bool [:D,D:]
FS . e is Element of the carrier of (D)
j is Relation-like D -defined D -valued total reflexive symmetric transitive Element of bool [:D,D:]
(FS . b) "\/" (FS . e) is Element of the carrier of (D)
dq9 is Element of D
q is Element of D
(D,L,S,dq9,q) is Element of the carrier of L
[dq9,q] is V18() set
{dq9,q} is non empty set
{dq9} is non empty trivial 1 -element set
{{dq9,q},{dq9}} is non empty set
S . [dq9,q] is set
z1 is Element of D
(D,L,S,dq9,z1) is Element of the carrier of L
[dq9,z1] is V18() set
{dq9,z1} is non empty set
{{dq9,z1},{dq9}} is non empty set
S . [dq9,z1] is set
z2 is Element of D
z3 is Element of D
(D,L,S,z2,z3) is Element of the carrier of L
[z2,z3] is V18() set
{z2,z3} is non empty set
{z2} is non empty trivial 1 -element set
{{z2,z3},{z2}} is non empty set
S . [z2,z3] is set
(D,L,S,z1,z2) is Element of the carrier of L
[z1,z2] is V18() set
{z1,z2} is non empty set
{z1} is non empty trivial 1 -element set
{{z1,z2},{z1}} is non empty set
S . [z1,z2] is set
(D,L,S,z3,q) is Element of the carrier of L
[z3,q] is V18() set
{z3,q} is non empty set
{z3} is non empty trivial 1 -element set
{{z3,q},{z3}} is non empty set
S . [z3,q] is set
h is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V63() cardinal set
h is Relation-like NAT -defined Function-like V63() FinSequence-like FinSubsequence-like set
dom h is V56() V57() V58() V59() V60() V61() V74() Element of bool NAT
h is Relation-like NAT -defined Function-like V63() FinSequence-like FinSubsequence-like set
dom h is V56() V57() V58() V59() V60() V61() V74() Element of bool NAT
len h is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
proj2 h is set
h is set
h is set
h . h is set
h is Relation-like NAT -defined D -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of D
h is non empty Relation-like NAT -defined D -valued Function-like V63() FinSequence-like FinSubsequence-like FinSequence of D
h . 1 is set
len h is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal Element of NAT
c<sub>29</sub> is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
h . c<sub>29</sub> is set
c<sub>29</sub> + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
h . (c<sub>29</sub> + 1) is set
[(h . c<sub>29</sub>),(h . (c<sub>29</sub> + 1))] is V18() set
{(h . c<sub>29</sub>),(h . (c<sub>29</sub> + 1))} is non empty set
{(h . c<sub>29</sub>)} is non empty trivial 1 -element set
{{(h . c<sub>29</sub>),(h . (c<sub>29</sub> + 1))},{(h . c<sub>29</sub>)}} is non empty set
[dq9,z1] is V18() Element of [:D,D:]
[(h . 1),z1] is V18() set
{(h . 1),z1} is non empty set
{(h . 1)} is non empty trivial 1 -element set
{{(h . 1),z1},{(h . 1)}} is non empty set
[z2,z3] is V18() Element of [:D,D:]
h . 3 is set
[(h . 3),z3] is V18() set
{(h . 3),z3} is non empty set
{(h . 3)} is non empty trivial 1 -element set
{{(h . 3),z3},{(h . 3)}} is non empty set
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal even Element of NAT
(2 * 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V72() V73() V74() V75() V76() cardinal non even Element of NAT
[z1,z2] is V18() Element of [:D,D:]
h . 2 is set
[(h . 2),z2] is V18() set
{(h . 2),z2} is non empty set
{(h . 2)} is non empty trivial 1 -element set
{{(h . 2),z2},{(h . 2)}} is non empty set
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal even Element of NAT
[z3,q] is V18() Element of [:D,D:]
h . 4 is set
[(h . 4),q] is V18() set
{(h . 4),q} is non empty set
{(h . 4)} is non empty trivial 1 -element set
{{(h . 4),q},{(h . 4)}} is non empty set
2 * 2 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal even Element of NAT
h . (len h) is set
h . 5 is set
L is non empty reflexive transitive antisymmetric with_suprema with_infima lower-bounded RelStr
the carrier of L is non empty set
(L) is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like quasi_total ( the carrier of L,L) ( the carrier of L,L) ( the carrier of L,L) 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 Relation-like set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty Relation-like set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty non empty-membered set
the Relation-like Function-like ( the carrier of L,L,(L)) is Relation-like Function-like ( the carrier of L,L,(L))
{ (( the Relation-like Function-like ( the carrier of L,L,(L)) . b<sub>1</sub>) `1) where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
union { (( the Relation-like Function-like ( the carrier of L,L,(L)) . b₁) `1) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
the Relation-like Function-like ( the carrier of L,L,(L)) . 0 is set
( the Relation-like Function-like ( the carrier of L,L,(L)) . 0) `1 is set
[ the carrier of L,(L)] is V18() set
{ the carrier of L,(L)} is non empty set
{ the carrier of L} is non empty trivial 1 -element set
{{ the carrier of L,(L)},{ the carrier of L}} is non empty set
[ the carrier of L,(L)] `1 is set
FS is non empty set
[:FS,FS:] is non empty Relation-like set
[:[:FS,FS:], the carrier of L:] is non empty Relation-like set
bool [:[:FS,FS:], the carrier of L:] is non empty non empty-membered set
{ (( the Relation-like Function-like ( the carrier of L,L,(L)) . b<sub>1</sub>) `2) where b₁ is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
union { (( the Relation-like Function-like ( the carrier of L,L,(L)) . b₁) `2) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT : verum } is set
(FS) is non empty reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V183() RelStr
EqRelLatt FS is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
LattPOSet (EqRelLatt FS) is non empty strict reflexive transitive antisymmetric with_suprema with_infima RelStr
the carrier of (EqRelLatt FS) is non empty set
K559((EqRelLatt FS)) is Relation-like the carrier of (EqRelLatt FS) -defined the carrier of (EqRelLatt FS) -valued total reflexive antisymmetric transitive Element of bool [: the carrier of (EqRelLatt FS), the carrier of (EqRelLatt FS):]
[: the carrier of (EqRelLatt FS), the carrier of (EqRelLatt FS):] is non empty Relation-like set
bool [: the carrier of (EqRelLatt FS), the carrier of (EqRelLatt FS):] is non empty non empty-membered set
RelStr(# the carrier of (EqRelLatt FS),K559((EqRelLatt FS)) #) is strict RelStr
FD is Relation-like [:FS,FS:] -defined the carrier of L -valued Function-like quasi_total (FS,L) (FS,L) (FS,L) Element of bool [:[:FS,FS:], the carrier of L:]
(FS,L,FD) is Relation-like the carrier of L -defined the carrier of (FS) -valued Function-like quasi_total Element of bool [: the carrier of L, the carrier of (FS):]
the carrier of (FS) is non empty set
[: the carrier of L, the carrier of (FS):] is non empty Relation-like set
bool [: the carrier of L, the carrier of (FS):] is non empty non empty-membered set
w is Element of the carrier of L
z is Element of the carrier of L
{w,z} is non empty Element of bool the carrier of L
bool the carrier of L is non empty non empty-membered set
(FS,L,FD) .: {w,z} is Element of bool the carrier of (FS)
bool the carrier of (FS) is non empty non empty-membered set
bool [:FS,FS:] is non empty non empty-membered set
w "\/" z is Element of the carrier of L
(FS,L,FD) . (w "\/" z) is Element of the carrier of (FS)
c<sub>11</sub> is Relation-like FS -defined FS -valued total reflexive symmetric transitive Element of bool [:FS,FS:]
(FS,L,FD) . z is Element of the carrier of (FS)
dq9 is Relation-like FS -defined FS -valued total reflexive symmetric transitive Element of bool [:FS,FS:]
(FS,L,FD) . w is Element of the carrier of (FS)
q is Relation-like FS -defined FS -valued total reflexive symmetric transitive Element of bool [:FS,FS:]
field dq9 is set
z "\/" w is Element of the carrier of L
Q is set
u is set
[Q,u] is V18() set
{Q,u} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,u},{Q}} is non empty set
v is Element of FS
a is Element of FS
(FS,L,FD,v,a) is Element of the carrier of L
[v,a] is V18() set
{v,a} is non empty set
{v} is non empty trivial 1 -element set
{{v,a},{v}} is non empty set
FD . [v,a] is set
field c<sub>11</sub> is set
q "\/" dq9 is Relation-like FS -defined FS -valued total reflexive symmetric transitive Element of bool [:FS,FS:]
Q is set
u is set
[Q,u] is V18() set
{Q,u} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,u},{Q}} is non empty set
v is Element of FS
a is Element of FS
(FS,L,FD,v,a) is Element of the carrier of L
[v,a] is V18() set
{v,a} is non empty set
{v} is non empty trivial 1 -element set
{{v,a},{v}} is non empty set
FD . [v,a] is set
b is Element of FS
(FS,L,FD,v,b) is Element of the carrier of L
[v,b] is V18() set
{v,b} is non empty set
{{v,b},{v}} is non empty set
FD . [v,b] is set
e is Element of FS
W is Element of FS
(FS,L,FD,e,W) is Element of the carrier of L
[e,W] is V18() set
{e,W} is non empty set
{e} is non empty trivial 1 -element set
{{e,W},{e}} is non empty set
FD . [e,W] is set
(FS,L,FD,b,e) is Element of the carrier of L
[b,e] is V18() set
{b,e} is non empty set
{b} is non empty trivial 1 -element set
{{b,e},{b}} is non empty set
FD . [b,e] is set
(FS,L,FD,W,a) is Element of the carrier of L
[W,a] is V18() set
{W,a} is non empty set
{W} is non empty trivial 1 -element set
{{W,a},{W}} is non empty set
FD . [W,a] is set
V is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V63() cardinal set
V is Relation-like NAT -defined Function-like V63() FinSequence-like FinSubsequence-like set
dom V is V56() V57() V58() V59() V60() V61() V74() Element of bool NAT
V is Relation-like NAT -defined Function-like V63() FinSequence-like FinSubsequence-like set
dom V is V56() V57() V58() V59() V60() V61() V74() Element of bool NAT
len V is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
V . 1 is set
q \/ dq9 is Relation-like FS -defined FS -valued Element of bool [:FS,FS:]
j is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
V . j is set
j + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
V . (j + 1) is set
[(V . j),(V . (j + 1))] is V18() set
{(V . j),(V . (j + 1))} is non empty set
{(V . j)} is non empty trivial 1 -element set
{{(V . j),(V . (j + 1))},{(V . j)}} is non empty set
[v,b] is V18() Element of [:FS,FS:]
[(V . 1),b] is V18() set
{(V . 1),b} is non empty set
{(V . 1)} is non empty trivial 1 -element set
{{(V . 1),b},{(V . 1)}} is non empty set
V . 2 is set
[(V . 1),(V . 2)] is V18() set
{(V . 1),(V . 2)} is non empty set
{{(V . 1),(V . 2)},{(V . 1)}} is non empty set
[e,W] is V18() Element of [:FS,FS:]
V . 3 is set
[(V . 3),W] is V18() set
{(V . 3),W} is non empty set
{(V . 3)} is non empty trivial 1 -element set
{{(V . 3),W},{(V . 3)}} is non empty set
V . 4 is set
[(V . 3),(V . 4)] is V18() set
{(V . 3),(V . 4)} is non empty set
{{(V . 3),(V . 4)},{(V . 3)}} is non empty set
[b,e] is V18() Element of [:FS,FS:]
V . 2 is set
[(V . 2),e] is V18() set
{(V . 2),e} is non empty set
{(V . 2)} is non empty trivial 1 -element set
{{(V . 2),e},{(V . 2)}} is non empty set
V . 3 is set
[(V . 2),(V . 3)] is V18() set
{(V . 2),(V . 3)} is non empty set
{{(V . 2),(V . 3)},{(V . 2)}} is non empty set
[W,a] is V18() Element of [:FS,FS:]
V . 4 is set
[(V . 4),a] is V18() set
{(V . 4),a} is non empty set
{(V . 4)} is non empty trivial 1 -element set
{{(V . 4),a},{(V . 4)}} is non empty set
V . 5 is set
[(V . 4),(V . 5)] is V18() set
{(V . 4),(V . 5)} is non empty set
{{(V . 4),(V . 5)},{(V . 4)}} is non empty set
V . 5 is set
V . (len V) is set
field q is set
Q is set
u is set
[Q,u] is V18() set
{Q,u} is non empty set
{Q} is non empty trivial 1 -element set
{{Q,u},{Q}} is non empty set
v is Element of FS
a is Element of FS
(FS,L,FD,v,a) is Element of the carrier of L
[v,a] is V18() set
{v,a} is non empty set
{v} is non empty trivial 1 -element set
{{v,a},{v}} is non empty set
FD . [v,a] is set
q \/ dq9 is Relation-like FS -defined FS -valued Element of bool [:FS,FS:]
dom (FS,L,FD) is Element of bool the carrier of L
"\/" (((FS,L,FD) .: {w,z}),(FS)) is Element of the carrier of (FS)
{((FS,L,FD) . w),((FS,L,FD) . z)} is non empty Element of bool the carrier of (FS)
"\/" ({((FS,L,FD) . w),((FS,L,FD) . z)},(FS)) is Element of the carrier of (FS)
((FS,L,FD) . w) "\/" ((FS,L,FD) . z) is Element of the carrier of (FS)
"\/" ({w,z},L) is Element of the carrier of L
(FS,L,FD) . ("\/" ({w,z},L)) is Element of the carrier of (FS)
f is Relation-like the carrier of L -defined the carrier of (FS) -valued Function-like quasi_total meet-preserving join-preserving Element of bool [: the carrier of L, the carrier of (FS):]
dom f is Element of bool the carrier of L
bool the carrier of L is non empty non empty-membered set
Image f is strict reflexive transitive antisymmetric V184((FS)) meet-inheriting join-inheriting SubRelStr of (FS)
rng f is Element of bool the carrier of (FS)
bool the carrier of (FS) is non empty non empty-membered set
subrelstr (rng f) is strict reflexive transitive antisymmetric V184((FS)) SubRelStr of (FS)
bool [:FS,FS:] is non empty non empty-membered set
the carrier of (Image f) is set
id FS is non empty Relation-like FS -defined FS -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:FS,FS:]
{{ the carrier of L}} is non empty trivial 1 -element set
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
the Relation-like Function-like ( the carrier of L,L,(L)) . (0 + 1) is set
w is non empty set
[:w,w:] is non empty Relation-like set
[:[:w,w:], the carrier of L:] is non empty Relation-like set
bool [:[:w,w:], the carrier of L:] is non empty non empty-membered set
c<sub>11</sub> is non empty set
[:c<sub>11</sub>,c<sub>11</sub>:] is non empty Relation-like set
[:[:c<sub>11</sub>,c<sub>11</sub>:], the carrier of L:] is non empty Relation-like set
bool [:[:c<sub>11</sub>,c<sub>11</sub>:], the carrier of L:] is non empty non empty-membered set
z is Relation-like [:w,w:] -defined the carrier of L -valued Function-like quasi_total (w,L) (w,L) (w,L) Element of bool [:[:w,w:], the carrier of L:]
dq9 is Relation-like [:c<sub>11</sub>,c<sub>11</sub>:] -defined the carrier of L -valued Function-like quasi_total (c<sub>11</sub>,L) (c<sub>11</sub>,L) (c<sub>11</sub>,L) Element of bool [:[:c<sub>11</sub>,c<sub>11</sub>:], the carrier of L:]
[w,z] is V18() set
{w,z} is non empty set
{w} is non empty trivial 1 -element set
{{w,z},{w}} is non empty set
[c<sub>11</sub>,dq9] is V18() set
{c<sub>11</sub>,dq9} is non empty set
{c<sub>11</sub>} is non empty trivial 1 -element set
{{c<sub>11</sub>,dq9},{c<sub>11</sub>}} 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,(L)) is non empty set
( the carrier of L,L,(L)) is epsilon-transitive epsilon-connected ordinal cardinal set
( the carrier of L,( the carrier of L,L,(L))) is non empty set
[:( the carrier of L,L,(L)),( the carrier of L,L,(L)):] is non empty Relation-like set
q is Relation-like [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:] -valued Function-like T-Sequence-like ( the carrier of L,L,(L))
( the carrier of L,L,(L),q) is Relation-like [:( the carrier of L,L,(L)),( the carrier of L,L,(L)):] -defined the carrier of L -valued Function-like quasi_total (( the carrier of L,L,(L)),L) (( the carrier of L,L,(L)),L) (( the carrier of L,L,(L)),L) Element of bool [:[:( the carrier of L,L,(L)),( the carrier of L,L,(L)):], the carrier of L:]
[:[:( the carrier of L,L,(L)),( the carrier of L,L,(L)):], the carrier of L:] is non empty Relation-like set
bool [:[:( the carrier of L,L,(L)),( the carrier of L,L,(L)):], the carrier of L:] is non empty non empty-membered set
( the carrier of L,L,(L),q,( the carrier of L,L,(L))) is Relation-like [:( the carrier of L,( the carrier of L,L,(L))),( the carrier of L,( the carrier of L,L,(L))):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:( the carrier of L,( the carrier of L,L,(L))),( the carrier of L,( the carrier of L,L,(L))):], the carrier of L:]
[:( the carrier of L,( the carrier of L,L,(L))),( the carrier of L,( the carrier of L,L,(L))):] is non empty Relation-like set
[:[:( the carrier of L,( the carrier of L,L,(L))),( the carrier of L,( the carrier of L,L,(L))):], the carrier of L:] is non empty Relation-like set
bool [:[:( the carrier of L,( the carrier of L,L,(L))),( the carrier of L,( the carrier of L,L,(L))):], the carrier of L:] is non empty non empty-membered set
( the carrier of L,{}) is non empty set
( the carrier of L,L,(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,(L)) . 1 is set
( the Relation-like Function-like ( the carrier of L,L,(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 non empty-membered set
{ [b₁,b₂,b₃,b₄] where b₁, b₂, b₃, b₄ is Element of the carrier of L : ( the carrier of L,L,(L),b₁,b₂) <= b₃ "\/" b₄ } 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 V18() V19() V20() Element of [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:]
[u,v,a] is V18() V19() set
[u,v] is V18() set
{u,v} is non empty set
{u} is non empty trivial 1 -element set
{{u,v},{u}} is non empty set
[[u,v],a] is V18() set
{[u,v],a} is non empty set
{[u,v]} is non empty trivial Relation-like Function-like constant 1 -element set
{{[u,v],a},{[u,v]}} is non empty set
[[u,v,a],b] is V18() set
{[u,v,a],b} is non empty set
{[u,v,a]} is non empty trivial 1 -element set
{{[u,v,a],b},{[u,v,a]}} is non empty set
( the carrier of L,L,(L),u,v) is Element of the carrier of L
(L) . [u,v] is set
a "\/" b is Element of the carrier of L
f . b is Element of the carrier of (FS)
e is Relation-like FS -defined FS -valued total reflexive symmetric transitive Element of bool [:FS,FS:]
[c₁₁,dq9] `2 is set
{{{ the carrier of L}}} is non empty trivial 1 -element set
{{ 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}},{{{ the carrier of L}}}} is non empty set
( the Relation-like Function-like ( the carrier of L,L,(L)) . 1) `1 is set
[c₁₁,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 1 -element set
{{( the carrier of L,{})}} is non empty trivial 1 -element set
{{{( the carrier of L,{})}}} is non empty trivial 1 -element set
{{( 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,{})}},{{{( 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 Relation-like set
( the carrier of L,L,(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 Relation-like set
bool [:[:( the carrier of L,{}),( the carrier of L,{}):], the carrier of L:] is non empty non empty-membered set
( the carrier of L,L,(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 Relation-like set
[:[:( the carrier of L,(succ {})),( the carrier of L,(succ {})):], the carrier of L:] is non empty Relation-like set
bool [:[:( the carrier of L,(succ {})),( the carrier of L,(succ {})):], the carrier of L:] is non empty non empty-membered set
(( the carrier of L,{}),L,( the carrier of L,L,(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,{}),L,(( the carrier of L,{}),L,( the carrier of L,L,(L),q,{})),( the carrier of L,L,(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 Relation-like set
[:[:(( the carrier of L,{})),(( the carrier of L,{})):], the carrier of L:] is non empty Relation-like set
bool [:[:(( the carrier of L,{})),(( the carrier of L,{})):], the carrier of L:] is non empty non empty-membered set
Q is Element of [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:]
( the carrier of L,L,(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 Relation-like set
[:[:( the carrier of L),( the carrier of L):], the carrier of L:] is non empty Relation-like set
bool [:[:( the carrier of L),( the carrier of L):], the carrier of L:] is non empty non empty-membered set
dom ( the carrier of L,L,(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 non empty-membered set
[{ the carrier of L},{{ the carrier of L}}] is V18() 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
W is Element of FS
V is Element of FS
(FS,L,FD,W,V) is Element of the carrier of L
[W,V] is V18() set
{W,V} is non empty set
{W} is non empty trivial 1 -element set
{{W,V},{W}} is non empty set
FD . [W,V] is set
( the carrier of L,L,(L),Q) . ({ the carrier of L},{{ the carrier of L}}) is set
( the carrier of L,L,(L),Q) . [{ the carrier of L},{{ the carrier of L}}] is set
Q `4_4 is Element of the carrier of L
(FS,(Image f)) is epsilon-transitive epsilon-connected ordinal natural V37() ext-real V43() V54() V55() V56() V57() V58() V59() V60() V61() V63() V74() V75() V76() cardinal Element of NAT
rng (L) is Element of bool the carrier of L
w is set
( the Relation-like Function-like ( the carrier of L,L,(L)) . 0) `2 is set
[ the carrier of L,(L)] `2 is set
z is set
(L) . z is set
FD . z is set
dom (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 non empty-membered set
rng FD is Element of bool the carrier of L
w is Relation-like FS -defined FS -valued total reflexive symmetric transitive Element of bool [:FS,FS:]
z is Relation-like FS -defined FS -valued total reflexive symmetric transitive Element of bool [:FS,FS:]
c₁₁ is set
dq9 is set
[c₁₁,dq9] is V18() set
{c₁₁,dq9} is non empty set
{c₁₁} is non empty trivial 1 -element set
{{c₁₁,dq9},{c₁₁}} is non empty set
w "\/" z is Relation-like FS -defined FS -valued total reflexive symmetric transitive Element of bool [:FS,FS:]
w is Relation-like FS -defined FS -valued total reflexive symmetric transitive Element of bool [:FS,FS:]