:: ABCMIZ_1 semantic presentation

REAL is V315() V316() V317() V321() V324() V325() V327() set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V315() V316() V317() V318() V319() V320() V321() V322() V324() Element of bool REAL
bool REAL is non empty set
omega is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V315() V316() V317() V318() V319() V320() V321() V322() V324() set
bool omega is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
1 is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real positive V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of NAT
2 is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real positive V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of NAT
[:NAT,REAL:] is Relation-like set
bool [:NAT,REAL:] is non empty set
bool (bool REAL) is non empty set
{} is non pair 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() set
the non pair 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() set is non pair 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() set
{{},1} is non empty finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
Trees is non empty constituted-Trees set
bool Trees is non empty set
FinTrees is non empty constituted-Trees constituted-FinTrees Element of bool Trees
PeanoNat is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier of PeanoNat is non empty set
FinTrees the carrier of PeanoNat is non empty functional constituted-DTrees DTree-set of the carrier of PeanoNat
TS PeanoNat is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of PeanoNat)
bool (FinTrees the carrier of PeanoNat) is non empty set
[:(TS PeanoNat),NAT:] is non empty non trivial Relation-like non finite set
bool [:(TS PeanoNat),NAT:] is non empty non trivial non finite set
[:NAT,(TS PeanoNat):] is non empty non trivial Relation-like non finite set
bool [:NAT,(TS PeanoNat):] is non empty non trivial non finite set
K635() is set
2 -tuples_on K635() is functional FinSequence-membered FinSequenceSet of K635()
K635() * is non empty functional FinSequence-membered FinSequenceSet of K635()
{ b₁ where b₁ is Relation-like NAT -defined K635() -valued Function-like finite FinSequence-like FinSubsequence-like Element of K635() * : len b₁ = 2 } is set
[:(2 -tuples_on K635()),K635():] is Relation-like set
bool [:(2 -tuples_on K635()),K635():] is non empty set
3 is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real positive V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of NAT
3 -tuples_on K635() is functional FinSequence-membered FinSequenceSet of K635()
{ b₁ where b₁ is Relation-like NAT -defined K635() -valued Function-like finite FinSequence-like FinSubsequence-like Element of K635() * : len b₁ = 3 } is set
[:(3 -tuples_on K635()),K635():] is Relation-like set
bool [:(3 -tuples_on K635()),K635():] is non empty set
K664() is Relation-like 2 -tuples_on K635() -defined K635() -valued Function-like quasi_total Element of bool [:(2 -tuples_on K635()),K635():]
COMPLEX is V315() V321() set
RAT is V315() V316() V317() V318() V321() set
INT is V315() V316() V317() V318() V319() V321() set
0 is non pair 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 V32() V33() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() V329() Element of NAT
<*> NAT is non pair empty proper Relation-like non-empty empty-yielding NAT -defined NAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() FinSequence of NAT
[:NAT,NAT:] is non empty non trivial Relation-like non finite set
union {} is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
Seg 1 is non empty trivial finite 1 -element V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b₁ & b₁ <= 1 ) } is set
{1} is non empty trivial finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
Seg 2 is non empty finite 2 -element V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b₁ & b₁ <= 2 ) } is set
{1,2} is non empty finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
Rank {} is epsilon-transitive set
K469(0) is non empty V239() set
{0} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() Element of bool NAT
C is set
T is Relation-like Function-like set
T . C is set
Union T is set
proj2 T is set
union (proj2 T) is set
proj1 T is set
T is Relation-like Function-like set
Union T is set
proj2 T is set
union (proj2 T) is set
C is set
T . C is set
C is Relation-like Function-like set
T is set
f1 is set
[T,f1] is pair non empty set
{T,f1} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T,f1},{T}} is non empty finite V38() set
f2 is set
x is set
[f2,x] is pair non empty set
{f2,x} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,x},{f2}} is non empty finite V38() set
a is set
b is set
[a,b] is pair non empty set
{a,b} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,b},{a}} is non empty finite V38() set
C is set
id C is Relation-like C -defined C -valued Function-like one-to-one total V99() V101() V102() V106() V350() Element of bool [:C,C:]
[:C,C:] is Relation-like set
bool [:C,C:] is non empty set
T is set
(id C) .: T is Element of bool C
bool C is non empty set
f1 is set
f2 is set
[f2,f1] is pair non empty set
{f2,f1} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,f1},{f2}} is non empty finite V38() set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
DTConMSA T is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod T is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union (coprod T) is non empty set
proj2 (coprod T) is non empty with_non-empty_elements set
union (proj2 (coprod T)) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) is non empty set
REL T is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(REL T) #) is non empty strict DTConstrStr
the carrier of (DTConMSA T) is non empty set
FinTrees the carrier of (DTConMSA T) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA T)
C -Terms T is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA T))
bool (FinTrees the carrier of (DTConMSA T)) is non empty set
f1 is non empty Relation-like the carrier of (DTConMSA T) -valued Function-like finite DecoratedTree-like Element of C -Terms T
f2 is set
x is set
[f2,x] is pair non empty set
{f2,x} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,x},{f2}} is non empty finite V38() set
f1 . {} is set
a is Element of the carrier of C
T . a is non empty set
b is Element of T . a
[b,a] is pair non empty Element of [:(T . a), the carrier of C:]
[:(T . a), the carrier of C:] is non empty Relation-like set
{b,a} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,a},{b}} is non empty finite V38() set
{{}} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{},(f1 . {})} is non empty finite set
a is Element of the carrier of C
T . a is non empty set
b is Element of T . a
[b,a] is pair non empty Element of [:(T . a), the carrier of C:]
[:(T . a), the carrier of C:] is non empty Relation-like set
{b,a} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,a},{b}} is non empty finite V38() set
i is set
pi1 is set
[i,pi1] is pair non empty set
{i,pi1} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,pi1},{i}} is non empty finite V38() set
[{},(f1 . {})] is pair non empty set
{{{},(f1 . {})},{{}}} is non empty finite V38() set
proj1 f1 is non empty finite V239() set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,T) is strict non empty MSAlgebra over C
the Sorts of (Free (C,T)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,T)) is non empty set
proj2 the Sorts of (Free (C,T)) is non empty set
union (proj2 the Sorts of (Free (C,T))) is set
f1 is non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,T))
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined bool NAT -valued Function-like constant total quasi_total Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
T \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
DTConMSA (T \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod (T \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union (coprod (T \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod (T \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod (T \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0})))) is non empty set
REL (T \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(REL (T \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))
C -Terms (T \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))) is non empty set
C is set
f1 is set
{f1} is non empty trivial finite 1 -element set
{f1} * is non empty functional FinSequence-membered FinSequenceSet of {f1}
T is set
card C is epsilon-transitive epsilon-connected ordinal cardinal set
card T is epsilon-transitive epsilon-connected ordinal cardinal set
f2 is Relation-like NAT -defined {f1} -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of {f1}
dom f2 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
len f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Seg (len f2) is finite len f2 -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b₁ & b₁ <= len f2 ) } is set
x is Relation-like NAT -defined {f1} -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of {f1}
dom x is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
a is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
f2 . a is set
rng f2 is trivial finite Element of bool {f1}
bool {f1} is non empty finite V38() set
x . a is set
rng x is trivial finite Element of bool {f1}
C is non empty non void V58() V259() ManySortedSign
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,T) is strict non empty MSAlgebra over C
the Sorts of (Free (C,T)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,T)) is non empty set
proj2 the Sorts of (Free (C,T)) is non empty set
union (proj2 the Sorts of (Free (C,T))) is set
f1 is Relation-like NAT -defined Union the Sorts of (Free (C,T)) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of Union the Sorts of (Free (C,T))
f2 is set
proj2 f1 is finite set
rng f1 is finite Element of bool (Union the Sorts of (Free (C,T)))
bool (Union the Sorts of (Free (C,T))) is non empty set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
the carrier' of C is non empty set
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined bool NAT -valued Function-like constant total quasi_total Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
T is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,T) is strict non empty MSAlgebra over C
the Sorts of (Free (C,T)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,T)) is non empty set
proj2 the Sorts of (Free (C,T)) is non empty set
union (proj2 the Sorts of (Free (C,T))) is set
T \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
DTConMSA (T \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod (T \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union (coprod (T \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod (T \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod (T \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0})))) is non empty set
REL (T \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(REL (T \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,T))
C -Terms (T \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))) is non empty set
a is Element of the carrier of C
(T \/ ( the carrier of C --> {0})) . a is non empty set
[:((T \/ ( the carrier of C --> {0})) . a), the carrier of C:] is non empty Relation-like set
b is Element of (T \/ ( the carrier of C --> {0})) . a
[b,a] is pair non empty Element of [:((T \/ ( the carrier of C --> {0})) . a), the carrier of C:]
{b,a} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,a},{b}} is non empty finite V38() set
root-tree [b,a] is non empty Relation-like [:((T \/ ( the carrier of C --> {0})) . a), the carrier of C:] -valued Function-like DecoratedTree-like Element of FinTrees [:((T \/ ( the carrier of C --> {0})) . a), the carrier of C:]
FinTrees [:((T \/ ( the carrier of C --> {0})) . a), the carrier of C:] is non empty functional constituted-DTrees DTree-set of [:((T \/ ( the carrier of C --> {0})) . a), the carrier of C:]
proj1 (root-tree [b,a]) is non empty finite V239() set
(root-tree [b,a]) . {} is set
rng (root-tree [b,a]) is non empty Relation-like (T \/ ( the carrier of C --> {0})) . a -defined the carrier of C -valued Element of bool [:((T \/ ( the carrier of C --> {0})) . a), the carrier of C:]
bool [:((T \/ ( the carrier of C --> {0})) . a), the carrier of C:] is non empty set
T . a is set
a is Element of the carrier' of C
Sym (a,(T \/ ( the carrier of C --> {0}))) is Element of NonTerminals (DTConMSA (T \/ ( the carrier of C --> {0})))
NonTerminals (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty Element of bool the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))
bool the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
[a, the carrier of C] is pair non empty set
{a, the carrier of C} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a, the carrier of C},{a}} is non empty finite V38() set
b is Relation-like NAT -defined FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding ArgumentSeq of Sym (a,(T \/ ( the carrier of C --> {0})))
rng b is functional finite constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))))
[a, the carrier of C] -tree b is non empty Relation-like Function-like DecoratedTree-like set
dom the Sorts of (Free (C,T)) is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
pi1 is set
the Sorts of (Free (C,T)) . pi1 is set
C -Terms (T,(T \/ ( the carrier of C --> {0}))) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA (T \/ ( the carrier of C --> {0})))
FreeMSA (T \/ ( the carrier of C --> {0})) is strict non-empty V172(C) MSAlgebra over C
FreeSort (T \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
FreeOper (T \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier' of C -defined Function-like total ManySortedFunction of the Arity of C * ((FreeSort (T \/ ( the carrier of C --> {0}))) #), the ResultSort of C * (FreeSort (T \/ ( the carrier of C --> {0})))
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
(FreeSort (T \/ ( the carrier of C --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of C * -defined Function-like total set
the Arity of C * ((FreeSort (T \/ ( the carrier of C --> {0}))) #) is Relation-like non-empty the carrier' of C -defined Function-like set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C * (FreeSort (T \/ ( the carrier of C --> {0}))) is Relation-like non-empty the carrier' of C -defined Function-like set
MSAlgebra(# (FreeSort (T \/ ( the carrier of C --> {0}))),(FreeOper (T \/ ( the carrier of C --> {0}))) #) is strict MSAlgebra over C
the Sorts of (FreeMSA (T \/ ( the carrier of C --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
(Sym (a,(T \/ ( the carrier of C --> {0})))) -tree b is non empty Relation-like the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (T \/ ( the carrier of C --> {0}))
the_sort_of ((Sym (a,(T \/ ( the carrier of C --> {0})))) -tree b) is Element of the carrier of C
the_result_sort_of a is Element of the carrier of C
the ResultSort of C . a is Element of the carrier of C
z is Element of the carrier of C
Union (C -Terms (T,(T \/ ( the carrier of C --> {0})))) is set
proj2 (C -Terms (T,(T \/ ( the carrier of C --> {0})))) is non empty set
union (proj2 (C -Terms (T,(T \/ ( the carrier of C --> {0}))))) is set
the_arity_of a is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the Arity of C . a is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of a) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
len b is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
x is non empty Relation-like the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (T \/ ( the carrier of C --> {0}))
b is set
a is Element of the carrier of C
[b,a] is pair non empty set
{b,a} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,a},{b}} is non empty finite V38() set
root-tree [b,a] is non empty Relation-like Function-like DecoratedTree-like set
T . a is set
i is Element of the carrier' of C
[i, the carrier of C] is pair non empty set
{i, the carrier of C} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i, the carrier of C},{i}} is non empty finite V38() set
pi1 is Relation-like NAT -defined Union the Sorts of (Free (C,T)) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of Union the Sorts of (Free (C,T))
[i, the carrier of C] -tree pi1 is non empty Relation-like Function-like DecoratedTree-like set
len pi1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
the_arity_of i is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of i) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Sym (i,(T \/ ( the carrier of C --> {0}))) is Element of NonTerminals (DTConMSA (T \/ ( the carrier of C --> {0})))
NonTerminals (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty Element of bool the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))
bool the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
C is set
T is set
f1 is set
the_rank_of C is epsilon-transitive epsilon-connected ordinal set
Rank (the_rank_of C) is epsilon-transitive set
bool (Rank (the_rank_of C)) is non empty set
{ b₁ where b₁ is Element of bool (Rank (the_rank_of C)) : ( C c= b₁ & ( for b₂, b₃ being set holds
( not [b₂,b₃] in b₁ or b₂ c= b₁ ) ) ) } is set
meet { b₁ where b₁ is Element of bool (Rank (the_rank_of C)) : ( C c= b₁ & ( for b₂, b₃ being set holds
( not [b₂,b₃] in b₁ or b₂ c= b₁ ) ) ) } is set
f1 is set
f2 is set
x is set
[f2,x] is pair non empty set
{f2,x} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,x},{f2}} is non empty finite V38() set
f2 is set
x is set
a is Element of bool (Rank (the_rank_of C))
f2 is set
x is set
[f2,x] is pair non empty set
{f2,x} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,x},{f2}} is non empty finite V38() set
a is set
b is set
i is Element of bool (Rank (the_rank_of C))
f2 is set
f2 /\ (Rank (the_rank_of C)) is set
a is Element of bool (Rank (the_rank_of C))
b is set
i is set
[b,i] is pair non empty set
{b,i} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,i},{b}} is non empty finite V38() set
f1 is set
T is set
f2 is set
x is set
[f2,x] is pair non empty set
{f2,x} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,x},{f2}} is non empty finite V38() set
a is set
({}) is set
C is set
T is set
[C,T] is pair non empty set
{C,T} is non empty finite set
{C} is non empty trivial finite 1 -element set
{{C,T},{C}} is non empty finite V38() set
C is set
C is set
T is set
(C) is set
(T) is set
f1 is set
f2 is set
[f1,f2] is pair non empty set
{f1,f2} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f2},{f1}} is non empty finite V38() set
C is set
union C is set
((union C)) is set
{ (b₁) where b₁ is Element of C : verum } is set
union { (b₁) where b₁ is Element of C : verum } is set
f1 is set
f2 is set
x is Element of C
(x) is set
f1 is set
f2 is set
[f1,f2] is pair non empty set
{f1,f2} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f2},{f1}} is non empty finite V38() set
x is set
a is Element of C
(a) is set
f1 is set
f2 is set
x is Element of C
(x) is set
F₁() is set
{ F₂(b₁) where b₁ is Element of F₁() : P₁[b₁] } is set
union { F₂(b₁) where b₁ is Element of F₁() : P₁[b₁] } is set
((union { F₂(b₁) where b₁ is Element of F₁() : P₁[b₁] } )) is set
{ (F₂(b₁)) where b₁ is Element of F₁() : P₁[b₁] } is set
union { (F₂(b₁)) where b₁ is Element of F₁() : P₁[b₁] } is set
f1 is set
f2 is set
(f2) is set
x is Element of F₁()
F₂(x) is set
f1 is set
f2 is set
[f1,f2] is pair non empty set
{f1,f2} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f2},{f1}} is non empty finite V38() set
x is set
a is Element of F₁()
F₂(a) is set
(F₂(a)) is set
f1 is set
f2 is set
x is Element of F₁()
F₂(x) is set
(F₂(x)) is set
C is set
(C) is set
T is set
C \/ T is set
((C \/ T)) is set
(T) is set
(C) \/ (T) is set
{C,T} is non empty finite set
{ (b₁) where b₁ is Element of {C,T} : verum } is set
union {C,T} is set
union { (b₁) where b₁ is Element of {C,T} : verum } is set
{(C),(T)} is non empty finite set
f2 is set
x is Element of {C,T}
(x) is set
f2 is set
C is non empty set
meet C is set
((meet C)) is set
f1 is set
f2 is set
[f1,f2] is pair non empty set
{f1,f2} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f2},{f1}} is non empty finite V38() set
x is set
(x) is set
C is set
(C) is set
T is set
(T) is set
(C) /\ (T) is set
(((C) /\ (T))) is set
f2 is set
x is set
[f2,x] is pair non empty set
{f2,x} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,x},{f2}} is non empty finite V38() set
C is non pair 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() set
(C) is set
{ [(b₁),b₂] where b₁ is Element of bool a₂, b₂ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : b₁ is finite } is set
{ [{},b₁] where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : verum } is set
C is Relation-like Function-like set
proj1 C is set
C . 0 is set
T is non empty Relation-like NAT -defined Function-like total set
Union T is set
proj2 T is non empty set
union (proj2 T) is set
f1 is non empty Relation-like NAT -defined Function-like total set
Union f1 is set
proj2 f1 is non empty set
union (proj2 f1) is set
f1 . 0 is set
f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
f2 + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 . (f2 + 1) is set
f1 . f2 is set
bool (f1 . f2) is non empty set
{ [(b₁),b₂] where b₁ is Element of bool (f1 . f2), b₂ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : b₁ is finite } is set
C is set
T is set
f1 is non empty Relation-like NAT -defined Function-like total set
Union f1 is set
proj2 f1 is non empty set
union (proj2 f1) is set
f1 . 0 is set
f2 is non empty Relation-like NAT -defined Function-like total set
Union f2 is set
proj2 f2 is non empty set
union (proj2 f2) is set
f2 . 0 is set
dom f1 is non empty V315() V316() V317() V318() V319() V320() V322() V324() Element of bool NAT
dom f2 is non empty V315() V316() V317() V318() V319() V320() V322() V324() Element of bool NAT
() is set
C is non empty Relation-like NAT -defined Function-like total set
C . 0 is set
T is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . T is set
T + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . (T + 1) is set
bool (C . T) is non empty set
{ [(b₁),b₂] where b₁ is Element of bool (C . T), b₂ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : b₁ is finite } is set
f1 is set
f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[{},f2] is pair non empty set
{{},f2} is non empty finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{}} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{{},f2},{{}}} is non empty finite V38() set
T is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
C . T is set
T is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . T is set
T + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . (T + 1) is set
f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
f1 + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
f1 + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . f2 is set
bool (C . f2) is non empty set
{ [(b₁),b₂] where b₁ is Element of bool (C . f2), b₂ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : b₁ is finite } is set
bool (C . T) is non empty set
{ [(b₁),b₂] where b₁ is Element of bool (C . T), b₂ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : b₁ is finite } is set
x is set
a is Element of bool (C . f2)
(a) is set
b is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[(a),b] is pair non empty set
{(a),b} is non empty finite set
{(a)} is non empty trivial finite 1 -element set
{{(a),b},{(a)}} is non empty finite V38() set
f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
C . f1 is set
T is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . T is set
C . f1 is set
bool () is non empty set
C is non empty Relation-like NAT -defined Function-like total set
C . 0 is set
T is finite Element of bool ()
Union C is set
proj2 C is non empty set
union (proj2 C) is set
f1 is set
f2 is set
dom C is non empty V315() V316() V317() V318() V319() V320() V322() V324() Element of bool NAT
x is set
C . x is set
a is set
C . a is set
f1 is Relation-like Function-like set
proj1 f1 is set
proj2 f1 is set
f2 is non empty finite V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() Element of bool NAT
sup f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V328() V329() set
x is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . x is set
a is set
f1 . a is set
b is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . b is set
C is non empty Relation-like NAT -defined Function-like total set
Union C is set
proj2 C is non empty set
union (proj2 C) is set
C . 0 is set
dom C is non empty V315() V316() V317() V318() V319() V320() V322() V324() Element of bool NAT
C is finite Element of bool ()
(C) is set
T is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
[(C),T] is pair non empty set
{(C),T} is non empty finite set
{(C)} is non empty trivial finite 1 -element set
{{(C),T},{(C)}} is non empty finite V38() set
f1 is non empty Relation-like NAT -defined Function-like total set
Union f1 is set
proj2 f1 is non empty set
union (proj2 f1) is set
f1 . 0 is set
f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 . f2 is set
f2 + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 . (f2 + 1) is set
bool (f1 . f2) is non empty set
{ [(b₁),b₂] where b₁ is Element of bool (f1 . f2), b₂ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : b₁ is finite } is set
dom f1 is non empty V315() V316() V317() V318() V319() V320() V322() V324() Element of bool NAT
{ [(b₁),b₂] where b₁ is Element of bool (), b₂ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : b₁ is finite } is set
C is non empty Relation-like NAT -defined Function-like total set
Union C is set
proj2 C is non empty set
union (proj2 C) is set
C . 0 is set
dom C is non empty V315() V316() V317() V318() V319() V320() V322() V324() Element of bool NAT
f1 is set
f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[{},f2] is pair non empty set
{{},f2} is non empty finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{}} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{{},f2},{{}}} is non empty finite V38() set
f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . f1 is set
f1 + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . (f1 + 1) is set
bool (C . f1) is non empty set
{ [(b₁),b₂] where b₁ is Element of bool (C . f1), b₂ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : b₁ is finite } is set
f2 is set
x is Element of bool (C . f1)
(x) is set
a is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[(x),a] is pair non empty set
{(x),a} is non empty finite set
{(x)} is non empty trivial finite 1 -element set
{{(x),a},{(x)}} is non empty finite V38() set
f1 is set
f2 is set
C . f2 is set
f1 is set
f2 is Element of bool ()
(f2) is set
x is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[(f2),x] is pair non empty set
{(f2),x} is non empty finite set
{(f2)} is non empty trivial finite 1 -element set
{{(f2),x},{(f2)}} is non empty finite V38() set
(()) is set
C is non empty Relation-like NAT -defined Function-like total set
Union C is set
proj2 C is non empty set
union (proj2 C) is set
C . 0 is set
T is set
f1 is set
[T,f1] is pair non empty set
{T,f1} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T,f1},{T}} is non empty finite V38() set
f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[{},f2] is pair non empty set
{{},f2} is non empty finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{}} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{{},f2},{{}}} is non empty finite V38() set
((C . 0)) is set
T is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
C . T is set
((C . T)) is set
T + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . (T + 1) is set
bool (C . T) is non empty set
{ [(b₁),b₂] where b₁ is Element of bool (C . T), b₂ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : b₁ is finite } is set
f2 is set
x is set
[f2,x] is pair non empty set
{f2,x} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,x},{f2}} is non empty finite V38() set
a is Element of bool (C . T)
(a) is set
b is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[(a),b] is pair non empty set
{(a),b} is non empty finite set
{(a)} is non empty trivial finite 1 -element set
{{(a),b},{(a)}} is non empty finite V38() set
f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . f1 is set
f1 + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . (f1 + 1) is set
((C . (T + 1))) is set
{ (b₁) where b₁ is Element of proj2 C : verum } is set
union { (b₁) where b₁ is Element of proj2 C : verum } is set
T is set
f1 is set
f2 is Element of proj2 C
(f2) is set
dom C is non empty V315() V316() V317() V318() V319() V320() V322() V324() Element of bool NAT
x is set
C . x is set
a is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . a is set
((C . a)) is set
C is set
the_rank_of C is epsilon-transitive epsilon-connected ordinal set
Rank (the_rank_of C) is epsilon-transitive set
C is set
(C) is set
the_rank_of (C) is epsilon-transitive epsilon-connected ordinal set
the_rank_of C is epsilon-transitive epsilon-connected ordinal set
Rank (the_rank_of C) is epsilon-transitive set
succ (the_rank_of C) is non empty epsilon-transitive epsilon-connected ordinal set
succ (succ (the_rank_of C)) is non empty epsilon-transitive epsilon-connected ordinal set
Rank (succ (succ (the_rank_of C))) is epsilon-transitive set
f1 is set
f2 is set
[f1,f2] is pair non empty set
{f1,f2} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f2},{f1}} is non empty finite V38() set
Rank omega is epsilon-transitive set
bool (Rank omega) is non empty set
C is finite Element of bool (Rank omega)
T is Relation-like Function-like set
proj1 T is set
proj2 T is set
f1 is set
f2 is set
T . f2 is set
the_rank_of f2 is epsilon-transitive epsilon-connected ordinal set
the_rank_of C is epsilon-transitive epsilon-connected ordinal set
f1 is non empty finite V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() Element of bool NAT
sup f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V328() V329() set
f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
1 + f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Rank (1 + f2) is epsilon-transitive set
a is set
T . a is set
the_rank_of a is epsilon-transitive epsilon-connected ordinal set
b is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
succ f2 is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of omega
the_rank_of C is epsilon-transitive epsilon-connected ordinal set
succ (1 + f2) is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of omega
(1 + f2) + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C is non empty Relation-like NAT -defined Function-like total set
Union C is set
proj2 C is non empty set
union (proj2 C) is set
C . 0 is set
T is set
dom C is non empty V315() V316() V317() V318() V319() V320() V322() V324() Element of bool NAT
f1 is set
C . f1 is set
x is set
a is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[{},a] is pair non empty set
{{},a} is non empty finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{}} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{{},a},{{}}} is non empty finite V38() set
a + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
succ a is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of omega
the_rank_of {} is epsilon-transitive epsilon-connected ordinal set
the_rank_of a is epsilon-transitive epsilon-connected ordinal set
Rank (a + 1) is epsilon-transitive set
succ (a + 1) is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of omega
succ (succ (a + 1)) is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of omega
Rank (succ (succ (a + 1))) is epsilon-transitive set
x is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . x is set
x + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . (x + 1) is set
bool (C . x) is non empty set
{ [(b₁),b₂] where b₁ is Element of bool (C . x), b₂ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : b₁ is finite } is set
a is set
b is Element of bool (C . x)
(b) is set
i is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[(b),i] is pair non empty set
{(b),i} is non empty finite set
{(b)} is non empty trivial finite 1 -element set
{{(b),i},{(b)}} is non empty finite V38() set
the_rank_of b is epsilon-transitive epsilon-connected ordinal set
pi1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
i \/ pi1 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() set
the_rank_of (b) is epsilon-transitive epsilon-connected ordinal set
the_rank_of i is epsilon-transitive epsilon-connected ordinal set
z is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
succ z is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of omega
z + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Rank (z + 1) is epsilon-transitive set
succ (z + 1) is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of omega
succ (succ (z + 1)) is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of omega
Rank (succ (succ (z + 1))) is epsilon-transitive set
f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . f2 is set
C is finite Element of bool ()
(C) is set
the_rank_of C is epsilon-transitive epsilon-connected ordinal set
the_rank_of (C) is epsilon-transitive epsilon-connected ordinal set
[{},0] is pair non empty set
{{},0} is non empty functional finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{}} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{{},0},{{}}} is non empty finite V38() set
C is Element of ()
C `1 is set
T is Element of bool ()
(T) is set
f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[(T),f1] is pair non empty set
{(T),f1} is non empty finite set
{(T)} is non empty trivial finite 1 -element set
{{(T),f1},{(T)}} is non empty finite V38() set
C is Element of ()
C `1 is finite set
T is Element of bool ()
(T) is set
f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[(T),f1] is pair non empty set
{(T),f1} is non empty finite set
{(T)} is non empty trivial finite 1 -element set
{{(T),f1},{(T)}} is non empty finite V38() set
C is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
[{},C] is pair non empty set
{{},C} is non empty finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{}} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{{},C},{{}}} is non empty finite V38() set
C is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
T is Element of bool ()
(T) is set
[(T),C] is pair non empty set
{(T),C} is non empty finite set
{(T)} is non empty trivial finite 1 -element set
{{(T),C},{(T)}} is non empty finite V38() set
{[(T),C]} is non empty trivial Relation-like Function-like constant finite 1 -element set
({[(T),C]}) is set
(T) \/ {[(T),C]} is non empty set
f1 is set
f2 is set
[f1,f2] is pair non empty set
{f1,f2} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,f2},{f1}} is non empty finite V38() set
C is Element of ()
{C} is non empty trivial finite 1 -element Element of bool ()
({C}) is set
(C) is finite Element of bool ()
(C) \/ {C} is non empty finite Element of bool ()
T is Element of bool ()
(T) is set
f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[(T),f1] is pair non empty set
{(T),f1} is non empty finite set
{(T)} is non empty trivial finite 1 -element set
{{(T),f1},{(T)}} is non empty finite V38() set
(T) \/ {C} is non empty set
C is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
T is Element of ()
(T) is finite Element of bool ()
{T} is non empty trivial finite 1 -element Element of bool ()
(T) \/ {T} is non empty finite Element of bool ()
[((T) \/ {T}),C] is pair non empty set
{((T) \/ {T}),C} is non empty finite V38() set
{((T) \/ {T})} is non empty trivial finite V38() 1 -element set
{{((T) \/ {T}),C},{((T) \/ {T})}} is non empty finite V38() set
f1 is Element of bool ()
(f1) is set
f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[(f1),f2] is pair non empty set
{(f1),f2} is non empty finite set
{(f1)} is non empty trivial finite 1 -element set
{{(f1),f2},{(f1)}} is non empty finite V38() set
({T}) is set
(f1) \/ {T} is non empty set
() * is non empty functional FinSequence-membered FinSequenceSet of ()
C is set
T is set
T is functional FinSequence-membered FinSequenceSet of ()
f1 is Relation-like NAT -defined () -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of ()
dom f1 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
f2 is Relation-like Function-like set
proj1 f2 is set
f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
f1 . f2 is set
(f1 . f2) `1 is set
f1 | f2 is Relation-like NAT -defined f2 -defined NAT -defined () -valued Function-like finite FinSubsequence-like set
rng (f1 | f2) is finite Element of bool ()
x is Relation-like Function-like set
proj1 x is set
C is functional FinSequence-membered FinSequenceSet of ()
T is functional FinSequence-membered FinSequenceSet of ()
f1 is set
f2 is Relation-like NAT -defined () -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of ()
dom f2 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
x is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
f2 . x is set
(f2 . x) `1 is set
f2 | x is Relation-like NAT -defined x -defined NAT -defined () -valued Function-like finite FinSubsequence-like Element of bool [:NAT,():]
[:NAT,():] is non empty non trivial Relation-like non finite set
bool [:NAT,():] is non empty non trivial non finite set
rng (f2 | x) is finite Element of bool ()
f1 is set
f2 is Relation-like NAT -defined () -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of ()
dom f2 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
x is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
f2 . x is set
(f2 . x) `1 is set
f2 | x is Relation-like NAT -defined x -defined NAT -defined () -valued Function-like finite FinSubsequence-like Element of bool [:NAT,():]
[:NAT,():] is non empty non trivial Relation-like non finite set
bool [:NAT,():] is non empty non trivial non finite set
rng (f2 | x) is finite Element of bool ()
() is functional FinSequence-membered FinSequenceSet of ()
<*> () is non pair empty Relation-like non-empty empty-yielding NAT -defined () -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of () *
() * is non empty functional FinSequence-membered FinSequenceSet of ()
C is Relation-like NAT -defined () -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of ()
dom C is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
T is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
C . T is set
(C . T) `1 is set
C | T is Relation-like NAT -defined T -defined NAT -defined () -valued Function-like finite FinSubsequence-like set
rng (C | T) is finite Element of bool ()
C is Relation-like NAT -defined () -valued Function-like finite FinSequence-like FinSubsequence-like Element of ()
C is Relation-like NAT -defined () -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like FinSequence of ()
dom C is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
T is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
f1 is Element of ()
C . T is set
f2 is Element of ()
(f1) is finite Element of bool ()
C | T is Relation-like NAT -defined T -defined NAT -defined () -valued Function-like finite FinSubsequence-like Element of bool [:NAT,():]
[:NAT,():] is non empty non trivial Relation-like non finite set
bool [:NAT,():] is non empty non trivial non finite set
rng (C | T) is finite Element of bool ()
C | T is Relation-like NAT -defined T -defined NAT -defined () -valued Function-like finite FinSubsequence-like set
dom (C | T) is finite Element of bool T
bool T is non empty finite V38() set
x is set
(C | T) . x is set
(dom C) /\ T is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
a is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
b is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
card a is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of omega
card T is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of omega
i is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
C . i is set
T is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
C . T is set
rng C is finite Element of bool ()
(C . T) `1 is set
C | T is Relation-like NAT -defined T -defined NAT -defined () -valued Function-like finite FinSubsequence-like set
rng (C | T) is finite Element of bool ()
f2 is set
f1 is Element of ()
(f1) is finite Element of bool ()
x is Element of ()
a is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
C . a is set
card T is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of omega
card a is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of omega
C is Relation-like NAT -defined () -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of ()
rng C is finite Element of bool ()
T is Element of ()
<*T*> is non empty trivial Relation-like NAT -defined () -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Element of () *
[1,T] is pair non empty set
{1,T} is non empty finite set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
C ^ <*T*> is non empty Relation-like NAT -defined () -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of ()
(T) is finite Element of bool ()
len C is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
1 + (len C) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C ^ <*T*>) . (1 + (len C)) is set
dom (C ^ <*T*>) is non empty finite V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() Element of bool NAT
len <*T*> is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of NAT
(len C) + (len <*T*>) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Seg ((len C) + (len <*T*>)) is finite (len C) + (len <*T*>) -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b<sub>1</sub> where b<sub>1</sub> is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> <= (len C) + (len <*T*>) ) } is set
(len C) + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Seg ((len C) + 1) is finite (len C) + 1 -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b<sub>1</sub> where b<sub>1</sub> is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> <= (len C) + 1 ) } is set
dom C is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
Seg (len C) is finite len C -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b<sub>1</sub> where b<sub>1</sub> is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> <= len C ) } is set
f1 is set
C . f1 is set
f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C ^ <*T*>) . f2 is set
f1 is set
f2 is Element of ()
x is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
(C ^ <*T*>) . x is set
a is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . a is set
f1 is set
proj1 (C ^ <*T*>) is non empty finite set
f2 is set
(C ^ <*T*>) . f1 is set
(C ^ <*T*>) . f2 is set
x is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
a is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C . x is set
(C ^ <*T*>) . x is set
C . a is set
(C ^ <*T*>) . a is set
f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
f2 is Element of ()
(C ^ <*T*>) . f1 is set
x is Element of ()
(f2) is finite Element of bool ()
a is set
C . a is set
b is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C ^ <*T*>) . b is set
C . f1 is set
a is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
C . a is set
(C ^ <*T*>) . a is set
C . f1 is set
C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
C ^ T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
dom C is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
f2 is Element of ()
C . f1 is set
x is Element of ()
(f2) is finite Element of bool ()
dom (C ^ T) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
(C ^ T) . f1 is set
a is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
(C ^ T) . a is set
len C is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Seg (len C) is finite len C -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b<sub>1</sub> where b<sub>1</sub> is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> <= len C ) } is set
len (C ^ T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Seg (len (C ^ T)) is finite len (C ^ T) -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b<sub>1</sub> where b<sub>1</sub> is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> <= len (C ^ T) ) } is set
b is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
C . b is set
C is Relation-like NAT -defined () -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of ()
rng C is finite Element of bool ()
((rng C)) is set
T is set
f1 is set
[T,f1] is pair non empty set
{T,f1} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T,f1},{T}} is non empty finite V38() set
dom C is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
f2 is Element of ()
x is set
C . x is set
(f2) is finite Element of bool ()
b is set
a is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
i is Element of ()
pi1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
C . pi1 is set
C is Element of ()
<*C*> is non empty trivial Relation-like NAT -defined () -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Element of () *
[1,C] is pair non empty set
{1,C} is non empty finite set
{{1,C},{1}} is non empty finite V38() set
{[1,C]} is non empty trivial Relation-like Function-like constant finite 1 -element set
(C) is finite Element of bool ()
(<*> ()) ^ <*C*> is non empty Relation-like NAT -defined () -valued Function-like finite {} + 1 -element FinSequence-like FinSubsequence-like Element of () *
{} + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
proj2 {} is non pair empty trivial 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered with_non-empty_elements V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() set
C is Element of ()
T is Element of ()
<*C,T*> is non empty Relation-like NAT -defined () -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like Element of () *
<*C*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,C] is pair non empty set
{1,C} is non empty finite set
{{1,C},{1}} is non empty finite V38() set
{[1,C]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*T*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,T] is pair non empty set
{1,T} is non empty finite set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*C*> ^ <*T*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
1 + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C) is finite Element of bool ()
(T) is finite Element of bool ()
{C} is non empty trivial finite 1 -element Element of bool ()
<*C*> is non empty trivial Relation-like NAT -defined () -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Element of () *
rng <*C*> is non empty trivial finite 1 -element Element of bool ()
C is Element of ()
T is Element of ()
f1 is Element of ()
<*C,T,f1*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
<*C*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,C] is pair non empty set
{1,C} is non empty finite set
{{1,C},{1}} is non empty finite V38() set
{[1,C]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*T*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,T] is pair non empty set
{1,T} is non empty finite set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*C*> ^ <*T*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
1 + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
<*f1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,f1] is pair non empty set
{1,f1} is non empty finite set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
(<*C*> ^ <*T*>) ^ <*f1*> is non empty Relation-like NAT -defined Function-like finite (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
(1 + 1) + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C) is finite Element of bool ()
(T) is finite Element of bool ()
{C} is non empty trivial finite 1 -element Element of bool ()
(f1) is finite Element of bool ()
{C,T} is non empty finite Element of bool ()
<*C,T*> is non empty Relation-like NAT -defined () -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like Element of () *
rng <*C,T*> is non empty finite Element of bool ()
C is Relation-like NAT -defined () -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of ()
C " is Relation-like Function-like one-to-one set
[:(),NAT:] is non empty non trivial Relation-like non finite set
bool [:(),NAT:] is non empty non trivial non finite set
proj1 (C ") is set
rng C is finite Element of bool ()
proj2 (C ") is set
dom C is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
() is set
() is set
() is set
() is set
() is set
{(),(),()} is non empty finite set
{(),()} is non empty finite set
<*(),()*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like set
<*()*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,()] is pair non empty set
{1,()} is non empty finite set
{{1,()},{1}} is non empty finite V38() set
{[1,()]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*()*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,()] is pair non empty set
{1,()} is non empty finite set
{{1,()},{1}} is non empty finite V38() set
{[1,()]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*()*> ^ <*()*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
1 + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
{()} is non empty trivial finite 1 -element set
{()} * is non empty functional FinSequence-membered FinSequenceSet of {()}
C is V259() ManySortedSign
the carrier of C is set
the carrier' of C is set
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
[: the carrier' of C,( the carrier of C *):] is Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . () is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the Arity of C . () is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . () is set
the ResultSort of C . () is set
{(),(),()} * is non empty functional FinSequence-membered FinSequenceSet of {(),(),()}
f1 is Element of {(),(),()}
<*f1*> is non empty trivial Relation-like NAT -defined {(),(),()} -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Element of {(),(),()} *
[1,f1] is pair non empty set
{1,f1} is non empty finite set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
T is Element of {(),(),()}
<*f1,T*> is non empty Relation-like NAT -defined {(),(),()} -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like Element of {(),(),()} *
<*f1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
<*T*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,T] is pair non empty set
{1,T} is non empty finite set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f1*> ^ <*T*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
f2 is Relation-like NAT -defined {(),(),()} -valued Function-like finite FinSequence-like FinSubsequence-like Element of {(),(),()} *
((),()) --> (<*f1,T*>,f2) is Relation-like {(),()} -defined {(),(),()} * -valued Function-like quasi_total finite Function-yielding V115() Element of bool [:{(),()},({(),(),()} *):]
[:{(),()},({(),(),()} *):] is non empty Relation-like set
bool [:{(),()},({(),(),()} *):] is non empty set
((),()) --> (T,f1) is Relation-like {(),()} -defined {(),(),()} -valued Function-like quasi_total finite Element of bool [:{(),()},{(),(),()}:]
[:{(),()},{(),(),()}:] is non empty Relation-like finite set
bool [:{(),()},{(),(),()}:] is non empty finite V38() set
ManySortedSign(# {(),(),()},{(),()},(((),()) --> (<*f1,T*>,f2)),(((),()) --> (T,f1)) #) is non empty V58() strict V259() ManySortedSign
a is non empty non void V58() strict V259() ManySortedSign
the carrier' of a is non empty set
the carrier of a is non empty set
the Arity of a is Relation-like the carrier' of a -defined the carrier of a * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of a,( the carrier of a *):]
the carrier of a * is non empty functional FinSequence-membered FinSequenceSet of the carrier of a
[: the carrier' of a,( the carrier of a *):] is non empty Relation-like set
bool [: the carrier' of a,( the carrier of a *):] is non empty set
the Arity of a . () is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the Arity of a . () is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the ResultSort of a is Relation-like the carrier' of a -defined the carrier of a -valued Function-like quasi_total Element of bool [: the carrier' of a, the carrier of a:]
[: the carrier' of a, the carrier of a:] is non empty Relation-like set
bool [: the carrier' of a, the carrier of a:] is non empty set
the ResultSort of a . () is set
the ResultSort of a . () is set
b is Element of the carrier' of a
the Arity of a . b is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
C is strict V259() ManySortedSign
the carrier' of C is set
T is strict V259() ManySortedSign
the carrier' of T is set
the carrier of C is set
the carrier of T is set
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
[: the carrier' of C,( the carrier of C *):] is Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . () is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the Arity of T is Relation-like the carrier' of T -defined the carrier of T * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of T,( the carrier of T *):]
the carrier of T * is non empty functional FinSequence-membered FinSequenceSet of the carrier of T
[: the carrier' of T,( the carrier of T *):] is Relation-like set
bool [: the carrier' of T,( the carrier of T *):] is non empty set
the Arity of T . () is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the Arity of C . () is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the Arity of T . () is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . () is set
the ResultSort of T is Relation-like the carrier' of T -defined the carrier of T -valued Function-like quasi_total Element of bool [: the carrier' of T, the carrier of T:]
[: the carrier' of T, the carrier of T:] is Relation-like set
bool [: the carrier' of T, the carrier of T:] is non empty set
the ResultSort of T . () is set
the ResultSort of C . () is set
the ResultSort of T . () is set
dom the Arity of C is Element of bool the carrier' of C
bool the carrier' of C is non empty set
dom the Arity of T is Element of bool the carrier' of T
bool the carrier' of T is non empty set
((),()) --> (<*(),()*>,<*()*>) is finite set
dom the ResultSort of C is Element of bool the carrier' of C
dom the ResultSort of T is Element of bool the carrier' of T
((),()) --> ((),()) is finite set
() is strict V259() ManySortedSign
C is non empty non void V58() V259() () ManySortedSign
the carrier' of C is non empty set
C is non empty non void V58() V259() () ManySortedSign
the carrier' of C is non empty set
T is Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C is non empty set
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(len (the_arity_of T)) |-> () is Relation-like NAT -defined Function-like finite len (the_arity_of T) -element FinSequence-like FinSubsequence-like set
Seg (len (the_arity_of T)) is finite len (the_arity_of T) -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b<sub>1</sub> where b<sub>1</sub> is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> <= len (the_arity_of T) ) } is set
(Seg (len (the_arity_of T))) --> () is Relation-like Seg (len (the_arity_of T)) -defined Seg (len (the_arity_of T)) -defined {()} -valued Function-like constant total total quasi_total finite FinSequence-like FinSubsequence-like Element of bool [:(Seg (len (the_arity_of T))),{()}:]
[:(Seg (len (the_arity_of T))),{()}:] is Relation-like finite set
bool [:(Seg (len (the_arity_of T))),{()}:] is non empty finite V38() set
len ((len (the_arity_of T)) |-> ()) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is Element of {()}
(len (the_arity_of T)) |-> f1 is Relation-like NAT -defined {()} -valued Function-like finite len (the_arity_of T) -element FinSequence-like FinSubsequence-like Element of (len (the_arity_of T)) -tuples_on {()}
(len (the_arity_of T)) -tuples_on {()} is non empty functional FinSequence-membered FinSequenceSet of {()}
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like NAT -defined {()} -valued Function-like finite FinSequence-like FinSubsequence-like Element of {()} * : len b<sub>1</sub> = len (the_arity_of T) } is set
(Seg (len (the_arity_of T))) --> f1 is Relation-like Seg (len (the_arity_of T)) -defined Seg (len (the_arity_of T)) -defined {()} -valued {f1} -valued Function-like constant total total quasi_total finite FinSequence-like FinSubsequence-like Element of bool [:(Seg (len (the_arity_of T))),{f1}:]
{f1} is non empty trivial finite 1 -element set
[:(Seg (len (the_arity_of T))),{f1}:] is Relation-like finite set
bool [:(Seg (len (the_arity_of T))),{f1}:] is non empty finite V38() set
C is non empty non void V58() V259() () ManySortedSign
the carrier of C is non empty set
the carrier' of C is non empty set
C is non empty non void V58() V259() () ManySortedSign
(C) is Element of the carrier' of C
the carrier' of C is non empty set
the_arity_of (C) is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C is non empty set
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . (C) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
(C) is Element of the carrier of C
<*(C)*> is non empty trivial Relation-like NAT -defined the carrier of C -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Element of the carrier of C *
[1,(C)] is pair non empty set
{1,(C)} is non empty finite set
{{1,(C)},{1}} is non empty finite V38() set
{[1,(C)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
T is non empty non void V58() V259() () ManySortedSign
(T) is Element of the carrier' of T
the carrier' of T is non empty set
the_result_sort_of (T) is Element of the carrier of T
the carrier of T is non empty set
the ResultSort of T is Relation-like the carrier' of T -defined the carrier of T -valued Function-like quasi_total Element of bool [: the carrier' of T, the carrier of T:]
[: the carrier' of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier' of T, the carrier of T:] is non empty set
the ResultSort of T . (T) is Element of the carrier of T
(T) is Element of the carrier of T
f1 is non empty non void V58() V259() () ManySortedSign
(f1) is Element of the carrier' of f1
the carrier' of f1 is non empty set
the_arity_of (f1) is Relation-like NAT -defined the carrier of f1 -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of f1 *
the carrier of f1 is non empty set
the carrier of f1 * is non empty functional FinSequence-membered FinSequenceSet of the carrier of f1
the Arity of f1 is Relation-like the carrier' of f1 -defined the carrier of f1 * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of f1,( the carrier of f1 *):]
[: the carrier' of f1,( the carrier of f1 *):] is non empty Relation-like set
bool [: the carrier' of f1,( the carrier of f1 *):] is non empty set
the Arity of f1 . (f1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of f1 *
(f1) is Element of the carrier of f1
(f1) is Element of the carrier of f1
<*(f1),(f1)*> is non empty Relation-like NAT -defined the carrier of f1 -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like Element of the carrier of f1 *
<*(f1)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(f1)] is pair non empty set
{1,(f1)} is non empty finite set
{{1,(f1)},{1}} is non empty finite V38() set
{[1,(f1)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(f1)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(f1)] is pair non empty set
{1,(f1)} is non empty finite set
{{1,(f1)},{1}} is non empty finite V38() set
{[1,(f1)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(f1)*> ^ <*(f1)*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
f2 is non empty non void V58() V259() () ManySortedSign
(f2) is Element of the carrier' of f2
the carrier' of f2 is non empty set
the_result_sort_of (f2) is Element of the carrier of f2
the carrier of f2 is non empty set
the ResultSort of f2 is Relation-like the carrier' of f2 -defined the carrier of f2 -valued Function-like quasi_total Element of bool [: the carrier' of f2, the carrier of f2:]
[: the carrier' of f2, the carrier of f2:] is non empty Relation-like set
bool [: the carrier' of f2, the carrier of f2:] is non empty set
the ResultSort of f2 . (f2) is Element of the carrier of f2
(f2) is Element of the carrier of f2
{()} is non empty trivial finite 1 -element set
[:(),NAT:] is non empty non trivial Relation-like non finite set
[:{()},[:(),NAT:]:] is non empty non trivial Relation-like non finite set
{()} is non empty trivial finite 1 -element set
[:{()},[:(),NAT:]:] is non empty non trivial Relation-like non finite set
[:{()},[:(),NAT:]:] is non empty non trivial Relation-like non finite set
() is set
() is set
() is set
() \/ () is non empty set
(() \/ ()) \/ () is non empty set
() is non empty set
C is set
T is set
f1 is set
[:T,f1:] is Relation-like set
the_rank_of C is epsilon-transitive epsilon-connected ordinal set
succ {} is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of omega
succ (succ {}) is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of omega
Rank (succ (succ {})) is epsilon-transitive set
f2 is set
x is set
[f2,x] is pair non empty set
{f2,x} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,x},{f2}} is non empty finite V38() set
C is Element of [:(),NAT:]
C `1 is set
C `2 is set
C is Element of ()
C `1 is set
C `2 is set
C is Element of ()
(C) is Element of [:(),NAT:]
((C)) is Relation-like NAT -defined () -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of ()
((C)) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C is Element of ()
(C) is Element of {(),(),()}
C `1 is set
{(),()} \/ () is non empty set
f1 is non empty Relation-like () -defined Function-like total set
f2 is non empty Relation-like () -defined Function-like total set
{(),(),()} * is non empty functional FinSequence-membered FinSequenceSet of {(),(),()}
a is Element of {(),(),()}
<*a*> is non empty trivial Relation-like NAT -defined {(),(),()} -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Element of {(),(),()} *
[1,a] is pair non empty set
{1,a} is non empty finite set
{{1,a},{1}} is non empty finite V38() set
{[1,a]} is non empty trivial Relation-like Function-like constant finite 1 -element set
x is Element of {(),(),()}
<*a,x*> is non empty Relation-like NAT -defined {(),(),()} -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like Element of {(),(),()} *
<*a*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
<*x*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,x] is pair non empty set
{1,x} is non empty finite set
{{1,x},{1}} is non empty finite V38() set
{[1,x]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*a*> ^ <*x*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined {(),(),()} -valued Function-like finite FinSequence-like FinSubsequence-like Element of {(),(),()} *
((),()) --> (<*a,x*>,i) is Relation-like {(),()} -defined {(),(),()} * -valued Function-like quasi_total finite Function-yielding V115() Element of bool [:{(),()},({(),(),()} *):]
[:{(),()},({(),(),()} *):] is non empty Relation-like set
bool [:{(),()},({(),(),()} *):] is non empty set
f1 +* (((),()) --> (<*a,x*>,i)) is Relation-like Function-like set
((),()) --> (x,a) is Relation-like {(),()} -defined {(),(),()} -valued Function-like quasi_total finite Element of bool [:{(),()},{(),(),()}:]
[:{(),()},{(),(),()}:] is non empty Relation-like finite set
bool [:{(),()},{(),(),()}:] is non empty finite V38() set
f2 +* (((),()) --> (x,a)) is Relation-like Function-like set
dom (((),()) --> (<*a,x*>,i)) is finite Element of bool {(),()}
bool {(),()} is non empty finite V38() set
dom (((),()) --> (x,a)) is finite Element of bool {(),()}
dom f1 is non empty Element of bool ()
bool () is non empty set
dom f2 is non empty Element of bool ()
proj1 (f1 +* (((),()) --> (<*a,x*>,i))) is set
proj1 (f2 +* (((),()) --> (x,a))) is set
proj2 f1 is non empty set
x2 is set
x1 is set
f1 . x1 is set
x2 is Element of ()
(x2) is Relation-like NAT -defined () -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of ()
(x2) is Element of [:(),NAT:]
((x2)) is Relation-like NAT -defined () -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of ()
len (x2) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
b is Element of {(),(),()}
(len (x2)) |-> b is Relation-like NAT -defined {(),(),()} -valued Function-like finite len (x2) -element FinSequence-like FinSubsequence-like Element of (len (x2)) -tuples_on {(),(),()}
(len (x2)) -tuples_on {(),(),()} is non empty functional FinSequence-membered FinSequenceSet of {(),(),()}
{ b₁ where b₁ is Relation-like NAT -defined {(),(),()} -valued Function-like finite FinSequence-like FinSubsequence-like Element of {(),(),()} * : len b₁ = len (x2) } is set
Seg (len (x2)) is finite len (x2) -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b₁ & b₁ <= len (x2) ) } is set
(Seg (len (x2))) --> b is Relation-like Seg (len (x2)) -defined Seg (len (x2)) -defined {(),(),()} -valued {b} -valued Function-like constant total total quasi_total finite FinSequence-like FinSubsequence-like Element of bool [:(Seg (len (x2))),{b}:]
{b} is non empty trivial finite 1 -element set
[:(Seg (len (x2))),{b}:] is Relation-like finite set
bool [:(Seg (len (x2))),{b}:] is non empty finite V38() set
rng (((),()) --> (<*a,x*>,i)) is functional finite FinSequence-membered Element of bool ({(),(),()} *)
bool ({(),(),()} *) is non empty set
(proj2 f1) \/ (rng (((),()) --> (<*a,x*>,i))) is non empty set
({(),(),()} *) \/ ({(),(),()} *) is non empty set
proj2 f2 is non empty set
x2 is set
x1 is set
f2 . x1 is set
x2 is Element of ()
(x2) is Element of {(),(),()}
rng (((),()) --> (x,a)) is finite Element of bool {(),(),()}
bool {(),(),()} is non empty finite V38() set
(proj2 f2) \/ (rng (((),()) --> (x,a))) is non empty set
{(),(),()} \/ {(),(),()} is non empty finite set
proj2 (f1 +* (((),()) --> (<*a,x*>,i))) is set
[:({(),()} \/ ()),({(),(),()} *):] is non empty Relation-like set
bool [:({(),()} \/ ()),({(),(),()} *):] is non empty set
proj2 (f2 +* (((),()) --> (x,a))) is set
[:({(),()} \/ ()),{(),(),()}:] is non empty Relation-like set
bool [:({(),()} \/ ()),{(),(),()}:] is non empty set
x2 is Relation-like {(),()} \/ () -defined {(),(),()} * -valued Function-like quasi_total Function-yielding V115() Element of bool [:({(),()} \/ ()),({(),(),()} *):]
x1 is Relation-like {(),()} \/ () -defined {(),(),()} -valued Function-like quasi_total Element of bool [:({(),()} \/ ()),{(),(),()}:]
ManySortedSign(# {(),(),()},({(),()} \/ ()),x2,x1 #) is non empty V58() strict V259() ManySortedSign
x2 is non empty non void V58() strict V259() ManySortedSign
the carrier of x2 is non empty set
the carrier' of x2 is non empty set
the Arity of x2 is Relation-like the carrier' of x2 -defined the carrier of x2 * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of x2,( the carrier of x2 *):]
the carrier of x2 * is non empty functional FinSequence-membered FinSequenceSet of the carrier of x2
[: the carrier' of x2,( the carrier of x2 *):] is non empty Relation-like set
bool [: the carrier' of x2,( the carrier of x2 *):] is non empty set
the Arity of x2 . () is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the Arity of x2 . () is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the ResultSort of x2 is Relation-like the carrier' of x2 -defined the carrier of x2 -valued Function-like quasi_total Element of bool [: the carrier' of x2, the carrier of x2:]
[: the carrier' of x2, the carrier of x2:] is non empty Relation-like set
bool [: the carrier' of x2, the carrier of x2:] is non empty set
the ResultSort of x2 . () is set
the ResultSort of x2 . () is set
(((),()) --> (<*a,x*>,i)) . () is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(((),()) --> (<*a,x*>,i)) . () is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(((),()) --> (x,a)) . () is set
(((),()) --> (x,a)) . () is set
p is Element of the carrier' of x2
the Arity of x2 . p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
b is Element of {(),(),()}
the Arity of x2 . p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of x2 *
c is Element of ()
f1 . c is set
(c) is Relation-like NAT -defined () -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of ()
(c) is Element of [:(),NAT:]
((c)) is Relation-like NAT -defined () -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of ()
len (c) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
a is Element of {()}
(len (c)) |-> a is Relation-like NAT -defined {()} -valued Function-like finite len (c) -element FinSequence-like FinSubsequence-like Element of (len (c)) -tuples_on {()}
(len (c)) -tuples_on {()} is non empty functional FinSequence-membered FinSequenceSet of {()}
{ b₁ where b₁ is Relation-like NAT -defined {()} -valued Function-like finite FinSequence-like FinSubsequence-like Element of {()} * : len b₁ = len (c) } is set
Seg (len (c)) is finite len (c) -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b₁ & b₁ <= len (c) ) } is set
(Seg (len (c))) --> a is Relation-like Seg (len (c)) -defined Seg (len (c)) -defined {()} -valued {a} -valued Function-like constant total total quasi_total finite FinSequence-like FinSubsequence-like Element of bool [:(Seg (len (c))),{a}:]
{a} is non empty trivial finite 1 -element set
[:(Seg (len (c))),{a}:] is Relation-like finite set
bool [:(Seg (len (c))),{a}:] is non empty finite V38() set
p is non empty non void V58() strict V259() () ManySortedSign
the carrier' of p is non empty set
the carrier of p is non empty set
the ResultSort of p is Relation-like the carrier' of p -defined the carrier of p -valued Function-like quasi_total Element of bool [: the carrier' of p, the carrier of p:]
[: the carrier' of p, the carrier of p:] is non empty Relation-like set
bool [: the carrier' of p, the carrier of p:] is non empty set
the carrier of p * is non empty functional FinSequence-membered FinSequenceSet of the carrier of p
the Arity of p is Relation-like the carrier' of p -defined the carrier of p * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of p,( the carrier of p *):]
[: the carrier' of p,( the carrier of p *):] is non empty Relation-like set
bool [: the carrier' of p,( the carrier of p *):] is non empty set
c is Element of the carrier' of p
the ResultSort of p . c is Element of the carrier of p
c `1 is set
the Arity of p . c is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of p *
card ( the Arity of p . c) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of omega
c `2 is set
(c `2) `1 is set
card ((c `2) `1) is epsilon-transitive epsilon-connected ordinal cardinal set
a is Element of ()
f2 . a is set
f1 . a is set
card (f1 . a) is epsilon-transitive epsilon-connected ordinal cardinal set
(a) is Relation-like NAT -defined () -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of ()
(a) is Element of [:(),NAT:]
((a)) is Relation-like NAT -defined () -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of ()
len (a) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(len (a)) |-> () is Relation-like NAT -defined Function-like finite len (a) -element FinSequence-like FinSubsequence-like set
Seg (len (a)) is finite len (a) -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b₁ & b₁ <= len (a) ) } is set
(Seg (len (a))) --> () is Relation-like Seg (len (a)) -defined Seg (len (a)) -defined {()} -valued Function-like constant total total quasi_total finite FinSequence-like FinSubsequence-like Element of bool [:(Seg (len (a))),{()}:]
[:(Seg (len (a))),{()}:] is Relation-like finite set
bool [:(Seg (len (a))),{()}:] is non empty finite V38() set
card H₂(a) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of omega
C is non empty non void V58() strict V259() () ManySortedSign
the carrier' of C is non empty set
the carrier of C is non empty set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
T is non empty non void V58() strict V259() () ManySortedSign
the carrier' of T is non empty set
the carrier of T is non empty set
the ResultSort of T is Relation-like the carrier' of T -defined the carrier of T -valued Function-like quasi_total Element of bool [: the carrier' of T, the carrier of T:]
[: the carrier' of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier' of T, the carrier of T:] is non empty set
the carrier of T * is non empty functional FinSequence-membered FinSequenceSet of the carrier of T
the Arity of T is Relation-like the carrier' of T -defined the carrier of T * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of T,( the carrier of T *):]
[: the carrier' of T,( the carrier of T *):] is non empty Relation-like set
bool [: the carrier' of T,( the carrier of T *):] is non empty set
f2 is Element of ()
x is Element of the carrier' of C
a is Element of the carrier' of T
the Arity of C . x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
card ( the Arity of C . x) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of omega
(f2) is Element of [:(),NAT:]
((f2)) is Relation-like NAT -defined () -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of ()
card ((f2)) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of omega
the Arity of T . a is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of T *
card ( the Arity of T . a) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of omega
b is Relation-like NAT -defined {()} -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of {()}
dom b is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
len b is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Seg (len b) is finite len b -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b₁ & b₁ <= len b ) } is set
i is Relation-like NAT -defined {()} -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of {()}
dom i is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
len i is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Seg (len i) is finite len i -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b₁ & b₁ <= len i ) } is set
pi1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
b . pi1 is set
rng b is trivial finite Element of bool {()}
bool {()} is non empty finite V38() set
i . pi1 is set
rng i is trivial finite Element of bool {()}
the Arity of C . f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the Arity of T . f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f2 is Element of the carrier' of C
the Arity of C . f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the Arity of T . f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f2 is Element of the carrier' of C
x is Element of the carrier' of T
the ResultSort of C . f2 is Element of the carrier of C
the ResultSort of T . f2 is set
f2 `1 is set
() is non empty non void V58() strict V259() () ManySortedSign
the carrier' of () is non empty set
C is Element of the carrier' of ()
the_result_sort_of C is Element of the carrier of ()
the carrier of () is non empty set
the ResultSort of () is Relation-like the carrier' of () -defined the carrier of () -valued Function-like quasi_total Element of bool [: the carrier' of (), the carrier of ():]
[: the carrier' of (), the carrier of ():] is non empty Relation-like set
bool [: the carrier' of (), the carrier of ():] is non empty set
the ResultSort of () . C is Element of the carrier of ()
the_arity_of C is Relation-like NAT -defined the carrier of () -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of () *
the carrier of () * is non empty functional FinSequence-membered FinSequenceSet of the carrier of ()
the Arity of () is Relation-like the carrier' of () -defined the carrier of () * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of (),( the carrier of () *):]
[: the carrier' of (),( the carrier of () *):] is non empty Relation-like set
bool [: the carrier' of (),( the carrier of () *):] is non empty set
the Arity of () . C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of () *
T is Element of the carrier' of ()
the_result_sort_of T is Element of the carrier of ()
the ResultSort of () . T is Element of the carrier of ()
the_arity_of T is Relation-like NAT -defined the carrier of () -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of () *
the Arity of () . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of () *
[{},0] is pair non empty set
{{},0} is non empty functional finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{}} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{{},0},{{}}} is non empty finite V38() set
[(),[{},0]] is pair non empty set
{(),[{},0]} is non empty finite set
{{(),[{},0]},{()}} is non empty finite V38() set
[(),[{},0]] is pair non empty set
{(),[{},0]} is non empty finite set
{{(),[{},0]},{()}} is non empty finite V38() set
[(<*> ()),0] is pair non empty Element of [:(() *),NAT:]
[:(() *),NAT:] is non empty non trivial Relation-like non finite set
{(<*> ()),0} is non empty functional finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{(<*> ())} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{(<*> ()),0},{(<*> ())}} is non empty finite V38() set
the carrier' of () is non empty set
f1 is Element of the carrier' of ()
f2 is Element of the carrier' of ()
the_result_sort_of f1 is Element of the carrier of ()
the carrier of () is non empty set
the ResultSort of () is Relation-like the carrier' of () -defined the carrier of () -valued Function-like quasi_total Element of bool [: the carrier' of (), the carrier of ():]
[: the carrier' of (), the carrier of ():] is non empty Relation-like set
bool [: the carrier' of (), the carrier of ():] is non empty set
the ResultSort of () . f1 is Element of the carrier of ()
the_arity_of f1 is Relation-like NAT -defined the carrier of () -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of () *
the carrier of () * is non empty functional FinSequence-membered FinSequenceSet of the carrier of ()
the Arity of () is Relation-like the carrier' of () -defined the carrier of () * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of (),( the carrier of () *):]
[: the carrier' of (),( the carrier of () *):] is non empty Relation-like set
bool [: the carrier' of (),( the carrier of () *):] is non empty set
the Arity of () . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of () *
the_result_sort_of f2 is Element of the carrier of ()
the ResultSort of () . f2 is Element of the carrier of ()
the_arity_of f2 is Relation-like NAT -defined the carrier of () -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of () *
the Arity of () . f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of () *
f1 `1 is set
len (the_arity_of f1) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 `2 is set
(f1 `2) `1 is set
card ((f1 `2) `1) is epsilon-transitive epsilon-connected ordinal cardinal set
[{},0] `1 is set
card ([{},0] `1) is epsilon-transitive epsilon-connected ordinal cardinal set
f2 `1 is set
len (the_arity_of f2) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f2 `2 is set
(f2 `2) `1 is set
card ((f2 `2) `1) is epsilon-transitive epsilon-connected ordinal cardinal set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
T is Element of the carrier' of C
the_result_sort_of T is Element of the carrier of C
the carrier of C is non empty set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . T is Element of the carrier of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
f1 is Element of the carrier' of C
the_result_sort_of f1 is Element of the carrier of C
the ResultSort of C . f1 is Element of the carrier of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
C is non empty non void V58() V259() () ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like the carrier of C -defined Function-like total set
T . () is set
T . () is set
T . () is set
f1 is non empty Relation-like the carrier of C -defined Function-like total set
f1 . () is set
f1 . () is set
f1 . () is set
f2 is set
T . f2 is set
f1 . f2 is set
T is non empty Relation-like the carrier of C -defined Function-like total set
T . () is set
T . () is set
T . () is set
IFEQ ((),(),(),{}) is set
IFEQ ((),(),(),{}) is set
IFEQ ((),(),(),{}) is set
C is non empty non void V58() V259() () ManySortedSign
(C) is non empty Relation-like the carrier of C -defined Function-like total set
the carrier of C is non empty set
(C) . () is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non empty MSAlgebra over C
the carrier' of C is non empty set
f1 is Element of the carrier' of C
the_result_sort_of f1 is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . f1 is Element of the carrier of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
f2 is Element of the carrier' of C
the_result_sort_of f2 is Element of the carrier of C
the ResultSort of C . f2 is Element of the carrier of C
the_arity_of f2 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the Arity of C . f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
[f1, the carrier of C] is pair non empty set
{f1, the carrier of C} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1, the carrier of C},{f1}} is non empty finite V38() set
root-tree [f1, the carrier of C] is non empty Relation-like Function-like DecoratedTree-like set
the Sorts of (Free (C,(C))) is non empty Relation-like the carrier of C -defined Function-like total set
the Sorts of (Free (C,(C))) . () is set
[f2, the carrier of C] is pair non empty set
{f2, the carrier of C} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2, the carrier of C},{f2}} is non empty finite V38() set
root-tree [f2, the carrier of C] is non empty Relation-like Function-like DecoratedTree-like set
the Sorts of (Free (C,(C))) . () is set
the Element of () is Element of ()
(C) is Element of the carrier of C
(C) . () is set
[ the Element of (),()] is pair non empty set
{ the Element of (),()} is non empty finite set
{ the Element of ()} is non empty trivial finite 1 -element set
{{ the Element of (),()},{ the Element of ()}} is non empty finite V38() set
root-tree [ the Element of (),()] is non empty Relation-like Function-like DecoratedTree-like set
the Sorts of (Free (C,(C))) . () is set
proj2 the Sorts of (Free (C,(C))) is non empty set
dom the Sorts of (Free (C,(C))) is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
a is set
the Sorts of (Free (C,(C))) . a is set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,T) is strict non empty MSAlgebra over C
the Sorts of (Free (C,T)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,T)) is non empty set
proj2 the Sorts of (Free (C,T)) is non empty set
union (proj2 the Sorts of (Free (C,T))) is set
C is non empty non void V58() V259() () () ManySortedSign
the carrier of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is Element of the carrier of C
the Sorts of (Free (C,(C))) . T is non empty set
the Element of the Sorts of (Free (C,(C))) . T is Element of the Sorts of (Free (C,(C))) . T
dom the Sorts of (Free (C,(C))) is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
C is set
T is non empty non void V58() V259() () () ManySortedSign
the carrier of T is non empty set
(T) is non empty Relation-like non empty-yielding the carrier of T -defined Function-like total set
Free (T,(T)) is strict non-empty non empty MSAlgebra over T
the Sorts of (Free (T,(T))) is non empty Relation-like non-empty non empty-yielding the carrier of T -defined Function-like total set
f1 is Element of the carrier of T
the Sorts of (Free (T,(T))) . f1 is non empty set
dom the Sorts of (Free (T,(T))) is non empty Element of bool the carrier of T
bool the carrier of T is non empty set
Union the Sorts of (Free (T,(T))) is non empty set
proj2 the Sorts of (Free (T,(T))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (T,(T)))) is set
f2 is set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
T is (C) Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C is non empty set
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
[T, the carrier of C] -tree {} is non empty Relation-like Function-like DecoratedTree-like set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
root-tree [T, the carrier of C] is non empty Relation-like Function-like DecoratedTree-like set
the_result_sort_of T is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . T is Element of the carrier of C
the Sorts of (Free (C,(C))) . (the_result_sort_of T) is non empty set
dom the Sorts of (Free (C,(C))) is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(the_arity_of T) . 1 is set
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
the_result_sort_of T is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . T is Element of the carrier of C
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined bool NAT -valued Function-like constant total quasi_total Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
(C) \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
x is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
<*x*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,x] is pair non empty set
{1,x} is non empty finite V38() non with_pair set
{{1,x},{1}} is non empty finite V38() set
{[1,x]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[T, the carrier of C] -tree <*x*> is non empty Relation-like Function-like DecoratedTree-like set
a is Element of the carrier of C
DTConMSA ((C) \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union (coprod ((C) \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod ((C) \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod ((C) \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0})))) is non empty set
REL ((C) \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(REL ((C) \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))
C -Terms ((C) \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))) is non empty set
b is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
<*b*> is non empty trivial Relation-like NAT -defined C -Terms ((C) \/ ( the carrier of C --> {0})) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding Element of (C -Terms ((C) \/ ( the carrier of C --> {0}))) *
(C -Terms ((C) \/ ( the carrier of C --> {0}))) * is non empty functional FinSequence-membered FinSequenceSet of C -Terms ((C) \/ ( the carrier of C --> {0}))
[1,b] is pair non empty set
{1,b} is non empty finite V38() set
{{1,b},{1}} is non empty finite V38() set
{[1,b]} is non empty trivial Relation-like Function-like constant finite 1 -element set
dom <*b*> is non empty trivial finite 1 -element V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() Element of bool NAT
<*a*> is non empty trivial Relation-like NAT -defined the carrier of C -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Element of the carrier of C *
[1,a] is pair non empty set
{1,a} is non empty finite set
{{1,a},{1}} is non empty finite V38() set
{[1,a]} is non empty trivial Relation-like Function-like constant finite 1 -element set
dom <*a*> is non empty trivial finite 1 -element V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() Element of bool NAT
C -Terms ((C),((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0})))
FreeMSA ((C) \/ ( the carrier of C --> {0})) is strict non-empty V172(C) MSAlgebra over C
FreeSort ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
FreeOper ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier' of C -defined Function-like total ManySortedFunction of the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #), the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0})))
(FreeSort ((C) \/ ( the carrier of C --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of C * -defined Function-like total set
the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #) is Relation-like non-empty the carrier' of C -defined Function-like set
the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0}))) is Relation-like non-empty the carrier' of C -defined Function-like set
MSAlgebra(# (FreeSort ((C) \/ ( the carrier of C --> {0}))),(FreeOper ((C) \/ ( the carrier of C --> {0}))) #) is strict MSAlgebra over C
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
i is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
pi1 is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
<*b*> . i is Relation-like Function-like set
the Sorts of (Free (C,(C))) . a is non empty set
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) . a is non empty set
the_sort_of pi1 is Element of the carrier of C
(the_arity_of T) . i is set
Sym (T,((C) \/ ( the carrier of C --> {0}))) is Element of NonTerminals (DTConMSA ((C) \/ ( the carrier of C --> {0})))
NonTerminals (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Element of bool the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))
bool the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) : ex b<sub>2</sub> being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b<sub>1</sub> ==> b<sub>2</sub> } is set
i is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding ArgumentSeq of Sym (T,((C) \/ ( the carrier of C --> {0})))
(Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree i is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
variables_in ((Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree i) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of (C) \/ ( the carrier of C --> {0})
C variables_in ((Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree i) is non empty Relation-like the carrier of C -defined Function-like total set
pi1 is set
(variables_in ((Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree i)) . pi1 is set
(C) . pi1 is set
x2 is set
rng i is functional finite constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))))
z is Element of the carrier of C
x1 is non empty Relation-like Function-like DecoratedTree-like set
C variables_in x1 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in x1) . z is set
C variables_in x is non empty Relation-like the carrier of C -defined Function-like total set
{x} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C variables_in x) . z is set
(C) . z is set
the_sort_of ((Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree i) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (the_result_sort_of T) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0})) : ( the_sort_of b<sub>1</sub> = the_result_sort_of T & variables_in b<sub>1</sub> c= (C) ) } is set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
T is Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C is non empty set
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(the_arity_of T) . 1 is set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
<*f1*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[T, the carrier of C] -tree <*f1*> is non empty Relation-like Function-like DecoratedTree-like set
f2 is Element of the carrier of C
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is Element of the carrier' of C
the carrier' of C is non empty set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
<*T*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,T] is pair non empty set
{1,T} is non empty finite V38() non with_pair set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*T*> is non empty Relation-like Function-like DecoratedTree-like set
the_result_sort_of (C) is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . (C) is Element of the carrier of C
the_arity_of (C) is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . (C) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
<*(C)*> is non empty trivial Relation-like NAT -defined the carrier of C -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Element of the carrier of C *
[1,(C)] is pair non empty set
{1,(C)} is non empty finite set
{{1,(C)},{1}} is non empty finite V38() set
{[1,(C)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
len (the_arity_of (C)) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(the_arity_of (C)) . 1 is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is Element of the carrier' of C
the carrier' of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*T*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,T] is pair non empty set
{1,T} is non empty finite V38() non with_pair set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*T*> is non empty Relation-like Function-like DecoratedTree-like set
<*f1*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*f1*> is non empty Relation-like Function-like DecoratedTree-like set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
(C) is Element of the carrier' of C
the carrier' of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*T*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,T] is pair non empty set
{1,T} is non empty finite V38() non with_pair set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*T*> is non empty Relation-like Function-like DecoratedTree-like set
(C,(C),T) . {} is set
[(C), the carrier of C] is pair non empty set
{(C), the carrier of C} is non empty finite set
{(C)} is non empty trivial finite 1 -element set
{{(C), the carrier of C},{(C)}} is non empty finite V38() set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is Element of the carrier of C
the non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C) is Element of the carrier' of C
the carrier' of C is non empty set
(C,(C), the non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(the_arity_of T) . 1 is set
(the_arity_of T) . 2 is set
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
the_result_sort_of T is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . T is Element of the carrier of C
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined bool NAT -valued Function-like constant total quasi_total Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
(C) \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
x is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
<*x,a*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
<*x*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x] is pair non empty set
{1,x} is non empty finite V38() non with_pair set
{{1,x},{1}} is non empty finite V38() set
{[1,x]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*a*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,a] is pair non empty set
{1,a} is non empty finite V38() non with_pair set
{{1,a},{1}} is non empty finite V38() set
{[1,a]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x*> ^ <*a*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[T, the carrier of C] -tree <*x,a*> is non empty Relation-like Function-like DecoratedTree-like set
b is Element of the carrier of C
i is Element of the carrier of C
DTConMSA ((C) \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union (coprod ((C) \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod ((C) \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod ((C) \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0})))) is non empty set
REL ((C) \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(REL ((C) \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))
C -Terms ((C) \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))) is non empty set
pi1 is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
z is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
<*pi1,z*> is non empty Relation-like NAT -defined C -Terms ((C) \/ ( the carrier of C --> {0})) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding Element of (C -Terms ((C) \/ ( the carrier of C --> {0}))) *
(C -Terms ((C) \/ ( the carrier of C --> {0}))) * is non empty functional FinSequence-membered FinSequenceSet of C -Terms ((C) \/ ( the carrier of C --> {0}))
<*pi1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[1,pi1] is pair non empty set
{1,pi1} is non empty finite V38() set
{{1,pi1},{1}} is non empty finite V38() set
{[1,pi1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*z*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[1,z] is pair non empty set
{1,z} is non empty finite V38() set
{{1,z},{1}} is non empty finite V38() set
{[1,z]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*pi1*> ^ <*z*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
dom <*pi1,z*> is non empty finite 2 -element V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() Element of bool NAT
<*b,i*> is non empty Relation-like NAT -defined the carrier of C -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like Element of the carrier of C *
<*b*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,b] is pair non empty set
{1,b} is non empty finite set
{{1,b},{1}} is non empty finite V38() set
{[1,b]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*i*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,i] is pair non empty set
{1,i} is non empty finite set
{{1,i},{1}} is non empty finite V38() set
{[1,i]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*b*> ^ <*i*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
dom <*b,i*> is non empty finite 2 -element V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() Element of bool NAT
C -Terms ((C),((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0})))
FreeMSA ((C) \/ ( the carrier of C --> {0})) is strict non-empty V172(C) MSAlgebra over C
FreeSort ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
FreeOper ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier' of C -defined Function-like total ManySortedFunction of the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #), the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0})))
(FreeSort ((C) \/ ( the carrier of C --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of C * -defined Function-like total set
the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #) is Relation-like non-empty the carrier' of C -defined Function-like set
the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0}))) is Relation-like non-empty the carrier' of C -defined Function-like set
MSAlgebra(# (FreeSort ((C) \/ ( the carrier of C --> {0}))),(FreeOper ((C) \/ ( the carrier of C --> {0}))) #) is strict MSAlgebra over C
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
x2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
x1 is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
<*pi1,z*> . x2 is Relation-like Function-like set
the Sorts of (Free (C,(C))) . b is non empty set
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) . b is non empty set
the Sorts of (Free (C,(C))) . i is non empty set
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) . i is non empty set
the_sort_of x1 is Element of the carrier of C
(the_arity_of T) . x2 is set
Sym (T,((C) \/ ( the carrier of C --> {0}))) is Element of NonTerminals (DTConMSA ((C) \/ ( the carrier of C --> {0})))
NonTerminals (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Element of bool the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))
bool the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) : ex b<sub>2</sub> being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b<sub>1</sub> ==> b<sub>2</sub> } is set
x2 is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding ArgumentSeq of Sym (T,((C) \/ ( the carrier of C --> {0})))
(Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree x2 is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
variables_in ((Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree x2) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of (C) \/ ( the carrier of C --> {0})
C variables_in ((Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree x2) is non empty Relation-like the carrier of C -defined Function-like total set
x1 is set
(variables_in ((Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree x2)) . x1 is set
(C) . x1 is set
p is set
rng x2 is functional finite constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))))
x2 is Element of the carrier of C
c is non empty Relation-like Function-like DecoratedTree-like set
C variables_in c is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in c) . x2 is set
C variables_in x is non empty Relation-like the carrier of C -defined Function-like total set
C variables_in a is non empty Relation-like the carrier of C -defined Function-like total set
{x,a} is non empty functional finite V38() non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C variables_in x) . x2 is set
(C) . x2 is set
(C variables_in a) . x2 is set
the_sort_of ((Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree x2) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (the_result_sort_of T) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0})) : ( the_sort_of b<sub>1</sub> = the_result_sort_of T & variables_in b<sub>1</sub> c= (C) ) } is set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
T is Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C is non empty set
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(the_arity_of T) . 1 is set
(the_arity_of T) . 2 is set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
<*f1,f2*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
<*f1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f2] is pair non empty set
{1,f2} is non empty finite V38() non with_pair set
{{1,f2},{1}} is non empty finite V38() set
{[1,f2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f1*> ^ <*f2*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[T, the carrier of C] -tree <*f1,f2*> is non empty Relation-like Function-like DecoratedTree-like set
x is Element of the carrier of C
a is Element of the carrier of C
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) is Element of the carrier' of C
the carrier' of C is non empty set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
<*T,f1*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
<*T*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,T] is pair non empty set
{1,T} is non empty finite V38() non with_pair set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*T*> ^ <*f1*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(), the carrier of C] -tree <*T,f1*> is non empty Relation-like Function-like DecoratedTree-like set
the_result_sort_of (C) is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . (C) is Element of the carrier of C
the_arity_of (C) is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . (C) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
<*(C),(C)*> is non empty Relation-like NAT -defined the carrier of C -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like Element of the carrier of C *
<*(C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(C)] is pair non empty set
{1,(C)} is non empty finite set
{{1,(C)},{1}} is non empty finite V38() set
{[1,(C)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(C)] is pair non empty set
{1,(C)} is non empty finite set
{{1,(C)},{1}} is non empty finite V38() set
{[1,(C)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(C)*> ^ <*(C)*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
len (the_arity_of (C)) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(the_arity_of (C)) . 1 is set
(the_arity_of (C)) . 2 is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) is Element of the carrier' of C
the carrier' of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),T,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*T,f2*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
<*T*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,T] is pair non empty set
{1,T} is non empty finite V38() non with_pair set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f2] is pair non empty set
{1,f2} is non empty finite V38() non with_pair set
{{1,f2},{1}} is non empty finite V38() set
{[1,f2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*T*> ^ <*f2*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(), the carrier of C] -tree <*T,f2*> is non empty Relation-like Function-like DecoratedTree-like set
<*f1,x*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
<*f1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x] is pair non empty set
{1,x} is non empty finite V38() non with_pair set
{{1,x},{1}} is non empty finite V38() set
{[1,x]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f1*> ^ <*x*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(), the carrier of C] -tree <*f1,x*> is non empty Relation-like Function-like DecoratedTree-like set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
(C) is Element of the carrier' of C
the carrier' of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*T,f1*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
<*T*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,T] is pair non empty set
{1,T} is non empty finite V38() non with_pair set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*T*> ^ <*f1*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(), the carrier of C] -tree <*T,f1*> is non empty Relation-like Function-like DecoratedTree-like set
(C,(C),T,f1) . {} is set
[(C), the carrier of C] is pair non empty set
{(C), the carrier of C} is non empty finite set
{(C)} is non empty trivial finite 1 -element set
{{(C), the carrier of C},{(C)}} is non empty finite V38() set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
the carrier' of C is non empty set
T is Element of the carrier of C
f1 is Element of the carrier' of C
the_result_sort_of f1 is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . f1 is Element of the carrier of C
C is non empty non void V58() V259() () ManySortedSign
(C) is Element of the carrier' of C
the carrier' of C is non empty set
(C) is Element of the carrier of C
the carrier of C is non empty set
the_result_sort_of (C) is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . (C) is Element of the carrier of C
(C) is Element of the carrier' of C
(C) is Element of the carrier of C
the_result_sort_of (C) is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . (C) is Element of the carrier of C
C is non empty non void V58() V259() () () ManySortedSign
the carrier of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined bool NAT -valued Function-like constant total quasi_total Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
(C) \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
FreeMSA ((C) \/ ( the carrier of C --> {0})) is strict non-empty V172(C) MSAlgebra over C
FreeSort ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
FreeOper ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier' of C -defined Function-like total ManySortedFunction of the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #), the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0})))
the carrier' of C is non empty set
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
(FreeSort ((C) \/ ( the carrier of C --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of C * -defined Function-like total set
the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #) is Relation-like non-empty the carrier' of C -defined Function-like set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0}))) is Relation-like non-empty the carrier' of C -defined Function-like set
MSAlgebra(# (FreeSort ((C) \/ ( the carrier of C --> {0}))),(FreeOper ((C) \/ ( the carrier of C --> {0}))) #) is strict MSAlgebra over C
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
Reverse ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier of C -defined Function-like total Function-yielding V115() ManySortedFunction of FreeGen ((C) \/ ( the carrier of C --> {0})),(C) \/ ( the carrier of C --> {0})
FreeGen ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total GeneratorSet of FreeMSA ((C) \/ ( the carrier of C --> {0}))
(Reverse ((C) \/ ( the carrier of C --> {0}))) "" (C) is non empty Relation-like the carrier of C -defined Function-like total set
f2 is Element of the carrier of C
x is Element of the carrier of C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
a is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0})))
GenMSAlg a is strict MSSubAlgebra of FreeMSA ((C) \/ ( the carrier of C --> {0}))
the Sorts of (Free (C,(C))) . f2 is non empty set
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) . f2 is non empty set
the Sorts of (Free (C,(C))) . x is non empty set
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) . x is non empty set
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,f2)
b is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,x)
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is set
dom the Sorts of (Free (C,(C))) is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
T is set
C is set
T is non empty non void V58() V259() () () ManySortedSign
(T) is Element of the carrier of T
the carrier of T is non empty set
(T) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (T,(T))))
(T) is non empty Relation-like non empty-yielding the carrier of T -defined Function-like total set
Free (T,(T)) is strict non-empty non empty MSAlgebra over T
the Sorts of (Free (T,(T))) is non empty Relation-like non-empty non empty-yielding the carrier of T -defined Function-like total set
Union the Sorts of (Free (T,(T))) is non empty set
proj2 the Sorts of (Free (T,(T))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (T,(T)))) is set
bool (Union the Sorts of (Free (T,(T)))) is non empty set
the Sorts of (Free (T,(T))) . (T) is non empty set
f1 is set
f2 is non empty non void V58() V259() () () ManySortedSign
(f2) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (f2,(f2))))
(f2) is non empty Relation-like non empty-yielding the carrier of f2 -defined Function-like total set
the carrier of f2 is non empty set
Free (f2,(f2)) is strict non-empty non empty MSAlgebra over f2
the Sorts of (Free (f2,(f2))) is non empty Relation-like non-empty non empty-yielding the carrier of f2 -defined Function-like total set
Union the Sorts of (Free (f2,(f2))) is non empty set
proj2 the Sorts of (Free (f2,(f2))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (f2,(f2)))) is set
bool (Union the Sorts of (Free (f2,(f2)))) is non empty set
(f2) is Element of the carrier of f2
the Sorts of (Free (f2,(f2))) . (f2) is non empty set
C is Element of ()
[C,()] is pair non empty set
{C,()} is non empty finite set
{C} is non empty trivial finite 1 -element set
{{C,()},{C}} is non empty finite V38() set
root-tree [C,()] is non empty Relation-like Function-like DecoratedTree-like set
T is non empty non void V58() V259() () () ManySortedSign
(T) is Element of the carrier of T
the carrier of T is non empty set
(T) is non empty Relation-like non empty-yielding the carrier of T -defined Function-like total set
(T) . () is set
(T) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (T,(T))))
Free (T,(T)) is strict non-empty non empty MSAlgebra over T
the Sorts of (Free (T,(T))) is non empty Relation-like non-empty non empty-yielding the carrier of T -defined Function-like total set
Union the Sorts of (Free (T,(T))) is non empty set
proj2 the Sorts of (Free (T,(T))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (T,(T)))) is set
bool (Union the Sorts of (Free (T,(T)))) is non empty set
the Sorts of (Free (T,(T))) . (T) is non empty set
C is Element of ()
T is Element of ()
f1 is non empty non void V58() V259() () () ManySortedSign
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (f1,(f1))
(f1) is Element of the carrier of f1
the carrier of f1 is non empty set
[C,()] is pair non empty set
{C,()} is non empty finite set
{C} is non empty trivial finite 1 -element set
{{C,()},{C}} is non empty finite V38() set
root-tree [C,()] is non empty Relation-like Function-like DecoratedTree-like set
f2 is non empty non void V58() V259() () () ManySortedSign
(T,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2,(f2))
(f2) is Element of the carrier of f2
the carrier of f2 is non empty set
[T,()] is pair non empty set
{T,()} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T,()},{T}} is non empty finite V38() set
root-tree [T,()] is non empty Relation-like Function-like DecoratedTree-like set
T is non empty non void V58() V259() () () ManySortedSign
(T) is non empty Relation-like non empty-yielding the carrier of T -defined Function-like total set
the carrier of T is non empty set
C is Element of ()
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (T,(T))
(T) is Element of the carrier of T
[C,()] is pair non empty set
{C,()} is non empty finite set
{C} is non empty trivial finite 1 -element set
{{C,()},{C}} is non empty finite V38() set
root-tree [C,()] is non empty Relation-like Function-like DecoratedTree-like set
(C,T) . {} is set
[C,(T)] is pair non empty Element of [:(), the carrier of T:]
[:(), the carrier of T:] is non empty Relation-like set
{C,(T)} is non empty finite set
{{C,(T)},{C}} is non empty finite V38() set
{ the carrier of T} is non empty trivial finite 1 -element set
the carrier' of T is non empty set
[: the carrier' of T,{ the carrier of T}:] is non empty Relation-like set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
the carrier of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
(C) * is non empty functional FinSequence-membered FinSequenceSet of (C)
T is (C) Element of the carrier' of C
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like DTree-yielding set
[T, the carrier of C] -tree f2 is non empty Relation-like Function-like DecoratedTree-like set
len f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined bool NAT -valued Function-like constant total quasi_total Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
(C) \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
C -Terms ((C),((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0})))
FreeMSA ((C) \/ ( the carrier of C --> {0})) is strict non-empty V172(C) MSAlgebra over C
FreeSort ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
FreeOper ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier' of C -defined Function-like total ManySortedFunction of the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #), the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0})))
(FreeSort ((C) \/ ( the carrier of C --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of C * -defined Function-like total set
the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #) is Relation-like non-empty the carrier' of C -defined Function-like set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0}))) is Relation-like non-empty the carrier' of C -defined Function-like set
MSAlgebra(# (FreeSort ((C) \/ ( the carrier of C --> {0}))),(FreeOper ((C) \/ ( the carrier of C --> {0}))) #) is strict MSAlgebra over C
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
DTConMSA ((C) \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union (coprod ((C) \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod ((C) \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod ((C) \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0})))) is non empty set
REL ((C) \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(REL ((C) \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))
C -Terms ((C) \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))) is non empty set
Sym (T,((C) \/ ( the carrier of C --> {0}))) is Element of NonTerminals (DTConMSA ((C) \/ ( the carrier of C --> {0})))
NonTerminals (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Element of bool the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))
bool the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) : ex b<sub>2</sub> being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b<sub>1</sub> ==> b<sub>2</sub> } is set
a is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding ArgumentSeq of Sym (T,((C) \/ ( the carrier of C --> {0})))
(Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree a is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
the_sort_of ((Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree a) is Element of the carrier of C
the_result_sort_of T is Element of the carrier of C
the ResultSort of C . T is Element of the carrier of C
variables_in ((Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree a) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of (C) \/ ( the carrier of C --> {0})
C variables_in ((Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree a) is non empty Relation-like the carrier of C -defined Function-like total set
(C -Terms ((C),((C) \/ ( the carrier of C --> {0})))) . (the_result_sort_of T) is set
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0})) : ( the_sort_of b<sub>1</sub> = the_result_sort_of T & variables_in b<sub>1</sub> c= (C) ) } is set
(Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree f2 is non empty Relation-like Function-like DecoratedTree-like set
proj2 f2 is finite set
Union (C -Terms ((C),((C) \/ ( the carrier of C --> {0})))) is set
proj2 (C -Terms ((C),((C) \/ ( the carrier of C --> {0})))) is non empty set
union (proj2 (C -Terms ((C),((C) \/ ( the carrier of C --> {0}))))) is set
b is set
dom f2 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
pi1 is set
f2 . pi1 is set
z is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
f2 . z is set
dom (the_arity_of T) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
(the_arity_of T) . z is set
rng (the_arity_of T) is finite Element of bool the carrier of C
bool the carrier of C is non empty set
{(C)} is non empty trivial finite 1 -element Element of bool the carrier of C
x2 is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
the_sort_of x2 is Element of the carrier of C
i is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
variables_in x2 is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of (C) \/ ( the carrier of C --> {0})
C variables_in x2 is non empty Relation-like the carrier of C -defined Function-like total set
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0})) : ( the_sort_of b<sub>1</sub> = (C) & variables_in b<sub>1</sub> c= (C) ) } is set
(C -Terms ((C),((C) \/ ( the carrier of C --> {0})))) . (C) is set
(FreeMSA ((C) \/ ( the carrier of C --> {0}))) | (C -Terms ((C),((C) \/ ( the carrier of C --> {0})))) is strict MSSubAlgebra of FreeMSA ((C) \/ ( the carrier of C --> {0}))
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) . (C) is non empty set
a is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
dom f2 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
f2 . a is set
dom (the_arity_of T) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
(the_arity_of T) . a is set
rng (the_arity_of T) is finite Element of bool the carrier of C
bool the carrier of C is non empty set
{(C)} is non empty trivial finite 1 -element Element of bool the carrier of C
b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
i is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
pi1 is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
FreeSort (((C) \/ ( the carrier of C --> {0})),(C)) is non empty functional constituted-DTrees Element of bool (TS (DTConMSA ((C) \/ ( the carrier of C --> {0}))))
TS (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))))
bool (TS (DTConMSA ((C) \/ ( the carrier of C --> {0})))) is non empty set
((C) \/ ( the carrier of C --> {0})) . (C) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like DecoratedTree-like Element of TS (DTConMSA ((C) \/ ( the carrier of C --> {0}))) : ( ex b<sub>2</sub> being set st
( b<sub>2</sub> in ((C) \/ ( the carrier of C --> {0})) . (C) & b<sub>1</sub> = root-tree [b<sub>2</sub>,(C)] ) or ex b<sub>2</sub> being Element of the carrier' of C st
( [b<sub>2</sub>, the carrier of C] = b<sub>1</sub> . {} & the_result_sort_of b<sub>2</sub> = (C) ) ) } is set
the_sort_of pi1 is Element of the carrier of C
dom the Sorts of (Free (C,(C))) is non empty Element of bool the carrier of C
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
f1 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
T is (C) Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C) * is non empty functional FinSequence-membered FinSequenceSet of (C)
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
[T, the carrier of C] -tree f1 is non empty Relation-like Function-like DecoratedTree-like set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 . {} is set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
T is (C) Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
the_result_sort_of T is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . T is Element of the carrier of C
f1 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined bool NAT -valued Function-like constant total quasi_total Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
(C) \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Sym (T,((C) \/ ( the carrier of C --> {0}))) is Element of NonTerminals (DTConMSA ((C) \/ ( the carrier of C --> {0})))
DTConMSA ((C) \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union (coprod ((C) \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod ((C) \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod ((C) \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0})))) is non empty set
REL ((C) \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(REL ((C) \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty set
NonTerminals (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Element of bool the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))
bool the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) : ex b<sub>2</sub> being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b<sub>1</sub> ==> b<sub>2</sub> } is set
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
(Sym (T,((C) \/ ( the carrier of C --> {0})))) -tree f1 is non empty Relation-like Function-like DecoratedTree-like set
C -Terms ((C),((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0})))
FreeMSA ((C) \/ ( the carrier of C --> {0})) is strict non-empty V172(C) MSAlgebra over C
FreeSort ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
FreeOper ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier' of C -defined Function-like total ManySortedFunction of the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #), the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0})))
(FreeSort ((C) \/ ( the carrier of C --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of C * -defined Function-like total set
the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #) is Relation-like non-empty the carrier' of C -defined Function-like set
the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0}))) is Relation-like non-empty the carrier' of C -defined Function-like set
MSAlgebra(# (FreeSort ((C) \/ ( the carrier of C --> {0}))),(FreeOper ((C) \/ ( the carrier of C --> {0}))) #) is strict MSAlgebra over C
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))
C -Terms ((C) \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))) is non empty set
a is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding ArgumentSeq of Sym (T,((C) \/ ( the carrier of C --> {0})))
rng a is functional finite constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))))
(C -Terms ((C),((C) \/ ( the carrier of C --> {0})))) . (the_result_sort_of T) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
the carrier' of C is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
(C) is Element of the carrier of C
(C) is (C,(C))
(C) is Element of the carrier of C
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined bool NAT -valued Function-like constant total quasi_total Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
(C) \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
a is set
x is Element of the carrier of C
[a,x] is pair non empty set
{a,x} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,x},{a}} is non empty finite V38() set
root-tree [a,x] is non empty Relation-like Function-like DecoratedTree-like set
(C) . x is set
a is set
x is Element of the carrier of C
[a,x] is pair non empty set
{a,x} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,x},{a}} is non empty finite V38() set
root-tree [a,x] is non empty Relation-like Function-like DecoratedTree-like set
(C) . x is set
b is Element of ()
(b,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[b,()] is pair non empty set
{b,()} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,()},{b}} is non empty finite V38() set
root-tree [b,()] is non empty Relation-like Function-like DecoratedTree-like set
DTConMSA ((C) \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union (coprod ((C) \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod ((C) \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod ((C) \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0})))) is non empty set
REL ((C) \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(REL ((C) \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))
x is Element of the carrier' of C
[x, the carrier of C] is pair non empty set
{x, the carrier of C} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x, the carrier of C},{x}} is non empty finite V38() set
a is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of Union the Sorts of (Free (C,(C)))
[x, the carrier of C] -tree a is non empty Relation-like Function-like DecoratedTree-like set
len a is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
the_arity_of x is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of x) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Sym (x,((C) \/ ( the carrier of C --> {0}))) is Element of NonTerminals (DTConMSA ((C) \/ ( the carrier of C --> {0})))
NonTerminals (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Element of bool the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))
bool the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) : ex b<sub>2</sub> being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b<sub>1</sub> ==> b<sub>2</sub> } is set
x is Element of the carrier' of C
[x, the carrier of C] is pair non empty set
{x, the carrier of C} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x, the carrier of C},{x}} is non empty finite V38() set
a is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of Union the Sorts of (Free (C,(C)))
[x, the carrier of C] -tree a is non empty Relation-like Function-like DecoratedTree-like set
len a is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
the_arity_of x is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of x) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Sym (x,((C) \/ ( the carrier of C --> {0}))) is Element of NonTerminals (DTConMSA ((C) \/ ( the carrier of C --> {0})))
NonTerminals (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Element of bool the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))
bool the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) : ex b<sub>2</sub> being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b<sub>1</sub> ==> b<sub>2</sub> } is set
dom a is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
dom (the_arity_of x) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
a . 1 is set
rng a is finite Element of bool (Union the Sorts of (Free (C,(C))))
a . 2 is set
C -Terms ((C) \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))) is non empty set
b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
i is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C variables_in b is non empty Relation-like the carrier of C -defined Function-like total set
pi1 is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
variables_in pi1 is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of (C) \/ ( the carrier of C --> {0})
C variables_in pi1 is non empty Relation-like the carrier of C -defined Function-like total set
C variables_in i is non empty Relation-like the carrier of C -defined Function-like total set
z is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
variables_in z is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of (C) \/ ( the carrier of C --> {0})
C variables_in z is non empty Relation-like the carrier of C -defined Function-like total set
<*(),()*> . 2 is set
<*(),()*> . 1 is set
the_sort_of pi1 is Element of the carrier of C
(the_arity_of x) . 1 is set
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0})) : ( the_sort_of b<sub>1</sub> = (C) & variables_in b<sub>1</sub> c= (C) ) } is set
C -Terms ((C),((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0})))
FreeMSA ((C) \/ ( the carrier of C --> {0})) is strict non-empty V172(C) MSAlgebra over C
FreeSort ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
FreeOper ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier' of C -defined Function-like total ManySortedFunction of the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #), the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0})))
(FreeSort ((C) \/ ( the carrier of C --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of C * -defined Function-like total set
the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #) is Relation-like non-empty the carrier' of C -defined Function-like set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0}))) is Relation-like non-empty the carrier' of C -defined Function-like set
MSAlgebra(# (FreeSort ((C) \/ ( the carrier of C --> {0}))),(FreeOper ((C) \/ ( the carrier of C --> {0}))) #) is strict MSAlgebra over C
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
(C -Terms ((C),((C) \/ ( the carrier of C --> {0})))) . (C) is set
the Sorts of (Free (C,(C))) . (C) is non empty set
the_sort_of z is Element of the carrier of C
(the_arity_of x) . 2 is set
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0})) : ( the_sort_of b<sub>1</sub> = (C) & variables_in b<sub>1</sub> c= (C) ) } is set
(C -Terms ((C),((C) \/ ( the carrier of C --> {0})))) . (C) is set
the Sorts of (Free (C,(C))) . (C) is non empty set
x2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
x1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
<*x2,x1*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
<*x2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x2] is pair non empty set
{1,x2} is non empty finite V38() non with_pair set
{{1,x2},{1}} is non empty finite V38() set
{[1,x2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x1] is pair non empty set
{1,x1} is non empty finite V38() non with_pair set
{{1,x1},{1}} is non empty finite V38() set
{[1,x1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x2*> ^ <*x1*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
(C,(C),x2,x1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
dom a is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
dom (the_arity_of x) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
a . 1 is set
rng a is finite Element of bool (Union the Sorts of (Free (C,(C))))
C -Terms ((C) \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))) is non empty set
b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C variables_in b is non empty Relation-like the carrier of C -defined Function-like total set
i is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0}))
variables_in i is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of (C) \/ ( the carrier of C --> {0})
C variables_in i is non empty Relation-like the carrier of C -defined Function-like total set
<*()*> . 1 is set
the_sort_of i is Element of the carrier of C
(the_arity_of x) . 1 is set
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms ((C) \/ ( the carrier of C --> {0})) : ( the_sort_of b<sub>1</sub> = (C) & variables_in b<sub>1</sub> c= (C) ) } is set
C -Terms ((C),((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0})))
FreeMSA ((C) \/ ( the carrier of C --> {0})) is strict non-empty V172(C) MSAlgebra over C
FreeSort ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
FreeOper ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier' of C -defined Function-like total ManySortedFunction of the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #), the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0})))
(FreeSort ((C) \/ ( the carrier of C --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of C * -defined Function-like total set
the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #) is Relation-like non-empty the carrier' of C -defined Function-like set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0}))) is Relation-like non-empty the carrier' of C -defined Function-like set
MSAlgebra(# (FreeSort ((C) \/ ( the carrier of C --> {0}))),(FreeOper ((C) \/ ( the carrier of C --> {0}))) #) is strict MSAlgebra over C
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
(C -Terms ((C),((C) \/ ( the carrier of C --> {0})))) . (C) is set
the Sorts of (Free (C,(C))) . (C) is non empty set
pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
<*pi1*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,pi1] is pair non empty set
{1,pi1} is non empty finite V38() non with_pair set
{{1,pi1},{1}} is non empty finite V38() set
{[1,pi1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
(C,(C),pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
b is (C) Element of the carrier' of C
[b, the carrier of C] is pair non empty set
{b, the carrier of C} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b, the carrier of C},{b}} is non empty finite V38() set
[b, the carrier of C] -tree a is non empty Relation-like Function-like DecoratedTree-like set
(C) * is non empty functional FinSequence-membered FinSequenceSet of (C)
i is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
(C,b,i) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
DTConMSA ((C) \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union (coprod ((C) \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod ((C) \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod ((C) \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0})))) is non empty set
REL ((C) \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod ((C) \/ ( the carrier of C --> {0}))))),(REL ((C) \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((C) \/ ( the carrier of C --> {0})))
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
(C) is (C,(C))
T is (C) Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f2 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,T,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
[T, the carrier of C] -tree f2 is non empty Relation-like Function-like DecoratedTree-like set
(C,T,f2) . {} is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*f1*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*f1*> is non empty Relation-like Function-like DecoratedTree-like set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
(C) is (C,(C))
T is (C) Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len x is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,T,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
[T, the carrier of C] -tree x is non empty Relation-like Function-like DecoratedTree-like set
(C,T,x) . {} is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*f1,f2*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
<*f1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f2] is pair non empty set
{1,f2} is non empty finite V38() non with_pair set
{{1,f2},{1}} is non empty finite V38() set
{[1,f2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f1*> ^ <*f2*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(), the carrier of C] -tree <*f1,f2*> is non empty Relation-like Function-like DecoratedTree-like set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) is (C,(C))
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*f1,f2*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
<*f1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f2] is pair non empty set
{1,f2} is non empty finite V38() non with_pair set
{{1,f2},{1}} is non empty finite V38() set
{[1,f2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f1*> ^ <*f2*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(), the carrier of C] -tree <*f1,f2*> is non empty Relation-like Function-like DecoratedTree-like set
(C,(C),T) . {} is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*T*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
[1,T] is pair non empty set
{1,T} is non empty finite V38() non with_pair set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*T*> is non empty Relation-like Function-like DecoratedTree-like set
([(), the carrier of C] -tree <*T*>) . {} is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
(C) is Element of the carrier of C
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
T . {} is set
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
f1 is Element of ()
(f1,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
(C) is Element of the carrier of C
[f1,()] is pair non empty set
{f1,()} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,()},{f1}} is non empty finite V38() set
root-tree [f1,()] is non empty Relation-like Function-like DecoratedTree-like set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
f2 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is (C) Element of the carrier' of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f1) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f2 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is (C) Element of the carrier' of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f1) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
[f1, the carrier of C] is pair non empty set
{f1, the carrier of C} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1, the carrier of C},{f1}} is non empty finite V38() set
[f1, the carrier of C] -tree f2 is non empty Relation-like Function-like DecoratedTree-like set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is Element of the carrier of C
(C) is (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*f1,f2*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
<*f1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f2] is pair non empty set
{1,f2} is non empty finite V38() non with_pair set
{{1,f2},{1}} is non empty finite V38() set
{[1,f2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f1*> ^ <*f2*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(), the carrier of C] -tree <*f1,f2*> is non empty Relation-like Function-like DecoratedTree-like set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
(C) is Element of the carrier of C
(C) is (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
(C) is Element of the carrier of C
(C) is Element of the carrier of C
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
T . {} is set
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
f1 is Element of ()
(f1,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
(C) is Element of the carrier of C
[f1,()] is pair non empty set
{f1,()} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,()},{f1}} is non empty finite V38() set
root-tree [f1,()] is non empty Relation-like Function-like DecoratedTree-like set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
f2 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is (C) Element of the carrier' of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f1) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f2 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is (C) Element of the carrier' of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f1) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
[f1, the carrier of C] is pair non empty set
{f1, the carrier of C} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1, the carrier of C},{f1}} is non empty finite V38() set
[f1, the carrier of C] -tree f2 is non empty Relation-like Function-like DecoratedTree-like set
(C) is (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*f1*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*f1*> is non empty Relation-like Function-like DecoratedTree-like set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
(C) is (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C) is (C,(C))
<*0*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like nonpair-yielding Element of NAT *
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
[1,0] is pair non empty set
{1,0} is non empty finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{1,0},{1}} is non empty finite V38() set
{[1,0]} is non empty trivial Relation-like Function-like constant finite 1 -element set
T | <*0*> is non empty Relation-like Function-like DecoratedTree-like set
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*f1*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*f1*> is non empty Relation-like Function-like DecoratedTree-like set
len <*f1*> is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of NAT
0 + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
<*f1*> . (0 + 1) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
the carrier' of C is non empty set
T is Element of the carrier' of C
the_result_sort_of T is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . T is Element of the carrier of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
f1 is Element of the carrier' of C
the_result_sort_of f1 is Element of the carrier of C
the ResultSort of C . f1 is Element of the carrier of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
[f1, the carrier of C] is pair non empty set
{f1, the carrier of C} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1, the carrier of C},{f1}} is non empty finite V38() set
root-tree [f1, the carrier of C] is non empty Relation-like Function-like DecoratedTree-like set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
the Sorts of (Free (C,(C))) . () is set
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C) is (C,(C))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*a*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,a] is pair non empty set
{1,a} is non empty finite V38() non with_pair set
{{1,a},{1}} is non empty finite V38() set
{[1,a]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*a*> is non empty Relation-like Function-like DecoratedTree-like set
x . {} is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C) is (C,(C))
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is (C,(C))
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
the non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C, the non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*f1*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*f1*> is non empty Relation-like Function-like DecoratedTree-like set
len <*f1*> is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of NAT
T | <*0*> is non empty Relation-like Function-like DecoratedTree-like set
0 + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
<*f1*> . (0 + 1) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*f1*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*f1*> is non empty Relation-like Function-like DecoratedTree-like set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C),f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
<*f2*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
[1,f2] is pair non empty set
{1,f2} is non empty finite V38() non with_pair set
{{1,f2},{1}} is non empty finite V38() set
{[1,f2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
len <*f2*> is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of NAT
T | <*0*> is non empty Relation-like Function-like DecoratedTree-like set
0 + 1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
<*f2*> . (0 + 1) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),(C,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C) is (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C) is (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
the non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b<sub>1</sub> is (C) } is set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
f1 is set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b<sub>1</sub> is (C) } is set
the non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
f1 is set
C is set
T is non empty non void V58() V259() () () ManySortedSign
(T) is Element of the carrier of T
the carrier of T is non empty set
(T) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (T,(T))))
(T) is non empty Relation-like non empty-yielding the carrier of T -defined Function-like total set
Free (T,(T)) is strict non-empty non empty MSAlgebra over T
the Sorts of (Free (T,(T))) is non empty Relation-like non-empty non empty-yielding the carrier of T -defined Function-like total set
Union the Sorts of (Free (T,(T))) is non empty set
proj2 the Sorts of (Free (T,(T))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (T,(T)))) is set
bool (Union the Sorts of (Free (T,(T)))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (T,(T)) : b<sub>1</sub> is (T) } is set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (T,(T))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (T,(T))
C is set
T is non empty non void V58() V259() () () ManySortedSign
(T) is Element of the carrier of T
the carrier of T is non empty set
f1 is set
f2 is non empty non void V58() V259() () () ManySortedSign
(f2) is Element of the carrier of f2
the carrier of f2 is non empty set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
the non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
the non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
the carrier' of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
f1 is Element of ()
(f1,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[f1,()] is pair non empty set
{f1,()} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,()},{f1}} is non empty finite V38() set
root-tree [f1,()] is non empty Relation-like Function-like DecoratedTree-like set
f2 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is (C) Element of the carrier' of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f1) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f2 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is (C) Element of the carrier' of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f1) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
the_result_sort_of f1 is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . f1 is Element of the carrier of C
(C) is (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is Element of the carrier of C
(C) is (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is (C,(C))
(C) is Element of the carrier of C
(C) is (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
the carrier' of C is non empty set
(C) is Element of the carrier of C
T is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len T is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is (C) Element of the carrier' of C
the_result_sort_of f1 is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . f1 is Element of the carrier of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f1) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f1,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C) is (C,(C))
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C) is (C,(C))
(C,(C,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,(C),f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C) is (C,(C))
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,(C),f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is Element of the carrier of C
the carrier of C is non empty set
T is Element of the carrier' of C
the_result_sort_of T is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . T is Element of the carrier of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
root-tree [T, the carrier of C] is non empty Relation-like Function-like DecoratedTree-like set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
the Sorts of (Free (C,(C))) . () is set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C) is Element of the carrier of C
(C) is (C,(C))
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),x,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*x,a*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
<*x*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x] is pair non empty set
{1,x} is non empty finite V38() non with_pair set
{{1,x},{1}} is non empty finite V38() set
{[1,x]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*a*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,a] is pair non empty set
{1,a} is non empty finite V38() non with_pair set
{{1,a},{1}} is non empty finite V38() set
{[1,a]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x*> ^ <*a*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(), the carrier of C] -tree <*x,a*> is non empty Relation-like Function-like DecoratedTree-like set
f2 . {} is set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is Element of the carrier of C
the carrier of C is non empty set
T is Element of the carrier' of C
the_result_sort_of T is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . T is Element of the carrier of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
root-tree [T, the carrier of C] is non empty Relation-like Function-like DecoratedTree-like set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
the Sorts of (Free (C,(C))) . () is set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C) is (C,(C))
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*x*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,x] is pair non empty set
{1,x} is non empty finite V38() non with_pair set
{{1,x},{1}} is non empty finite V38() set
{[1,x]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*x*> is non empty Relation-like Function-like DecoratedTree-like set
f2 . {} is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
the carrier' of C is non empty set
T is Element of the carrier' of C
the_result_sort_of T is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . T is Element of the carrier of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
f1 is Element of the carrier' of C
the_result_sort_of f1 is Element of the carrier of C
the ResultSort of C . f1 is Element of the carrier of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
root-tree [T, the carrier of C] is non empty Relation-like Function-like DecoratedTree-like set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b<sub>1</sub> is (C) } is set
bool (C) is non empty set
{ [b<sub>2</sub>,b<sub>1</sub>] where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)), b<sub>2</sub> is functional finite constituted-DTrees Element of bool (C) : b<sub>1</sub> is (C) } is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is set
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b<sub>1</sub> is (C) } is set
bool (C) is non empty set
{ [b<sub>2</sub>,b<sub>1</sub>] where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)), b<sub>2</sub> is functional finite constituted-DTrees Element of bool (C) : b<sub>1</sub> is (C) } is set
the non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
[{}, the non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))] is pair non empty set
{{}, the non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))} is non empty functional finite V38() non with_pair set
{{}} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{{}, the non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))},{{}}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty set
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b<sub>1</sub> is (C) } is set
bool (C) is non empty set
{ [b<sub>2</sub>,b<sub>1</sub>] where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)), b<sub>2</sub> is functional finite constituted-DTrees Element of bool (C) : b<sub>1</sub> is (C) } is set
the Element of (C) is Element of (C)
C is set
T is non empty non void V58() V259() () () ManySortedSign
(T) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (T,(T))))
(T) is non empty Relation-like non empty-yielding the carrier of T -defined Function-like total set
the carrier of T is non empty set
Free (T,(T)) is strict non-empty non empty MSAlgebra over T
the Sorts of (Free (T,(T))) is non empty Relation-like non-empty non empty-yielding the carrier of T -defined Function-like total set
Union the Sorts of (Free (T,(T))) is non empty set
proj2 the Sorts of (Free (T,(T))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (T,(T)))) is set
bool (Union the Sorts of (Free (T,(T)))) is non empty set
(T) is Element of the carrier of T
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (T,(T)) : b<sub>1</sub> is (T) } is set
bool (T) is non empty set
(T) is Element of the carrier of T
(T) is non empty set
{ [b<sub>2</sub>,b<sub>1</sub>] where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (T,(T)), b<sub>2</sub> is functional finite constituted-DTrees Element of bool (T) : b<sub>1</sub> is (T) } is set
f2 is functional finite constituted-DTrees Element of bool (T)
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (T,(T))
[f2,f1] is pair non empty Element of [:(bool (T)),(Union the Sorts of (Free (T,(T)))):]
[:(bool (T)),(Union the Sorts of (Free (T,(T)))):] is non empty Relation-like set
{f2,f1} is non empty finite V38() set
{f2} is non empty trivial finite V38() 1 -element set
{{f2,f1},{f2}} is non empty finite V38() set
f1 is functional finite constituted-DTrees Element of bool (T)
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (T) (T,(T))
[f1,f2] is pair non empty Element of [:(bool (T)),(Union the Sorts of (Free (T,(T)))):]
[:(bool (T)),(Union the Sorts of (Free (T,(T)))):] is non empty Relation-like set
{f1,f2} is non empty finite V38() set
{f1} is non empty trivial finite V38() 1 -element set
{{f1,f2},{f1}} is non empty finite V38() set
a is functional finite constituted-DTrees Element of bool (T)
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (T,(T))
[a,x] is pair non empty Element of [:(bool (T)),(Union the Sorts of (Free (T,(T)))):]
{a,x} is non empty finite V38() set
{a} is non empty trivial finite V38() 1 -element set
{{a,x},{a}} is non empty finite V38() set
C is set
T is set
[C,T] is pair non empty set
{C,T} is non empty finite set
{C} is non empty trivial finite 1 -element set
{{C,T},{C}} is non empty finite V38() set
f1 is non empty non void V58() V259() () () ManySortedSign
(f1) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (f1,(f1))))
(f1) is non empty Relation-like non empty-yielding the carrier of f1 -defined Function-like total set
the carrier of f1 is non empty set
Free (f1,(f1)) is strict non-empty non empty MSAlgebra over f1
the Sorts of (Free (f1,(f1))) is non empty Relation-like non-empty non empty-yielding the carrier of f1 -defined Function-like total set
Union the Sorts of (Free (f1,(f1))) is non empty set
proj2 the Sorts of (Free (f1,(f1))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (f1,(f1)))) is set
bool (Union the Sorts of (Free (f1,(f1)))) is non empty set
(f1) is Element of the carrier of f1
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (f1,(f1)) : b<sub>1</sub> is (f1) } is set
bool (f1) is non empty set
(f1) is Element of the carrier of f1
f2 is functional finite constituted-DTrees Element of bool (f1)
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (f1) (f1,(f1))
[f2,x] is pair non empty Element of [:(bool (f1)),(Union the Sorts of (Free (f1,(f1)))):]
[:(bool (f1)),(Union the Sorts of (Free (f1,(f1)))):] is non empty Relation-like set
{f2,x} is non empty finite V38() set
{f2} is non empty trivial finite V38() 1 -element set
{{f2,x},{f2}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
T is (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b<sub>1</sub> is (C) } is set
bool (C) is non empty set
(C) is Element of the carrier of C
f1 is functional finite constituted-DTrees Element of bool (C)
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
[f1,f2] is pair non empty Element of [:(bool (C)),(Union the Sorts of (Free (C,(C)))):]
[:(bool (C)),(Union the Sorts of (Free (C,(C)))):] is non empty Relation-like set
{f1,f2} is non empty finite V38() set
{f1} is non empty trivial finite V38() 1 -element set
{{f1,f2},{f1}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
the carrier' of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
f2 is Element of ()
(f2,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[f2,()] is pair non empty set
{f2,()} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,()},{f2}} is non empty finite V38() set
root-tree [f2,()] is non empty Relation-like Function-like DecoratedTree-like set
x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len x is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f2 is (C) Element of the carrier' of C
the_arity_of f2 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f2) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f2,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len x is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f2 is (C) Element of the carrier' of C
the_arity_of f2 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f2) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f2,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
the_result_sort_of f2 is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . f2 is Element of the carrier of C
(C) is Element of the carrier of C
(C) is (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is Element of the carrier of C
(C) is (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f2,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is Element of the carrier of C
(C) is (C,(C))
(C) is (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
the carrier' of C is non empty set
(C) is Element of the carrier of C
T is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len T is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is (C) Element of the carrier' of C
the_result_sort_of f1 is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . f1 is Element of the carrier of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f1) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f1,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C) is Element of the carrier of C
(C) is (C,(C))
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),x,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is Element of the carrier of C
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b<sub>1</sub> is (C) } is set
(C) is non empty set
(C) is Element of the carrier of C
bool (C) is non empty set
{ [b<sub>2</sub>,b<sub>1</sub>] where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)), b<sub>2</sub> is functional finite constituted-DTrees Element of bool (C) : b<sub>1</sub> is (C) } is set
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined bool NAT -valued Function-like constant total quasi_total Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
(C) \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
FreeMSA ((C) \/ ( the carrier of C --> {0})) is strict non-empty V172(C) MSAlgebra over C
FreeSort ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
FreeOper ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier' of C -defined Function-like total ManySortedFunction of the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #), the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0})))
the carrier' of C is non empty set
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
(FreeSort ((C) \/ ( the carrier of C --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of C * -defined Function-like total set
the Arity of C * ((FreeSort ((C) \/ ( the carrier of C --> {0}))) #) is Relation-like non-empty the carrier' of C -defined Function-like set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C * (FreeSort ((C) \/ ( the carrier of C --> {0}))) is Relation-like non-empty the carrier' of C -defined Function-like set
MSAlgebra(# (FreeSort ((C) \/ ( the carrier of C --> {0}))),(FreeOper ((C) \/ ( the carrier of C --> {0}))) #) is strict MSAlgebra over C
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() set
Reverse ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier of C -defined Function-like total Function-yielding V115() ManySortedFunction of FreeGen ((C) \/ ( the carrier of C --> {0})),(C) \/ ( the carrier of C --> {0})
FreeGen ((C) \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total GeneratorSet of FreeMSA ((C) \/ ( the carrier of C --> {0}))
(Reverse ((C) \/ ( the carrier of C --> {0}))) "" (C) is non empty Relation-like the carrier of C -defined Function-like total set
f2 is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0})))
GenMSAlg f2 is strict MSSubAlgebra of FreeMSA ((C) \/ ( the carrier of C --> {0}))
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) . (C) is non empty set
the Sorts of (Free (C,(C))) . (C) is non empty set
the Sorts of (FreeMSA ((C) \/ ( the carrier of C --> {0}))) . (C) is non empty set
f2 is set
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f2 is set
f2 is set
T is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is Element of the carrier of C
f2 is set
f1 is non empty non void V58() V259() () () ManySortedSign
(f1) is Element of the carrier of f1
the carrier of f1 is non empty set
a is set
x is non empty non void V58() V259() () () ManySortedSign
(x) is Element of the carrier of x
the carrier of x is non empty set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b<sub>1</sub> is (C) } is set
bool (C) is non empty set
(C) is Element of the carrier of C
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b<sub>1</sub> is (C) } is set
bool (C) is non empty set
(C) is Element of the carrier of C
T is functional finite constituted-DTrees Element of bool (C)
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
[T,f1] is pair non empty set
{T,f1} is non empty finite V38() set
{T} is non empty trivial finite V38() 1 -element set
{{T,f1},{T}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
T is pair non empty (C)
T `1 is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C) is Element of the carrier of C
f1 is functional finite constituted-DTrees Element of bool (C)
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
[f1,f2] is pair non empty Element of [:(bool (C)),(Union the Sorts of (Free (C,(C)))):]
[:(bool (C)),(Union the Sorts of (Free (C,(C)))):] is non empty Relation-like set
{f1,f2} is non empty finite V38() set
{f1} is non empty trivial finite V38() 1 -element set
{{f1,f2},{f1}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
C is non empty non void V58() V259() () () ManySortedSign
T is pair non empty (C)
T `1 is finite set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b<sub>1</sub> where b<sub>1</sub> is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b<sub>1</sub> is (C) } is set
bool (C) is non empty set
(C) is Element of the carrier of C
f1 is functional finite constituted-DTrees Element of bool (C)
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
[f1,f2] is pair non empty Element of [:(bool (C)),(Union the Sorts of (Free (C,(C)))):]
[:(bool (C)),(Union the Sorts of (Free (C,(C)))):] is non empty Relation-like set
{f1,f2} is non empty finite V38() set
{f1} is non empty trivial finite V38() 1 -element set
{{f1,f2},{f1}} is non empty finite V38() set
T `2 is set
(C) is Element of the carrier of C
f1 is functional finite constituted-DTrees Element of bool (C)
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
[f1,f2] is pair non empty Element of [:(bool (C)),(Union the Sorts of (Free (C,(C)))):]
[:(bool (C)),(Union the Sorts of (Free (C,(C)))):] is non empty Relation-like set
{f1,f2} is non empty finite V38() set
{f1} is non empty trivial finite V38() 1 -element set
{{f1,f2},{f1}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
f2 is non empty non void V58() V259() () () ManySortedSign
(f2) is Element of the carrier of f2
the carrier of f2 is non empty set
(f2) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (f2,(f2))))
(f2) is non empty Relation-like non empty-yielding the carrier of f2 -defined Function-like total set
Free (f2,(f2)) is strict non-empty non empty MSAlgebra over f2
the Sorts of (Free (f2,(f2))) is non empty Relation-like non-empty non empty-yielding the carrier of f2 -defined Function-like total set
Union the Sorts of (Free (f2,(f2))) is non empty set
proj2 the Sorts of (Free (f2,(f2))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (f2,(f2)))) is set
bool (Union the Sorts of (Free (f2,(f2)))) is non empty set
(f2) is Element of the carrier of f2
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2,(f2)) : b₁ is (f2) } is set
bool (f2) is non empty set
f1 is functional finite constituted-DTrees Element of bool (C)
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f1,T) is pair non empty (C)
{f1,T} is non empty finite V38() set
{f1} is non empty trivial finite V38() 1 -element set
{{f1,T},{f1}} is non empty finite V38() set
(C,(C,f1,T)) is functional finite constituted-DTrees Element of bool (C)
a is functional finite constituted-DTrees Element of bool (f2)
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2) (f2,(f2))
(f2,a,x) is pair non empty (f2)
{a,x} is non empty finite V38() set
{a} is non empty trivial finite V38() 1 -element set
{{a,x},{a}} is non empty finite V38() set
(f2,(f2,a,x)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2) (f2,(f2))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C) is Element of the carrier of C
T is functional finite constituted-DTrees Element of bool (C)
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,f2) is pair non empty (C)
{T,f2} is non empty finite V38() set
{T} is non empty trivial finite V38() 1 -element set
{{T,f2},{T}} is non empty finite V38() set
f1 is functional finite constituted-DTrees Element of bool (C)
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f1,x) is pair non empty (C)
{f1,x} is non empty finite V38() set
{f1} is non empty trivial finite V38() 1 -element set
{{f1,x},{f1}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
T is pair non empty (C)
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
(C,(C,T),(C,T)) is pair non empty (C)
{(C,T),(C,T)} is non empty finite V38() set
{(C,T)} is non empty trivial finite V38() 1 -element set
{{(C,T),(C,T)},{(C,T)}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
T is pair non empty (C)
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
f1 is pair non empty (C)
(C,f1) is functional finite constituted-DTrees Element of bool (C)
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,T),(C,T)) is pair non empty (C)
{(C,T),(C,T)} is non empty finite V38() set
{(C,T)} is non empty trivial finite V38() 1 -element set
{{(C,T),(C,T)},{(C,T)}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
{f1} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
T is pair non empty (C)
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
{f1} \/ (C,T) is non empty finite set
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
[({f1} \/ (C,T)),(C,T)] is pair non empty set
{({f1} \/ (C,T)),(C,T)} is non empty finite V38() set
{({f1} \/ (C,T))} is non empty trivial finite V38() 1 -element set
{{({f1} \/ (C,T)),(C,T)},{({f1} \/ (C,T))}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
f2 is non empty non void V58() V259() () () ManySortedSign
(f2) is Element of the carrier of f2
the carrier of f2 is non empty set
T is pair non empty (C)
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,f1) is pair non empty (C)
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
{f1} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
{f1} \/ (C,T) is non empty finite set
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
[({f1} \/ (C,T)),(C,T)] is pair non empty set
{({f1} \/ (C,T)),(C,T)} is non empty finite V38() set
{({f1} \/ (C,T))} is non empty trivial finite V38() 1 -element set
{{({f1} \/ (C,T)),(C,T)},{({f1} \/ (C,T))}} is non empty finite V38() set
(C,(C,T,f1)) is functional finite constituted-DTrees Element of bool (C)
x is pair non empty (f2)
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2) (f2,(f2))
(f2,x,a) is pair non empty (f2)
(f2) is non empty Relation-like non empty-yielding the carrier of f2 -defined Function-like total set
Free (f2,(f2)) is strict non-empty non empty MSAlgebra over f2
the Sorts of (Free (f2,(f2))) is non empty Relation-like non-empty non empty-yielding the carrier of f2 -defined Function-like total set
Union the Sorts of (Free (f2,(f2))) is non empty set
proj2 the Sorts of (Free (f2,(f2))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (f2,(f2)))) is set
{a} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (f2,(f2))))
bool (Union the Sorts of (Free (f2,(f2)))) is non empty set
(f2,x) is functional finite constituted-DTrees Element of bool (f2)
(f2) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (f2,(f2))))
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2,(f2)) : b₁ is (f2) } is set
bool (f2) is non empty set
{a} \/ (f2,x) is non empty finite set
(f2,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2) (f2,(f2))
(f2) is Element of the carrier of f2
[({a} \/ (f2,x)),(f2,x)] is pair non empty set
{({a} \/ (f2,x)),(f2,x)} is non empty finite V38() set
{({a} \/ (f2,x))} is non empty trivial finite V38() 1 -element set
{{({a} \/ (f2,x)),(f2,x)},{({a} \/ (f2,x))}} is non empty finite V38() set
(f2,(f2,x,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2) (f2,(f2))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is pair non empty (C)
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,f1) is pair non empty (C)
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
{f1} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
{f1} \/ (C,T) is non empty finite set
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
[({f1} \/ (C,T)),(C,T)] is pair non empty set
{({f1} \/ (C,T)),(C,T)} is non empty finite V38() set
{({f1} \/ (C,T))} is non empty trivial finite V38() 1 -element set
{{({f1} \/ (C,T)),(C,T)},{({f1} \/ (C,T))}} is non empty finite V38() set
(C,(C,T,f1),f1) is pair non empty (C)
(C,(C,T,f1)) is functional finite constituted-DTrees Element of bool (C)
{f1} \/ (C,(C,T,f1)) is non empty finite set
(C,(C,T,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
[({f1} \/ (C,(C,T,f1))),(C,(C,T,f1))] is pair non empty set
{({f1} \/ (C,(C,T,f1))),(C,(C,T,f1))} is non empty finite V38() set
{({f1} \/ (C,(C,T,f1)))} is non empty trivial finite V38() 1 -element set
{{({f1} \/ (C,(C,T,f1))),(C,(C,T,f1))},{({f1} \/ (C,(C,T,f1)))}} is non empty finite V38() set
{f1} \/ ({f1} \/ (C,T)) is non empty finite set
[({f1} \/ ({f1} \/ (C,T))),(C,(C,T,f1))] is pair non empty set
{({f1} \/ ({f1} \/ (C,T))),(C,(C,T,f1))} is non empty finite V38() set
{({f1} \/ ({f1} \/ (C,T)))} is non empty trivial finite V38() 1 -element set
{{({f1} \/ ({f1} \/ (C,T))),(C,(C,T,f1))},{({f1} \/ ({f1} \/ (C,T)))}} is non empty finite V38() set
{f1} \/ {f1} is non empty finite V38() non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
({f1} \/ {f1}) \/ (C,T) is non empty finite set
[(({f1} \/ {f1}) \/ (C,T)),(C,(C,T,f1))] is pair non empty set
{(({f1} \/ {f1}) \/ (C,T)),(C,(C,T,f1))} is non empty finite V38() set
{(({f1} \/ {f1}) \/ (C,T))} is non empty trivial finite V38() 1 -element set
{{(({f1} \/ {f1}) \/ (C,T)),(C,(C,T,f1))},{(({f1} \/ {f1}) \/ (C,T))}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is pair non empty (C)
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,f2) is pair non empty (C)
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
{f2} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
{f2} \/ (C,T) is non empty finite set
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
[({f2} \/ (C,T)),(C,T)] is pair non empty set
{({f2} \/ (C,T)),(C,T)} is non empty finite V38() set
{({f2} \/ (C,T))} is non empty trivial finite V38() 1 -element set
{{({f2} \/ (C,T)),(C,T)},{({f2} \/ (C,T))}} is non empty finite V38() set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,T,f2),f1) is pair non empty (C)
{f1} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
(C,(C,T,f2)) is functional finite constituted-DTrees Element of bool (C)
{f1} \/ (C,(C,T,f2)) is non empty finite set
(C,(C,T,f2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
[({f1} \/ (C,(C,T,f2))),(C,(C,T,f2))] is pair non empty set
{({f1} \/ (C,(C,T,f2))),(C,(C,T,f2))} is non empty finite V38() set
{({f1} \/ (C,(C,T,f2)))} is non empty trivial finite V38() 1 -element set
{{({f1} \/ (C,(C,T,f2))),(C,(C,T,f2))},{({f1} \/ (C,(C,T,f2)))}} is non empty finite V38() set
(C,T,f1) is pair non empty (C)
{f1} \/ (C,T) is non empty finite set
[({f1} \/ (C,T)),(C,T)] is pair non empty set
{({f1} \/ (C,T)),(C,T)} is non empty finite V38() set
{({f1} \/ (C,T))} is non empty trivial finite V38() 1 -element set
{{({f1} \/ (C,T)),(C,T)},{({f1} \/ (C,T))}} is non empty finite V38() set
(C,(C,T,f1),f2) is pair non empty (C)
(C,(C,T,f1)) is functional finite constituted-DTrees Element of bool (C)
{f2} \/ (C,(C,T,f1)) is non empty finite set
(C,(C,T,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
[({f2} \/ (C,(C,T,f1))),(C,(C,T,f1))] is pair non empty set
{({f2} \/ (C,(C,T,f1))),(C,(C,T,f1))} is non empty finite V38() set
{({f2} \/ (C,(C,T,f1)))} is non empty trivial finite V38() 1 -element set
{{({f2} \/ (C,(C,T,f1))),(C,(C,T,f1))},{({f2} \/ (C,(C,T,f1)))}} is non empty finite V38() set
{f1} \/ ({f2} \/ (C,T)) is non empty finite set
[({f1} \/ ({f2} \/ (C,T))),(C,(C,T,f2))] is pair non empty set
{({f1} \/ ({f2} \/ (C,T))),(C,(C,T,f2))} is non empty finite V38() set
{({f1} \/ ({f2} \/ (C,T)))} is non empty trivial finite V38() 1 -element set
{{({f1} \/ ({f2} \/ (C,T))),(C,(C,T,f2))},{({f1} \/ ({f2} \/ (C,T)))}} is non empty finite V38() set
{f2} \/ ({f1} \/ (C,T)) is non empty finite set
[({f2} \/ ({f1} \/ (C,T))),(C,(C,T,f2))] is pair non empty set
{({f2} \/ ({f1} \/ (C,T))),(C,(C,T,f2))} is non empty finite V38() set
{({f2} \/ ({f1} \/ (C,T)))} is non empty trivial finite V38() 1 -element set
{{({f2} \/ ({f1} \/ (C,T))),(C,(C,T,f2))},{({f2} \/ ({f1} \/ (C,T)))}} is non empty finite V38() set
[({f2} \/ ({f1} \/ (C,T))),(C,T)] is pair non empty set
{({f2} \/ ({f1} \/ (C,T))),(C,T)} is non empty finite V38() set
{{({f2} \/ ({f1} \/ (C,T))),(C,T)},{({f2} \/ ({f1} \/ (C,T)))}} is non empty finite V38() set
[({f2} \/ (C,(C,T,f1))),(C,T)] is pair non empty set
{({f2} \/ (C,(C,T,f1))),(C,T)} is non empty finite V38() set
{{({f2} \/ (C,(C,T,f1))),(C,T)},{({f2} \/ (C,(C,T,f1)))}} is non empty finite V38() set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
f1 is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
DTConMSA f1 is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod f1 is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union (coprod f1) is non empty set
proj2 (coprod f1) is non empty with_non-empty_elements set
union (proj2 (coprod f1)) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1)) is non empty set
REL f1 is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1)) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(REL f1) #) is non empty strict DTConstrStr
the carrier of (DTConMSA f1) is non empty set
FinTrees the carrier of (DTConMSA f1) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA f1)
C -Terms f1 is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA f1))
bool (FinTrees the carrier of (DTConMSA f1)) is non empty set
f2 is non empty Relation-like the carrier of (DTConMSA f1) -valued Function-like finite DecoratedTree-like Element of C -Terms f1
variables_in f2 is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of f1
C variables_in f2 is non empty Relation-like the carrier of C -defined Function-like total set
T is Element of the carrier of C
(variables_in f2) . T is set
x is Element of the carrier of C
f1 . x is non empty set
[:(f1 . x), the carrier of C:] is non empty Relation-like set
a is Element of f1 . x
[a,x] is pair non empty Element of [:(f1 . x), the carrier of C:]
{a,x} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,x},{a}} is non empty finite V38() set
root-tree [a,x] is non empty Relation-like [:(f1 . x), the carrier of C:] -valued Function-like DecoratedTree-like Element of FinTrees [:(f1 . x), the carrier of C:]
FinTrees [:(f1 . x), the carrier of C:] is non empty functional constituted-DTrees DTree-set of [:(f1 . x), the carrier of C:]
C variables_in (root-tree [a,x]) is non empty Relation-like the carrier of C -defined Function-like total set
b is Element of the carrier of C
(C variables_in (root-tree [a,x])) . b is set
x is Element of the carrier' of C
Sym (x,f1) is Element of NonTerminals (DTConMSA f1)
NonTerminals (DTConMSA f1) is non empty Element of bool the carrier of (DTConMSA f1)
bool the carrier of (DTConMSA f1) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA f1) : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
[x, the carrier of C] is pair non empty set
{x, the carrier of C} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x, the carrier of C},{x}} is non empty finite V38() set
a is Relation-like NAT -defined FinTrees the carrier of (DTConMSA f1) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding ArgumentSeq of Sym (x,f1)
rng a is functional finite constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA f1))
[x, the carrier of C] -tree a is non empty Relation-like Function-like DecoratedTree-like set
C variables_in ([x, the carrier of C] -tree a) is non empty Relation-like the carrier of C -defined Function-like total set
b is Element of the carrier of C
(C variables_in ([x, the carrier of C] -tree a)) . b is set
{ H₂(b₁) where b₁ is non empty Relation-like the carrier of (DTConMSA f1) -valued Function-like finite DecoratedTree-like Element of C -Terms f1 : b₁ in rng a } is set
pi1 is set
z is non empty Relation-like the carrier of (DTConMSA f1) -valued Function-like finite DecoratedTree-like Element of C -Terms f1
C variables_in z is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in z) . b is set
union { H₂(b₁) where b₁ is non empty Relation-like the carrier of (DTConMSA f1) -valued Function-like finite DecoratedTree-like Element of C -Terms f1 : b₁ in rng a } is set
pi1 is set
z is non empty Relation-like Function-like DecoratedTree-like set
C variables_in z is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in z) . b is set
dom a is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
x2 is set
a . x2 is Relation-like Function-like set
x1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
a . x1 is Relation-like Function-like set
x2 is non empty Relation-like the carrier of (DTConMSA f1) -valued Function-like finite DecoratedTree-like Element of C -Terms f1
C variables_in x2 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in x2) . b is set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
f1 is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,f1) is strict non empty MSAlgebra over C
the Sorts of (Free (C,f1)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,f1)) is non empty set
proj2 the Sorts of (Free (C,f1)) is non empty set
union (proj2 the Sorts of (Free (C,f1))) is set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,f1))
C variables_in f2 is non empty Relation-like the carrier of C -defined Function-like total set
T is Element of the carrier of C
(C variables_in f2) . T is set
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined bool NAT -valued Function-like constant total quasi_total Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
f1 \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
DTConMSA (f1 \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod (f1 \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union (coprod (f1 \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod (f1 \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod (f1 \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (f1 \/ ( the carrier of C --> {0})))) is non empty set
REL (f1 \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (f1 \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (f1 \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (f1 \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (f1 \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (f1 \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (f1 \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (f1 \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (f1 \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (f1 \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (f1 \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (f1 \/ ( the carrier of C --> {0}))))),(REL (f1 \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA (f1 \/ ( the carrier of C --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA (f1 \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA (f1 \/ ( the carrier of C --> {0})))
C -Terms (f1 \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA (f1 \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA (f1 \/ ( the carrier of C --> {0})))) is non empty set
x is non empty Relation-like the carrier of (DTConMSA (f1 \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (f1 \/ ( the carrier of C --> {0}))
C variables_in x is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in x) . T is set
variables_in x is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of f1 \/ ( the carrier of C --> {0})
(variables_in x) . T is finite set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,T) is strict non empty MSAlgebra over C
the Sorts of (Free (C,T)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,T)) is non empty set
proj2 the Sorts of (Free (C,T)) is non empty set
union (proj2 the Sorts of (Free (C,T))) is set
f1 is Element of the carrier of C
T . f1 is set
bool (T . f1) is non empty Element of bool (bool (T . f1))
bool (T . f1) is non empty set
bool (bool (T . f1)) is non empty set
[:(Union the Sorts of (Free (C,T))),(bool (T . f1)):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,T))),(bool (T . f1)):] is non empty set
f2 is Relation-like Union the Sorts of (Free (C,T)) -defined bool (T . f1) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,T))),(bool (T . f1)):]
x is Relation-like Union the Sorts of (Free (C,T)) -defined bool (T . f1) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,T))),(bool (T . f1)):]
a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,T))
f2 . a is Element of bool (T . f1)
b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,T))
C variables_in b is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in b) . f1 is finite set
x . a is Element of bool (T . f1)
f2 is set
x is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,T))
C variables_in x is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in x) . f1 is finite set
f2 is Relation-like Function-like set
proj1 f2 is set
proj2 f2 is set
x is Relation-like Union the Sorts of (Free (C,T)) -defined bool (T . f1) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,T))),(bool (T . f1)):]
a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,T))
x . a is Element of bool (T . f1)
C variables_in a is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in a) . f1 is finite set
b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,T))
C variables_in b is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in b) . f1 is finite set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in T) . (C) is finite set
(C) . (C) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) is Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in T) . (C) is finite set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in T) . (C) is finite set
((C,T)) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) is finite Element of bool ()
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in T) . (C) is finite set
((C,T)) is set
((C,T)) is set
C is non empty non void V58() V259() () () ManySortedSign
T is Element of ()
(T,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
(C) is Element of the carrier of C
[T,()] is pair non empty set
{T,()} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T,()},{T}} is non empty finite V38() set
root-tree [T,()] is non empty Relation-like Function-like DecoratedTree-like set
(C,(T,C)) is finite Element of bool ()
C variables_in (T,C) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (T,C)) . (C) is finite set
{T} is non empty trivial finite 1 -element Element of bool ()
C is non empty non void V58() V259() () () ManySortedSign
T is Element of ()
(T,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
(C) is Element of the carrier of C
[T,()] is pair non empty set
{T,()} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T,()},{T}} is non empty finite V38() set
root-tree [T,()] is non empty Relation-like Function-like DecoratedTree-like set
(C,(T,C)) is finite Element of bool ()
(C,(T,C)) is finite Element of bool ()
C variables_in (T,C) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (T,C)) . (C) is finite set
((C,(T,C))) is set
{T} is non empty trivial finite 1 -element Element of bool ()
(T) is finite Element of bool ()
{T} \/ (T) is non empty finite Element of bool ()
({T}) is set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is Element of the carrier of C
T is (C) Element of the carrier' of C
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) is finite Element of bool ()
C variables_in f1 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in f1) . (C) is finite set
f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like DTree-yielding set
[T, the carrier of C] -tree f2 is non empty Relation-like Function-like DecoratedTree-like set
proj2 f2 is finite set
{ (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in proj2 f2 } is set
union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in proj2 f2 } is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
the Sorts of (Free (C,(C))) . (C) is non empty set
(C) * is non empty functional FinSequence-membered FinSequenceSet of (C)
a is set
b is non empty Relation-like Function-like DecoratedTree-like set
C variables_in b is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in b) . (C) is set
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,i) is finite Element of bool ()
C variables_in i is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in i) . (C) is finite set
a is set
b is set
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,i) is finite Element of bool ()
C variables_in i is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in i) . (C) is finite set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is Element of the carrier of C
T is (C) Element of the carrier' of C
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) is finite Element of bool ()
(C,f1) is finite Element of bool ()
C variables_in f1 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in f1) . (C) is finite set
((C,f1)) is set
f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like DTree-yielding set
[T, the carrier of C] -tree f2 is non empty Relation-like Function-like DecoratedTree-like set
proj2 f2 is finite set
{ (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in proj2 f2 } is set
union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in proj2 f2 } is set
{ (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in proj2 f2 } is set
the Element of { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in proj2 f2 } is Element of { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in proj2 f2 }
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,i) is finite Element of bool ()
(C,i) is finite Element of bool ()
C variables_in i is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in i) . (C) is finite set
((C,i)) is set
b is non empty set
{ (b₁) where b₁ is Element of b : verum } is set
pi1 is set
z is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,z) is finite Element of bool ()
(C,z) is finite Element of bool ()
C variables_in z is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in z) . (C) is finite set
((C,z)) is set
x2 is Element of b
(x2) is set
pi1 is set
z is Element of b
(z) is set
x2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,x2) is finite Element of bool ()
C variables_in x2 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in x2) . (C) is finite set
(C,x2) is finite Element of bool ()
((C,x2)) is set
union b is set
((union b)) is set
union { (b₁) where b₁ is Element of b : verum } is set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
T is (C) Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,(C,T,f1)) is finite Element of bool ()
C variables_in (C,T,f1) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,T,f1)) . (C) is finite set
rng f1 is finite Element of bool (Union the Sorts of (Free (C,(C))))
{ (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in rng f1 } is set
union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in rng f1 } is set
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
[T, the carrier of C] -tree f1 is non empty Relation-like Function-like DecoratedTree-like set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
T is (C) Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,(C,T,f1)) is finite Element of bool ()
(C,(C,T,f1)) is finite Element of bool ()
C variables_in (C,T,f1) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,T,f1)) . (C) is finite set
((C,(C,T,f1))) is set
rng f1 is finite Element of bool (Union the Sorts of (Free (C,(C))))
{ (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in rng f1 } is set
union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in rng f1 } is set
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
[T, the carrier of C] -tree f1 is non empty Relation-like Function-like DecoratedTree-like set
C is ManySortedSign
the carrier of C is set
[[0]] the carrier of C is Relation-like empty-yielding the carrier of C -defined Function-like total V159() set
the carrier of C --> {} is Relation-like the carrier of C -defined {{}} -valued Function-like constant total quasi_total Function-yielding V115() Element of bool [: the carrier of C,{{}}:]
{{}} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
[: the carrier of C,{{}}:] is Relation-like set
bool [: the carrier of C,{{}}:] is non empty set
T is set
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
[T, the carrier of C] -tree {} is non empty Relation-like Function-like DecoratedTree-like set
C variables_in ([T, the carrier of C] -tree {}) is Relation-like the carrier of C -defined Function-like total set
f1 is set
proj2 {} is non pair empty trivial 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered with_non-empty_elements V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() set
f2 is set
(C variables_in ([T, the carrier of C] -tree {})) . f1 is set
x is non empty Relation-like Function-like DecoratedTree-like set
C variables_in x is Relation-like the carrier of C -defined Function-like total set
(C variables_in x) . f1 is set
([[0]] the carrier of C) . f1 is non pair 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() set
x is non empty Relation-like Function-like DecoratedTree-like set
C variables_in x is Relation-like the carrier of C -defined Function-like total set
(C variables_in x) . f1 is set
C is ManySortedSign
the carrier of C is set
T is set
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
f1 is non empty Relation-like Function-like DecoratedTree-like set
<*f1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[1,f1] is pair non empty set
{1,f1} is non empty finite set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[T, the carrier of C] -tree <*f1*> is non empty Relation-like Function-like DecoratedTree-like set
C variables_in ([T, the carrier of C] -tree <*f1*>) is Relation-like the carrier of C -defined Function-like total set
C variables_in f1 is Relation-like the carrier of C -defined Function-like total set
f2 is set
{f1} is non empty trivial functional finite 1 -element set
proj2 <*f1*> is non empty trivial finite 1 -element set
x is set
(C variables_in ([T, the carrier of C] -tree <*f1*>)) . f2 is set
a is non empty Relation-like Function-like DecoratedTree-like set
C variables_in a is Relation-like the carrier of C -defined Function-like total set
(C variables_in a) . f2 is set
(C variables_in f1) . f2 is set
a is non empty Relation-like Function-like DecoratedTree-like set
C variables_in a is Relation-like the carrier of C -defined Function-like total set
(C variables_in a) . f2 is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C,(C,(C),T)) is finite Element of bool ()
C variables_in (C,(C),T) is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in (C,(C),T)) . (C) is finite set
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in T) . (C) is finite set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*T*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,T] is pair non empty set
{1,T} is non empty finite V38() non with_pair set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*T*> is non empty Relation-like Function-like DecoratedTree-like set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C,(C,(C),T)) is finite Element of bool ()
(C,(C,(C),T)) is finite Element of bool ()
C variables_in (C,(C),T) is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in (C,(C),T)) . (C) is finite set
((C,(C,(C),T))) is set
(C,T) is finite Element of bool ()
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in T) . (C) is finite set
((C,T)) is set
C is ManySortedSign
the carrier of C is set
T is set
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
f1 is non empty Relation-like Function-like DecoratedTree-like set
f2 is non empty Relation-like Function-like DecoratedTree-like set
<*f1,f2*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding set
<*f1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[1,f1] is pair non empty set
{1,f1} is non empty finite set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[1,f2] is pair non empty set
{1,f2} is non empty finite set
{{1,f2},{1}} is non empty finite V38() set
{[1,f2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f1*> ^ <*f2*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[T, the carrier of C] -tree <*f1,f2*> is non empty Relation-like Function-like DecoratedTree-like set
C variables_in ([T, the carrier of C] -tree <*f1,f2*>) is Relation-like the carrier of C -defined Function-like total set
C variables_in f1 is Relation-like the carrier of C -defined Function-like total set
C variables_in f2 is Relation-like the carrier of C -defined Function-like total set
(C variables_in f1) \/ (C variables_in f2) is Relation-like the carrier of C -defined Function-like total set
x is set
{f1,f2} is non empty functional finite set
proj2 <*f1,f2*> is non empty finite set
a is set
(C variables_in ([T, the carrier of C] -tree <*f1,f2*>)) . x is set
b is non empty Relation-like Function-like DecoratedTree-like set
C variables_in b is Relation-like the carrier of C -defined Function-like total set
(C variables_in b) . x is set
(C variables_in f1) . x is set
(C variables_in f2) . x is set
b is non empty Relation-like Function-like DecoratedTree-like set
C variables_in b is Relation-like the carrier of C -defined Function-like total set
(C variables_in b) . x is set
((C variables_in f1) . x) \/ ((C variables_in f2) . x) is set
((C variables_in f1) \/ (C variables_in f2)) . x is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in T) . (C) is finite set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C,(C,(C),f1,T)) is finite Element of bool ()
C variables_in (C,(C),f1,T) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,(C),f1,T)) . (C) is finite set
(C,f1) is finite Element of bool ()
C variables_in f1 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in f1) . (C) is finite set
(C,f1) \/ (C,T) is finite Element of bool ()
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*f1,T*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
<*f1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*T*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,T] is pair non empty set
{1,T} is non empty finite V38() non with_pair set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f1*> ^ <*T*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(), the carrier of C] -tree <*f1,T*> is non empty Relation-like Function-like DecoratedTree-like set
(C variables_in f1) \/ (C variables_in T) is non empty Relation-like the carrier of C -defined Function-like total set
((C variables_in f1) \/ (C variables_in T)) . () is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) is finite Element of bool ()
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in T) . (C) is finite set
((C,T)) is set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C,(C,(C),f1,T)) is finite Element of bool ()
(C,(C,(C),f1,T)) is finite Element of bool ()
C variables_in (C,(C),f1,T) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,(C),f1,T)) . (C) is finite set
((C,(C,(C),f1,T))) is set
(C,f1) is finite Element of bool ()
(C,f1) is finite Element of bool ()
C variables_in f1 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in f1) . (C) is finite set
((C,f1)) is set
(C,f1) \/ (C,T) is finite Element of bool ()
(C,f1) \/ (C,T) is finite Element of bool ()
(((C,f1) \/ (C,T))) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C,T)) is finite Element of bool ()
C variables_in (C,T) is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in (C,T)) . (C) is finite set
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in T) . (C) is finite set
(C) is (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
[(C), the carrier of C] is pair non empty set
{(C), the carrier of C} is non empty finite set
{(C)} is non empty trivial finite 1 -element set
{{(C), the carrier of C},{(C)}} is non empty finite V38() set
<*f1*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,f1] is pair non empty set
{1,f1} is non empty finite V38() non with_pair set
{{1,f1},{1}} is non empty finite V38() set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(C), the carrier of C] -tree <*f1*> is non empty Relation-like Function-like DecoratedTree-like set
(C) is (C,(C))
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*T*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,T] is pair non empty set
{1,T} is non empty finite V38() non with_pair set
{{1,T},{1}} is non empty finite V38() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*T*> is non empty Relation-like Function-like DecoratedTree-like set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C,T)) is finite Element of bool ()
(C,(C,T)) is finite Element of bool ()
C variables_in (C,T) is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in (C,T)) . (C) is finite set
((C,(C,T))) is set
(C,T) is finite Element of bool ()
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in T) . (C) is finite set
((C,T)) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) . (C) is set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
T is pair non empty (C)
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C,(C),(C)) .: (C,T) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,T)) is Element of bool ((C) . (C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
(C,(C,T)) is finite Element of bool ()
C variables_in (C,T) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,T)) . (C) is finite set
(union ((C,(C),(C)) .: (C,T))) \/ (C,(C,T)) is set
bool () is non empty Element of bool (bool ())
bool (bool ()) is non empty set
bool (bool ()) is non empty set
union (bool ()) is Element of bool ()
C is non empty non void V58() V259() () () ManySortedSign
T is pair non empty (C)
(C,T) is Element of bool ()
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) . (C) is set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C,(C),(C)) .: (C,T) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,T)) is Element of bool ((C) . (C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
(C,(C,T)) is finite Element of bool ()
C variables_in (C,T) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,T)) . (C) is finite set
(union ((C,(C),(C)) .: (C,T))) \/ (C,(C,T)) is set
f1 is set
f2 is set
(C,(C),(C)) . f2 is set
x is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C variables_in x is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in x) . (C) is finite set
C is non empty non void V58() V259() () () ManySortedSign
T is pair non empty (C)
(C,T) is finite Element of bool ()
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) . (C) is set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C,(C),(C)) .: (C,T) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,T)) is Element of bool ((C) . (C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
(C,(C,T)) is finite Element of bool ()
C variables_in (C,T) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,T)) . (C) is finite set
(union ((C,(C),(C)) .: (C,T))) \/ (C,(C,T)) is set
((C,T)) is set
C is non empty non void V58() V259() () () ManySortedSign
T is pair non empty (C)
(C,T) is finite Element of bool ()
(C,T) is finite Element of bool ()
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) . (C) is set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C,(C),(C)) .: (C,T) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,T)) is Element of bool ((C) . (C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
(C,(C,T)) is finite Element of bool ()
C variables_in (C,T) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,T)) . (C) is finite set
(union ((C,(C),(C)) .: (C,T))) \/ (C,(C,T)) is set
((C,T)) is set
((C,T)) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is pair non empty (C)
(C,T) is finite Element of bool ()
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C) . (C) is set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C,(C),(C)) .: (C,T) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,T)) is Element of bool ((C) . (C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
(C,(C,T)) is finite Element of bool ()
C variables_in (C,T) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,T)) . (C) is finite set
(union ((C,(C),(C)) .: (C,T))) \/ (C,(C,T)) is set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,f1) is pair non empty (C)
{f1} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
{f1} \/ (C,T) is non empty finite set
[({f1} \/ (C,T)),(C,T)] is pair non empty set
{({f1} \/ (C,T)),(C,T)} is non empty finite V38() set
{({f1} \/ (C,T))} is non empty trivial finite V38() 1 -element set
{{({f1} \/ (C,T)),(C,T)},{({f1} \/ (C,T))}} is non empty finite V38() set
(C,(C,T,f1)) is finite Element of bool ()
(C,(C,T,f1)) is functional finite constituted-DTrees Element of bool (C)
(C,(C),(C)) .: (C,(C,T,f1)) is finite Element of bool (bool ((C) . (C)))
union ((C,(C),(C)) .: (C,(C,T,f1))) is Element of bool ((C) . (C))
(C,(C,T,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,(C,T,f1))) is finite Element of bool ()
C variables_in (C,(C,T,f1)) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,(C,T,f1))) . (C) is finite set
(union ((C,(C),(C)) .: (C,(C,T,f1)))) \/ (C,(C,(C,T,f1))) is set
(C,f1) is finite Element of bool ()
C variables_in f1 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in f1) . (C) is finite set
(C,f1) \/ (C,T) is finite Element of bool ()
dom (C,(C),(C)) is Element of bool (Union the Sorts of (Free (C,(C))))
(union ((C,(C),(C)) .: (C,(C,T,f1)))) \/ (C,(C,T)) is set
(C,(C),(C)) .: ({f1} \/ (C,T)) is finite Element of bool (bool ((C) . (C)))
union ((C,(C),(C)) .: ({f1} \/ (C,T))) is Element of bool ((C) . (C))
(union ((C,(C),(C)) .: ({f1} \/ (C,T)))) \/ (C,(C,T)) is set
(C,(C),(C)) .: {f1} is finite Element of bool (bool ((C) . (C)))
((C,(C),(C)) .: {f1}) \/ ((C,(C),(C)) .: (C,T)) is finite Element of bool (bool ((C) . (C)))
union (((C,(C),(C)) .: {f1}) \/ ((C,(C),(C)) .: (C,T))) is Element of bool ((C) . (C))
(union (((C,(C),(C)) .: {f1}) \/ ((C,(C),(C)) .: (C,T)))) \/ (C,(C,T)) is set
union ((C,(C),(C)) .: {f1}) is Element of bool ((C) . (C))
(union ((C,(C),(C)) .: {f1})) \/ (union ((C,(C),(C)) .: (C,T))) is Element of bool ((C) . (C))
((union ((C,(C),(C)) .: {f1})) \/ (union ((C,(C),(C)) .: (C,T)))) \/ (C,(C,T)) is set
Im ((C,(C),(C)),f1) is set
{f1} is non empty trivial functional finite V38() 1 -element non with_pair set
(C,(C),(C)) .: {f1} is finite set
union (Im ((C,(C),(C)),f1)) is set
(union (Im ((C,(C),(C)),f1))) \/ (C,T) is set
(C,(C),(C)) . f1 is Element of bool ((C) . (C))
{((C,(C),(C)) . f1)} is non empty trivial finite 1 -element Element of bool (bool ((C) . (C)))
union {((C,(C),(C)) . f1)} is Element of bool ((C) . (C))
(union {((C,(C),(C)) . f1)}) \/ (C,T) is set
((C,(C),(C)) . f1) \/ (C,T) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
T is pair non empty (C)
(C,T) is finite Element of bool ()
(C,T) is finite Element of bool ()
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C) . (C) is set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C,(C),(C)) .: (C,T) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,T)) is Element of bool ((C) . (C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
(C,(C,T)) is finite Element of bool ()
C variables_in (C,T) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,T)) . (C) is finite set
(union ((C,(C),(C)) .: (C,T))) \/ (C,(C,T)) is set
((C,T)) is set
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,f1) is pair non empty (C)
{f1} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
{f1} \/ (C,T) is non empty finite set
[({f1} \/ (C,T)),(C,T)] is pair non empty set
{({f1} \/ (C,T)),(C,T)} is non empty finite V38() set
{({f1} \/ (C,T))} is non empty trivial finite V38() 1 -element set
{{({f1} \/ (C,T)),(C,T)},{({f1} \/ (C,T))}} is non empty finite V38() set
(C,(C,T,f1)) is finite Element of bool ()
(C,(C,T,f1)) is finite Element of bool ()
(C,(C,T,f1)) is functional finite constituted-DTrees Element of bool (C)
(C,(C),(C)) .: (C,(C,T,f1)) is finite Element of bool (bool ((C) . (C)))
union ((C,(C),(C)) .: (C,(C,T,f1))) is Element of bool ((C) . (C))
(C,(C,T,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,(C,T,f1))) is finite Element of bool ()
C variables_in (C,(C,T,f1)) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,(C,T,f1))) . (C) is finite set
(union ((C,(C),(C)) .: (C,(C,T,f1)))) \/ (C,(C,(C,T,f1))) is set
((C,(C,T,f1))) is set
(C,f1) is finite Element of bool ()
(C,f1) is finite Element of bool ()
C variables_in f1 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in f1) . (C) is finite set
((C,f1)) is set
(C,f1) \/ (C,T) is finite Element of bool ()
(C,f1) \/ (C,T) is finite Element of bool ()
(((C,f1) \/ (C,T))) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in T) . (C) is finite set
f1 is functional finite constituted-DTrees Element of bool (C)
(C,f1,T) is pair non empty (C)
{f1,T} is non empty finite V38() set
{f1} is non empty trivial finite V38() 1 -element set
{{f1,T},{f1}} is non empty finite V38() set
(C,(C,f1,T)) is finite Element of bool ()
(C) . (C) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,(C,f1,T)) is functional finite constituted-DTrees Element of bool (C)
(C,(C),(C)) .: (C,(C,f1,T)) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,(C,f1,T))) is Element of bool ((C) . (C))
(C,(C,f1,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,(C,f1,T))) is finite Element of bool ()
C variables_in (C,(C,f1,T)) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,(C,f1,T))) . (C) is finite set
(union ((C,(C),(C)) .: (C,(C,f1,T)))) \/ (C,(C,(C,f1,T))) is set
{ (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } is set
union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } is set
(union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } ) \/ (C,T) is set
(C,(C),(C)) .: f1 is finite Element of bool (bool ((C) . (C)))
a is set
dom (C,(C),(C)) is Element of bool (Union the Sorts of (Free (C,(C))))
b is set
(C,(C),(C)) . b is set
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,i) is finite Element of bool ()
C variables_in i is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in i) . (C) is finite set
a is set
b is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,b) is finite Element of bool ()
C variables_in b is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in b) . (C) is finite set
(C,(C),(C)) . b is Element of bool ((C) . (C))
dom (C,(C),(C)) is Element of bool (Union the Sorts of (Free (C,(C))))
(union ((C,(C),(C)) .: (C,(C,f1,T)))) \/ (C,T) is set
union ((C,(C),(C)) .: f1) is Element of bool ((C) . (C))
(union ((C,(C),(C)) .: f1)) \/ (C,T) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is finite Element of bool ()
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in T) . (C) is finite set
((C,T)) is set
f1 is functional finite constituted-DTrees Element of bool (C)
(C,f1,T) is pair non empty (C)
{f1,T} is non empty finite V38() set
{f1} is non empty trivial finite V38() 1 -element set
{{f1,T},{f1}} is non empty finite V38() set
(C,(C,f1,T)) is finite Element of bool ()
(C,(C,f1,T)) is finite Element of bool ()
(C) . (C) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,(C,f1,T)) is functional finite constituted-DTrees Element of bool (C)
(C,(C),(C)) .: (C,(C,f1,T)) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,(C,f1,T))) is Element of bool ((C) . (C))
(C,(C,f1,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,(C,f1,T))) is finite Element of bool ()
C variables_in (C,(C,f1,T)) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,(C,f1,T))) . (C) is finite set
(union ((C,(C),(C)) .: (C,(C,f1,T)))) \/ (C,(C,(C,f1,T))) is set
((C,(C,f1,T))) is set
{ (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } is set
union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } is set
(union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } ) \/ (C,T) is set
{ (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } is set
union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } is set
a is set
b is set
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,i) is finite Element of bool ()
C variables_in i is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in i) . (C) is finite set
(C,i) is finite Element of bool ()
((C,i)) is set
a is set
b is set
[a,b] is pair non empty set
{a,b} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,b},{a}} is non empty finite V38() set
i is set
pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,pi1) is finite Element of bool ()
(C,pi1) is finite Element of bool ()
C variables_in pi1 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in pi1) . (C) is finite set
((C,pi1)) is set
((union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } )) is set
a is set
b is set
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,i) is finite Element of bool ()
(C,i) is finite Element of bool ()
C variables_in i is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in i) . (C) is finite set
((C,i)) is set
(union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } ) \/ (C,T) is set
(((union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } ) \/ (C,T))) is set
((union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } )) \/ (C,T) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
{} (C) is non pair empty proper 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of bool (C)
bool (C) is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,({} (C)),T) is pair non empty (C)
{({} (C)),T} is non empty functional finite V38() non with_pair set
{({} (C))} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{({} (C)),T},{({} (C))}} is non empty finite V38() set
(C,(C,({} (C)),T)) is finite Element of bool ()
(C) is Element of the carrier of C
(C) . (C) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,(C,({} (C)),T)) is functional finite constituted-DTrees Element of bool (C)
(C,(C),(C)) .: (C,(C,({} (C)),T)) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,(C,({} (C)),T))) is Element of bool ((C) . (C))
(C,(C,({} (C)),T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,(C,({} (C)),T))) is finite Element of bool ()
C variables_in (C,(C,({} (C)),T)) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,(C,({} (C)),T))) . (C) is finite set
(union ((C,(C),(C)) .: (C,(C,({} (C)),T)))) \/ (C,(C,(C,({} (C)),T))) is set
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in T) . (C) is finite set
{ (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in {} (C) } is set
x is set
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,a) is finite Element of bool ()
C variables_in a is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in a) . (C) is finite set
union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in {} (C) } is set
(union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in {} (C) } ) \/ (C,T) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in T) . (C) is finite set
Union (C variables_in T) is set
proj2 (C variables_in T) is non empty set
union (proj2 (C variables_in T)) is set
Union (C variables_in T) is set
proj2 (C variables_in T) is non empty set
union (proj2 (C variables_in T)) is set
the Element of Union (C variables_in T) is Element of Union (C variables_in T)
dom (C variables_in T) is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
(C) . () is set
(C) . () is set
(C) is Element of the carrier of C
(C variables_in T) . (C) is finite set
(C) is Element of the carrier of C
(C variables_in T) . (C) is finite set
f2 is set
(C variables_in T) . f2 is set
C is non empty non void V58() V259() () () ManySortedSign
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier' of C is non empty set
T is Element of the carrier' of C
the_result_sort_of T is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . T is Element of the carrier of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
f1 is Element of the carrier' of C
the_result_sort_of f1 is Element of the carrier of C
the ResultSort of C . f1 is Element of the carrier of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
[T, the carrier of C] is pair non empty set
{T, the carrier of C} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T, the carrier of C},{T}} is non empty finite V38() set
root-tree [T, the carrier of C] is non empty Relation-like Function-like DecoratedTree-like set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
the Sorts of (Free (C,(C))) . (C) is non empty set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
<*> (Union the Sorts of (Free (C,(C)))) is non pair empty Relation-like non-empty empty-yielding NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[T, the carrier of C] -tree (<*> (Union the Sorts of (Free (C,(C))))) is non empty Relation-like Function-like DecoratedTree-like set
(C,f2) is finite Element of bool ()
C variables_in f2 is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in f2) . (C) is finite set
a is set
rng (<*> (Union the Sorts of (Free (C,(C))))) is non pair empty trivial proper 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered with_non-empty_elements V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
{ (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in rng (<*> (Union the Sorts of (Free (C,(C))))) } is set
union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in rng (<*> (Union the Sorts of (Free (C,(C))))) } is set
b is set
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,i) is finite Element of bool ()
C variables_in i is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in i) . (C) is finite set
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C) is Element of the carrier of C
the carrier' of C is non empty set
T is Element of the carrier' of C
the_result_sort_of T is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . T is Element of the carrier of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
f1 is Element of the carrier' of C
the_result_sort_of f1 is Element of the carrier of C
the ResultSort of C . f1 is Element of the carrier of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
[f1, the carrier of C] is pair non empty set
{f1, the carrier of C} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1, the carrier of C},{f1}} is non empty finite V38() set
root-tree [f1, the carrier of C] is non empty Relation-like Function-like DecoratedTree-like set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
<*> (Union the Sorts of (Free (C,(C)))) is non pair empty Relation-like non-empty empty-yielding NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[f1, the carrier of C] -tree (<*> (Union the Sorts of (Free (C,(C))))) is non empty Relation-like Function-like DecoratedTree-like set
(C,x) is finite Element of bool ()
C variables_in x is non empty Relation-like the carrier of C -defined Function-like total set
(C) is Element of the carrier of C
(C variables_in x) . (C) is finite set
b is set
rng (<*> (Union the Sorts of (Free (C,(C))))) is non pair empty trivial proper 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered with_non-empty_elements V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
{ (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in rng (<*> (Union the Sorts of (Free (C,(C))))) } is set
union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in rng (<*> (Union the Sorts of (Free (C,(C))))) } is set
i is set
pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,pi1) is finite Element of bool ()
C variables_in pi1 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in pi1) . (C) is finite set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
{} (C) is non pair empty proper 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of bool (C)
bool (C) is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C) (C,(C))
(C,({} (C)),T) is pair non empty (C)
{({} (C)),T} is non empty functional finite V38() non with_pair set
{({} (C))} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{({} (C)),T},{({} (C))}} is non empty finite V38() set
(C,(C,({} (C)),T)) is finite Element of bool ()
(C) is Element of the carrier of C
(C) . (C) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,(C,({} (C)),T)) is functional finite constituted-DTrees Element of bool (C)
(C,(C),(C)) .: (C,(C,({} (C)),T)) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,(C,({} (C)),T))) is Element of bool ((C) . (C))
(C,(C,({} (C)),T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,(C,({} (C)),T))) is finite Element of bool ()
C variables_in (C,(C,({} (C)),T)) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,(C,({} (C)),T))) . (C) is finite set
(union ((C,(C),(C)) .: (C,(C,({} (C)),T)))) \/ (C,(C,(C,({} (C)),T))) is set
(C,T) is finite Element of bool ()
C variables_in T is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in T) . (C) is finite set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
{} (C) is non pair empty proper 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of bool (C)
bool (C) is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C) (C,(C))
(C,({} (C)),T) is pair non empty (C)
{({} (C)),T} is non empty functional finite V38() non with_pair set
{({} (C))} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{({} (C)),T},{({} (C))}} is non empty finite V38() set
f1 is pair non empty (C)
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
(C) is Element of the carrier of C
the non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C) (C,(C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C) (C,(C))
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
{} (C) is non pair empty proper 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of bool (C)
bool (C) is non empty set
(C,({} (C)), the non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C) (C,(C))) is pair non empty (C) (C)
{({} (C)), the non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C) (C,(C))} is non empty functional finite V38() non with_pair set
{({} (C))} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{({} (C)), the non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C) (C,(C))},{({} (C))}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
(C) is Element of the carrier of C
T is pair non empty (C) (C)
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C) (C,(C))
(C,T,f1) is pair non empty (C)
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
{f1} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
{f1} \/ (C,T) is non empty finite set
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
[({f1} \/ (C,T)),(C,T)] is pair non empty set
{({f1} \/ (C,T)),(C,T)} is non empty finite V38() set
{({f1} \/ (C,T))} is non empty trivial finite V38() 1 -element set
{{({f1} \/ (C,T)),(C,T)},{({f1} \/ (C,T))}} is non empty finite V38() set
(C,(C,T,f1)) is finite Element of bool ()
(C) is Element of the carrier of C
(C) . (C) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,(C,T,f1)) is functional finite constituted-DTrees Element of bool (C)
(C,(C),(C)) .: (C,(C,T,f1)) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,(C,T,f1))) is Element of bool ((C) . (C))
(C,(C,T,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,(C,T,f1))) is finite Element of bool ()
C variables_in (C,(C,T,f1)) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,(C,T,f1))) . (C) is finite set
(union ((C,(C),(C)) .: (C,(C,T,f1)))) \/ (C,(C,(C,T,f1))) is set
(C,f1) is finite Element of bool ()
C variables_in f1 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in f1) . (C) is finite set
(C,T) is finite Element of bool ()
(C,(C),(C)) .: (C,T) is finite Element of bool (bool ((C) . (C)))
union ((C,(C),(C)) .: (C,T)) is Element of bool ((C) . (C))
(C,(C,T)) is finite Element of bool ()
C variables_in (C,T) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,T)) . (C) is finite set
(union ((C,(C),(C)) .: (C,T))) \/ (C,(C,T)) is set
(C,f1) \/ (C,T) is finite Element of bool ()
{} \/ (C,T) is finite set
{ (b₁) where b₁ is finite Element of bool () : verum } is set
InclPoset { (b₁) where b₁ is finite Element of bool () : verum } is strict total V203() V204() V205() RelStr
(InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ) ~ is strict total V203() V204() V205() RelStr
the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ) is set
the InternalRel of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ) is Relation-like the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ) -defined the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ) -valued total V99() V102() V106() Element of bool [: the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ), the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ):]
[: the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ), the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ):] is Relation-like set
bool [: the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ), the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ):] is non empty set
the InternalRel of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ) ~ is Relation-like the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ) -defined the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ) -valued Element of bool [: the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ), the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ):]
RelStr(# the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ),( the InternalRel of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ) ~) #) is strict RelStr
the finite Element of bool () is finite Element of bool ()
( the finite Element of bool ()) is set
f1 is non empty set
InclPoset f1 is non empty strict total V203() V204() V205() RelStr
f2 is non empty total V203() V204() V205() RelStr
f2 ~ is non empty strict total V203() V204() V205() RelStr
the carrier of f2 is non empty set
the InternalRel of f2 is Relation-like the carrier of f2 -defined the carrier of f2 -valued total V99() V102() V106() Element of bool [: the carrier of f2, the carrier of f2:]
[: the carrier of f2, the carrier of f2:] is non empty Relation-like set
bool [: the carrier of f2, the carrier of f2:] is non empty set
the InternalRel of f2 ~ is Relation-like the carrier of f2 -defined the carrier of f2 -valued Element of bool [: the carrier of f2, the carrier of f2:]
RelStr(# the carrier of f2,( the InternalRel of f2 ~) #) is non empty strict RelStr
() is non empty strict total V203() V204() V205() RelStr
the carrier of () is non empty set
C is Element of the carrier of ()
T is Element of the carrier of ()
the finite Element of bool () is finite Element of bool ()
( the finite Element of bool ()) is set
x is non empty set
InclPoset x is non empty strict total V203() V204() V205() RelStr
(InclPoset x) ~ is non empty strict total V203() V204() V205() RelStr
the carrier of (InclPoset x) is non empty set
the InternalRel of (InclPoset x) is Relation-like the carrier of (InclPoset x) -defined the carrier of (InclPoset x) -valued total V99() V102() V106() Element of bool [: the carrier of (InclPoset x), the carrier of (InclPoset x):]
[: the carrier of (InclPoset x), the carrier of (InclPoset x):] is non empty Relation-like set
bool [: the carrier of (InclPoset x), the carrier of (InclPoset x):] is non empty set
the InternalRel of (InclPoset x) ~ is Relation-like the carrier of (InclPoset x) -defined the carrier of (InclPoset x) -valued Element of bool [: the carrier of (InclPoset x), the carrier of (InclPoset x):]
RelStr(# the carrier of (InclPoset x),( the InternalRel of (InclPoset x) ~) #) is non empty strict RelStr
the carrier of ((InclPoset x) ~) is non empty set
b is Element of the carrier of ((InclPoset x) ~)
~ b is Element of the carrier of (InclPoset x)
a is Element of the carrier of ((InclPoset x) ~)
~ a is Element of the carrier of (InclPoset x)
C is set
(C) is set
the finite Element of bool () is finite Element of bool ()
( the finite Element of bool ()) is set
f2 is non empty set
InclPoset f2 is non empty strict total V203() V204() V205() RelStr
the carrier of (InclPoset f2) is non empty set
x is finite Element of bool ()
(x) is set
x is finite Element of bool ()
(x) is set
the finite Element of bool () is finite Element of bool ()
( the finite Element of bool ()) is set
f2 is set
f1 is non empty set
a is finite Element of bool ()
(a) is set
x is set
b is finite Element of bool ()
(b) is set
f2 \/ x is set
a \/ b is finite Element of bool ()
((a \/ b)) is set
InclPoset f1 is non empty strict total V203() V204() V205() RelStr
f2 is set
a is finite Element of bool ()
(a) is set
x is set
b is finite Element of bool ()
(b) is set
f2 /\ x is set
i is finite Element of bool ()
pi1 is finite Element of bool ()
i /\ pi1 is finite Element of bool ()
((i /\ pi1)) is set
C is Element of the carrier of ()
T is Element of the carrier of ()
C "\/" T is Element of the carrier of ()
C /\ T is set
C "/\" T is Element of the carrier of ()
C \/ T is set
the finite Element of bool () is finite Element of bool ()
( the finite Element of bool ()) is set
x is non empty set
InclPoset x is non empty strict total V203() V204() V205() RelStr
(InclPoset x) ~ is non empty strict total V203() V204() V205() RelStr
the carrier of (InclPoset x) is non empty set
the InternalRel of (InclPoset x) is Relation-like the carrier of (InclPoset x) -defined the carrier of (InclPoset x) -valued total V99() V102() V106() Element of bool [: the carrier of (InclPoset x), the carrier of (InclPoset x):]
[: the carrier of (InclPoset x), the carrier of (InclPoset x):] is non empty Relation-like set
bool [: the carrier of (InclPoset x), the carrier of (InclPoset x):] is non empty set
the InternalRel of (InclPoset x) ~ is Relation-like the carrier of (InclPoset x) -defined the carrier of (InclPoset x) -valued Element of bool [: the carrier of (InclPoset x), the carrier of (InclPoset x):]
RelStr(# the carrier of (InclPoset x),( the InternalRel of (InclPoset x) ~) #) is non empty strict RelStr
the carrier of ((InclPoset x) ~) is non empty set
z is finite Element of bool ()
(z) is set
x2 is finite Element of bool ()
(x2) is set
i is Element of the carrier of (InclPoset x)
i ~ is Element of the carrier of ((InclPoset x) ~)
a is Element of the carrier of ((InclPoset x) ~)
pi1 is Element of the carrier of (InclPoset x)
pi1 ~ is Element of the carrier of ((InclPoset x) ~)
b is Element of the carrier of ((InclPoset x) ~)
x1 is finite Element of bool ()
x2 is finite Element of bool ()
x1 /\ x2 is finite Element of bool ()
((x1 /\ x2)) is set
i "/\" pi1 is Element of the carrier of (InclPoset x)
z \/ x2 is finite Element of bool ()
((z \/ x2)) is set
i \/ pi1 is set
i "\/" pi1 is Element of the carrier of (InclPoset x)
C is Element of the carrier of ()
T is Element of the carrier of ()
C "\/" T is Element of the carrier of ()
C /\ T is set
C "/\" T is Element of the carrier of ()
C \/ T is set
bool the carrier of () is non empty set
C is non empty Element of bool the carrier of ()
"\/" (C,()) is Element of the carrier of ()
meet C is set
the Element of C is Element of C
f1 is Element of C
(f1) is set
((meet C)) is set
f1 is Element of the carrier of ()
f2 is Element of the carrier of ()
f2 is Element of the carrier of ()
x is set
a is Element of the carrier of ()
C is non empty directed Element of bool the carrier of ()
Top () is Element of the carrier of ()
{} () is non pair empty proper 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of bool ()
() ~ is non empty strict total V203() V204() V205() RelStr
the InternalRel of () is Relation-like the carrier of () -defined the carrier of () -valued total V99() V102() V106() Element of bool [: the carrier of (), the carrier of ():]
[: the carrier of (), the carrier of ():] is non empty Relation-like set
bool [: the carrier of (), the carrier of ():] is non empty set
the InternalRel of () ~ is Relation-like the carrier of () -defined the carrier of () -valued Element of bool [: the carrier of (), the carrier of ():]
RelStr(# the carrier of (),( the InternalRel of () ~) #) is non empty strict RelStr
Bottom (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ) is Element of the carrier of (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } )
(Bottom (InclPoset { (b₁) where b₁ is finite Element of bool () : verum } )) ~ is Element of the carrier of ((InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ) ~)
the carrier of ((InclPoset { (b₁) where b₁ is finite Element of bool () : verum } ) ~) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty set
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
{ [b₂,b₁] where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)), b₂ is functional finite constituted-DTrees Element of bool (C) : b₁ is (C) } is set
[:(C), the carrier of ():] is non empty Relation-like set
bool [:(C), the carrier of ():] is non empty set
T is Relation-like (C) -defined the carrier of () -valued Function-like quasi_total Element of bool [:(C), the carrier of ():]
f1 is Relation-like (C) -defined the carrier of () -valued Function-like quasi_total Element of bool [:(C), the carrier of ():]
f2 is Element of (C)
T . f2 is Element of the carrier of ()
x is pair non empty (C)
(C,x) is finite Element of bool ()
(C,x) is finite Element of bool ()
(C) is Element of the carrier of C
(C) . (C) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,x) is functional finite constituted-DTrees Element of bool (C)
(C,(C),(C)) .: (C,x) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,x)) is Element of bool ((C) . (C))
(C,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,x)) is finite Element of bool ()
C variables_in (C,x) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,x)) . (C) is finite set
(union ((C,(C),(C)) .: (C,x))) \/ (C,(C,x)) is set
((C,x)) is set
f1 . f2 is Element of the carrier of ()
T is set
f1 is pair non empty (C)
(C,f1) is finite Element of bool ()
(C,f1) is finite Element of bool ()
(C) is Element of the carrier of C
(C) . (C) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,f1) is functional finite constituted-DTrees Element of bool (C)
(C,(C),(C)) .: (C,f1) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,f1)) is Element of bool ((C) . (C))
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,f1)) is finite Element of bool ()
C variables_in (C,f1) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,f1)) . (C) is finite set
(union ((C,(C),(C)) .: (C,f1))) \/ (C,(C,f1)) is set
((C,f1)) is set
T is Relation-like Function-like set
proj1 T is set
proj2 T is set
f1 is set
f2 is set
T . f2 is set
x is pair non empty (C)
(C,x) is finite Element of bool ()
(C,x) is finite Element of bool ()
(C) is Element of the carrier of C
(C) . (C) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,x) is functional finite constituted-DTrees Element of bool (C)
(C,(C),(C)) .: (C,x) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,x)) is Element of bool ((C) . (C))
(C,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,x)) is finite Element of bool ()
C variables_in (C,x) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,x)) . (C) is finite set
(union ((C,(C),(C)) .: (C,x))) \/ (C,(C,x)) is set
((C,x)) is set
((C,x)) is set
f1 is Relation-like (C) -defined the carrier of () -valued Function-like quasi_total Element of bool [:(C), the carrier of ():]
f2 is pair non empty (C)
f1 . f2 is set
(C,f2) is finite Element of bool ()
(C,f2) is finite Element of bool ()
(C) is Element of the carrier of C
(C) . (C) is set
bool ((C) . (C)) is non empty Element of bool (bool ((C) . (C)))
bool ((C) . (C)) is non empty set
bool (bool ((C) . (C))) is non empty set
(C,(C),(C)) is Relation-like Union the Sorts of (Free (C,(C))) -defined bool ((C) . (C)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):]
[:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(bool ((C) . (C))):] is non empty set
(C,f2) is functional finite constituted-DTrees Element of bool (C)
(C,(C),(C)) .: (C,f2) is finite Element of bool (bool ((C) . (C)))
bool (bool ((C) . (C))) is non empty set
union ((C,(C),(C)) .: (C,f2)) is Element of bool ((C) . (C))
(C,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,f2)) is finite Element of bool ()
C variables_in (C,f2) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,f2)) . (C) is finite set
(union ((C,(C),(C)) .: (C,f2))) \/ (C,(C,f2)) is set
((C,f2)) is set
x is pair non empty (C)
(C,x) is finite Element of bool ()
(C,x) is finite Element of bool ()
(C,x) is functional finite constituted-DTrees Element of bool (C)
(C,(C),(C)) .: (C,x) is finite Element of bool (bool ((C) . (C)))
union ((C,(C),(C)) .: (C,x)) is Element of bool ((C) . (C))
(C,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,x)) is finite Element of bool ()
C variables_in (C,x) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,x)) . (C) is finite set
(union ((C,(C),(C)) .: (C,x))) \/ (C,(C,x)) is set
((C,x)) is set
C is non empty non void V58() V259() () () ManySortedSign
T is pair non empty (C) (C)
{T} is non empty trivial Relation-like finite 1 -element set
id {T} is non empty Relation-like {T} -defined {T} -valued Function-like one-to-one total finite V99() V101() V102() V106() V350() Element of bool [:{T},{T}:]
[:{T},{T}:] is non empty Relation-like finite set
bool [:{T},{T}:] is non empty finite V38() set
RelStr(# {T},(id {T}) #) is non empty strict total V203() V204() V205() RelStr
(C) is non empty set
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
{ [b₂,b₁] where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)), b₂ is functional finite constituted-DTrees Element of bool (C) : b₁ is (C) } is set
the carrier of RelStr(# {T},(id {T}) #) is non empty set
[: the carrier of RelStr(# {T},(id {T}) #), the carrier of ():] is non empty Relation-like set
bool [: the carrier of RelStr(# {T},(id {T}) #), the carrier of ():] is non empty set
(C) is Relation-like (C) -defined the carrier of () -valued Function-like quasi_total Element of bool [:(C), the carrier of ():]
[:(C), the carrier of ():] is non empty Relation-like set
bool [:(C), the carrier of ():] is non empty set
(C) | {T} is Relation-like {T} -defined (C) -defined the carrier of () -valued Function-like finite Element of bool [:(C), the carrier of ():]
(C) | the carrier of RelStr(# {T},(id {T}) #) is Relation-like (C) -defined the carrier of RelStr(# {T},(id {T}) #) -defined (C) -defined the carrier of () -valued Function-like Element of bool [:(C), the carrier of ():]
f2 is Relation-like the carrier of RelStr(# {T},(id {T}) #) -defined the carrier of () -valued Function-like quasi_total Element of bool [: the carrier of RelStr(# {T},(id {T}) #), the carrier of ():]
x is Element of the carrier of RelStr(# {T},(id {T}) #)
a is Element of the carrier of RelStr(# {T},(id {T}) #)
{x,a} is non empty finite Element of bool the carrier of RelStr(# {T},(id {T}) #)
bool the carrier of RelStr(# {T},(id {T}) #) is non empty set
f2 .: {x,a} is finite Element of bool the carrier of ()
"\/" ((f2 .: {x,a}),()) is Element of the carrier of ()
"\/" ({x,a},RelStr(# {T},(id {T}) #)) is Element of the carrier of RelStr(# {T},(id {T}) #)
f2 . ("\/" ({x,a},RelStr(# {T},(id {T}) #))) is Element of the carrier of ()
dom f2 is Element of bool the carrier of RelStr(# {T},(id {T}) #)
Im (f2,T) is set
f2 .: {T} is finite set
f2 . x is Element of the carrier of ()
{(f2 . x)} is non empty trivial finite 1 -element Element of bool the carrier of ()
F₁() is non empty non void V58() V259() () () ManySortedSign
(F₁()) is non empty Relation-like non empty-yielding the carrier of F₁() -defined Function-like total set
the carrier of F₁() is non empty set
Free (F₁(),(F₁())) is strict non-empty non empty MSAlgebra over F₁()
the Sorts of (Free (F₁(),(F₁()))) is non empty Relation-like non-empty non empty-yielding the carrier of F₁() -defined Function-like total set
Union the Sorts of (Free (F₁(),(F₁()))) is non empty set
proj2 the Sorts of (Free (F₁(),(F₁()))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (F₁(),(F₁())))) is set
the carrier' of F₁() is non empty set
(F₁()) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (F₁(),(F₁()))))
bool (Union the Sorts of (Free (F₁(),(F₁())))) is non empty set
(F₁()) is Element of the carrier of F₁()
the Sorts of (Free (F₁(),(F₁()))) . (F₁()) is non empty set
(F₁()) is Element of the carrier of F₁()
(F₁()) is (F₁(),(F₁()))
(F₁()) is Element of the carrier of F₁()
(F₁()) is (F₁(),(F₁()))
F₂() is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
the carrier of F₁() --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of F₁() -defined bool NAT -valued Function-like constant total quasi_total Element of bool [: the carrier of F₁(),(bool NAT):]
[: the carrier of F₁(),(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of F₁(),(bool NAT):] is non empty non trivial non finite set
(F₁()) \/ ( the carrier of F₁() --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of F₁() -defined Function-like total set
DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of F₁()} is non empty trivial finite 1 -element set
[: the carrier' of F₁(),{ the carrier of F₁()}:] is non empty Relation-like set
coprod ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of F₁() -defined Function-like total set
Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty set
proj2 (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod ((F₁()) \/ ( the carrier of F₁() --> {0})))) is set
[: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0})))) is non empty set
REL ((F₁()) \/ ( the carrier of F₁() --> {0})) is Relation-like [: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0})))) -defined ([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) * -valued Element of bool [:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) *):]
([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))
[:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(REL ((F₁()) \/ ( the carrier of F₁() --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
F₁() -Terms ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))) is non empty set
x is Element of the carrier of F₁()
((F₁()) \/ ( the carrier of F₁() --> {0})) . x is non empty set
[:(((F₁()) \/ ( the carrier of F₁() --> {0})) . x), the carrier of F₁():] is non empty Relation-like set
a is Element of ((F₁()) \/ ( the carrier of F₁() --> {0})) . x
[a,x] is pair non empty Element of [:(((F₁()) \/ ( the carrier of F₁() --> {0})) . x), the carrier of F₁():]
{a,x} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,x},{a}} is non empty finite V38() set
root-tree [a,x] is non empty Relation-like [:(((F₁()) \/ ( the carrier of F₁() --> {0})) . x), the carrier of F₁():] -valued Function-like DecoratedTree-like Element of FinTrees [:(((F₁()) \/ ( the carrier of F₁() --> {0})) . x), the carrier of F₁():]
FinTrees [:(((F₁()) \/ ( the carrier of F₁() --> {0})) . x), the carrier of F₁():] is non empty functional constituted-DTrees DTree-set of [:(((F₁()) \/ ( the carrier of F₁() --> {0})) . x), the carrier of F₁():]
(root-tree [a,x]) . {} is set
((root-tree [a,x]) . {}) `2 is set
i is Element of ()
(i,F<sub>1</sub>()) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) (F<sub>1</sub>(),(F<sub>1</sub>()))
[i,()] is pair non empty set
{i,()} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,()},{i}} is non empty finite V38() set
root-tree [i,()] is non empty Relation-like Function-like DecoratedTree-like set
pi1 is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (F<sub>1</sub>())
len pi1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
i is (F<sub>1</sub>()) Element of the carrier' of F<sub>1</sub>()
the_arity_of i is Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
the carrier of F<sub>1</sub>() * is non empty functional FinSequence-membered FinSequenceSet of the carrier of F<sub>1</sub>()
the Arity of F<sub>1</sub>() is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):]
[: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty Relation-like set
bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty set
the Arity of F<sub>1</sub>() . i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
len (the_arity_of i) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(F<sub>1</sub>(),i,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
pi1 is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (F<sub>1</sub>())
len pi1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
i is (F<sub>1</sub>()) Element of the carrier' of F<sub>1</sub>()
the_arity_of i is Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
the carrier of F<sub>1</sub>() * is non empty functional FinSequence-membered FinSequenceSet of the carrier of F<sub>1</sub>()
the Arity of F<sub>1</sub>() is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):]
[: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty Relation-like set
bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty set
the Arity of F<sub>1</sub>() . i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
len (the_arity_of i) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(F<sub>1</sub>(),i,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
[i, the carrier of F<sub>1</sub>()] is pair non empty set
{i, the carrier of F<sub>1</sub>()} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i, the carrier of F<sub>1</sub>()},{i}} is non empty finite V38() set
[i, the carrier of F<sub>1</sub>()] -tree pi1 is non empty Relation-like Function-like DecoratedTree-like set
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
(F<sub>1</sub>(),(F<sub>1</sub>()),i) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
(F<sub>1</sub>(),(F<sub>1</sub>()),i) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
the_arity_of (F<sub>1</sub>()) is Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
the carrier of F<sub>1</sub>() * is non empty functional FinSequence-membered FinSequenceSet of the carrier of F<sub>1</sub>()
the Arity of F<sub>1</sub>() is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):]
[: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty Relation-like set
bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty set
the Arity of F<sub>1</sub>() . (F<sub>1</sub>()) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
<*(F<sub>1</sub>())*> is non empty trivial Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
[1,(F<sub>1</sub>())] is pair non empty set
{1,(F<sub>1</sub>())} is non empty finite set
{{1,(F<sub>1</sub>())},{1}} is non empty finite V38() set
{[1,(F<sub>1</sub>())]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(F<sub>1</sub>())*> . 1 is set
len <*(F<sub>1</sub>())*> is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of NAT
[(F<sub>1</sub>()), the carrier of F<sub>1</sub>()] is pair non empty set
{(F<sub>1</sub>()), the carrier of F<sub>1</sub>()} is non empty finite set
{(F<sub>1</sub>())} is non empty trivial finite 1 -element set
{{(F<sub>1</sub>()), the carrier of F<sub>1</sub>()},{(F<sub>1</sub>())}} is non empty finite V38() set
<*i*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) *
(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
[1,i] is pair non empty set
{1,i} is non empty finite V38() non with_pair set
{{1,i},{1}} is non empty finite V38() set
{[1,i]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(F<sub>1</sub>()), the carrier of F<sub>1</sub>()] -tree <*i*> is non empty Relation-like Function-like DecoratedTree-like set
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
(F<sub>1</sub>(),(F<sub>1</sub>()),i,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
(F<sub>1</sub>(),(F<sub>1</sub>()),i,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
the_arity_of (F<sub>1</sub>()) is Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
the carrier of F<sub>1</sub>() * is non empty functional FinSequence-membered FinSequenceSet of the carrier of F<sub>1</sub>()
the Arity of F<sub>1</sub>() is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):]
[: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty Relation-like set
bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty set
the Arity of F<sub>1</sub>() . (F<sub>1</sub>()) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
<*(F<sub>1</sub>()),(F<sub>1</sub>())*> is non empty Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
<*(F<sub>1</sub>())*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(F<sub>1</sub>())] is pair non empty set
{1,(F<sub>1</sub>())} is non empty finite set
{{1,(F<sub>1</sub>())},{1}} is non empty finite V38() set
{[1,(F<sub>1</sub>())]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(F<sub>1</sub>())*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(F<sub>1</sub>())] is pair non empty set
{1,(F<sub>1</sub>())} is non empty finite set
{{1,(F<sub>1</sub>())},{1}} is non empty finite V38() set
{[1,(F<sub>1</sub>())]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(F<sub>1</sub>())*> ^ <*(F<sub>1</sub>())*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
<*(F<sub>1</sub>()),(F<sub>1</sub>())*> . 1 is set
<*(F<sub>1</sub>()),(F<sub>1</sub>())*> . 2 is set
len <*(F<sub>1</sub>()),(F<sub>1</sub>())*> is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of NAT
[(F<sub>1</sub>()), the carrier of F<sub>1</sub>()] is pair non empty set
{(F<sub>1</sub>()), the carrier of F<sub>1</sub>()} is non empty finite set
{(F<sub>1</sub>())} is non empty trivial finite 1 -element set
{{(F<sub>1</sub>()), the carrier of F<sub>1</sub>()},{(F<sub>1</sub>())}} is non empty finite V38() set
<*i,pi1*> is non empty Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) *
(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
<*i*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,i] is pair non empty set
{1,i} is non empty finite V38() non with_pair set
{{1,i},{1}} is non empty finite V38() set
{[1,i]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*pi1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,pi1] is pair non empty set
{1,pi1} is non empty finite V38() non with_pair set
{{1,pi1},{1}} is non empty finite V38() set
{[1,pi1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*i*> ^ <*pi1*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(F<sub>1</sub>()), the carrier of F<sub>1</sub>()] -tree <*i,pi1*> is non empty Relation-like Function-like DecoratedTree-like set
x is Element of the carrier' of F<sub>1</sub>()
Sym (x,((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is Element of NonTerminals (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))
NonTerminals (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is non empty Element of bool the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))
bool the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) : ex b<sub>2</sub> being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b<sub>1</sub> ==> b<sub>2</sub> } is set
[x, the carrier of F<sub>1</sub>()] is pair non empty set
{x, the carrier of F<sub>1</sub>()} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x, the carrier of F<sub>1</sub>()},{x}} is non empty finite V38() set
a is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding ArgumentSeq of Sym (x,((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))
rng a is functional finite constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))))
[x, the carrier of F<sub>1</sub>()] -tree a is non empty Relation-like Function-like DecoratedTree-like set
i is Element of ()
(i,F<sub>1</sub>()) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) (F<sub>1</sub>(),(F<sub>1</sub>()))
[i,()] is pair non empty set
{i,()} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,()},{i}} is non empty finite V38() set
root-tree [i,()] is non empty Relation-like Function-like DecoratedTree-like set
pi1 is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (F<sub>1</sub>())
len pi1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
i is (F<sub>1</sub>()) Element of the carrier' of F<sub>1</sub>()
the_arity_of i is Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
the carrier of F<sub>1</sub>() * is non empty functional FinSequence-membered FinSequenceSet of the carrier of F<sub>1</sub>()
the Arity of F<sub>1</sub>() is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):]
[: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty Relation-like set
bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty set
the Arity of F<sub>1</sub>() . i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
len (the_arity_of i) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(F<sub>1</sub>(),i,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
pi1 is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (F<sub>1</sub>())
len pi1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
i is (F<sub>1</sub>()) Element of the carrier' of F<sub>1</sub>()
the_arity_of i is Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
the carrier of F<sub>1</sub>() * is non empty functional FinSequence-membered FinSequenceSet of the carrier of F<sub>1</sub>()
the Arity of F<sub>1</sub>() is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):]
[: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty Relation-like set
bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty set
the Arity of F<sub>1</sub>() . i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
len (the_arity_of i) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(F<sub>1</sub>(),i,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
[i, the carrier of F<sub>1</sub>()] is pair non empty set
{i, the carrier of F<sub>1</sub>()} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i, the carrier of F<sub>1</sub>()},{i}} is non empty finite V38() set
[i, the carrier of F<sub>1</sub>()] -tree pi1 is non empty Relation-like Function-like DecoratedTree-like set
z is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
rng pi1 is finite Element of bool (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))))
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
(F<sub>1</sub>(),(F<sub>1</sub>()),i) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
(F<sub>1</sub>(),(F<sub>1</sub>()),i) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
the_arity_of (F<sub>1</sub>()) is Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
the carrier of F<sub>1</sub>() * is non empty functional FinSequence-membered FinSequenceSet of the carrier of F<sub>1</sub>()
the Arity of F<sub>1</sub>() is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):]
[: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty Relation-like set
bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty set
the Arity of F<sub>1</sub>() . (F<sub>1</sub>()) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
<*(F<sub>1</sub>())*> is non empty trivial Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
[1,(F<sub>1</sub>())] is pair non empty set
{1,(F<sub>1</sub>())} is non empty finite set
{{1,(F<sub>1</sub>())},{1}} is non empty finite V38() set
{[1,(F<sub>1</sub>())]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(F<sub>1</sub>())*> . 1 is set
len <*(F<sub>1</sub>())*> is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of NAT
[(F<sub>1</sub>()), the carrier of F<sub>1</sub>()] is pair non empty set
{(F<sub>1</sub>()), the carrier of F<sub>1</sub>()} is non empty finite set
{(F<sub>1</sub>())} is non empty trivial finite 1 -element set
{{(F<sub>1</sub>()), the carrier of F<sub>1</sub>()},{(F<sub>1</sub>())}} is non empty finite V38() set
<*i*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) *
(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
[1,i] is pair non empty set
{1,i} is non empty finite V38() non with_pair set
{{1,i},{1}} is non empty finite V38() set
{[1,i]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(F<sub>1</sub>()), the carrier of F<sub>1</sub>()] -tree <*i*> is non empty Relation-like Function-like DecoratedTree-like set
rng <*i*> is non empty trivial finite 1 -element non with_pair Element of bool (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))))
{i} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))))
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
(F<sub>1</sub>(),(F<sub>1</sub>()),i,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
(F<sub>1</sub>(),(F<sub>1</sub>()),i,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
the_arity_of (F<sub>1</sub>()) is Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
the carrier of F<sub>1</sub>() * is non empty functional FinSequence-membered FinSequenceSet of the carrier of F<sub>1</sub>()
the Arity of F<sub>1</sub>() is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):]
[: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty Relation-like set
bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty set
the Arity of F<sub>1</sub>() . (F<sub>1</sub>()) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
<*(F<sub>1</sub>()),(F<sub>1</sub>())*> is non empty Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
<*(F<sub>1</sub>())*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(F<sub>1</sub>())] is pair non empty set
{1,(F<sub>1</sub>())} is non empty finite set
{{1,(F<sub>1</sub>())},{1}} is non empty finite V38() set
{[1,(F<sub>1</sub>())]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(F<sub>1</sub>())*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(F<sub>1</sub>())] is pair non empty set
{1,(F<sub>1</sub>())} is non empty finite set
{{1,(F<sub>1</sub>())},{1}} is non empty finite V38() set
{[1,(F<sub>1</sub>())]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(F<sub>1</sub>())*> ^ <*(F<sub>1</sub>())*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
<*(F<sub>1</sub>()),(F<sub>1</sub>())*> . 1 is set
<*(F<sub>1</sub>()),(F<sub>1</sub>())*> . 2 is set
len <*(F<sub>1</sub>()),(F<sub>1</sub>())*> is non pair non empty epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() V328() V329() Element of NAT
[(F<sub>1</sub>()), the carrier of F<sub>1</sub>()] is pair non empty set
{(F<sub>1</sub>()), the carrier of F<sub>1</sub>()} is non empty finite set
{(F<sub>1</sub>())} is non empty trivial finite 1 -element set
{{(F<sub>1</sub>()), the carrier of F<sub>1</sub>()},{(F<sub>1</sub>())}} is non empty finite V38() set
<*i,pi1*> is non empty Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) *
(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
<*i*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,i] is pair non empty set
{1,i} is non empty finite V38() non with_pair set
{{1,i},{1}} is non empty finite V38() set
{[1,i]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*pi1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,pi1] is pair non empty set
{1,pi1} is non empty finite V38() non with_pair set
{{1,pi1},{1}} is non empty finite V38() set
{[1,pi1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*i*> ^ <*pi1*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(F<sub>1</sub>()), the carrier of F<sub>1</sub>()] -tree <*i,pi1*> is non empty Relation-like Function-like DecoratedTree-like set
rng <*i,pi1*> is non empty finite non with_pair Element of bool (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))))
{i,pi1} is non empty functional finite V38() non with_pair Element of bool (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))))
C is ManySortedSign
the carrier of C is set
{{}} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
the carrier' of C is non empty set
T is non empty Relation-like the carrier of C -defined Function-like total set
dom T is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
T " {{}} is set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
rng the ResultSort of C is Element of bool the carrier of C
f1 is Element of the carrier of C
T . f1 is set
f2 is set
the ResultSort of C . f2 is set
x is Element of the carrier' of C
a is Element of the carrier' of C
the_result_sort_of a is Element of the carrier of C
the ResultSort of C . a is Element of the carrier of C
f1 is set
T . f1 is set
f2 is Element of the carrier of C
T . f2 is set
x is Element of the carrier' of C
the_result_sort_of x is Element of the carrier of C
the ResultSort of C . x is Element of the carrier of C
[{},0] is pair non empty set
{{},0} is non empty functional finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{{},0},{{}}} is non empty finite V38() set
[(),[{},0]] is pair non empty set
{(),[{},0]} is non empty finite set
{{(),[{},0]},{()}} is non empty finite V38() set
[(),[{},0]] is pair non empty set
{(),[{},0]} is non empty finite set
{{(),[{},0]},{()}} is non empty finite V38() set
[(),[{},0]] is pair non empty set
{(),[{},0]} is non empty finite set
{{(),[{},0]},{()}} is non empty finite V38() set
[(<*> ()),0] is pair non empty Element of [:(() *),NAT:]
[:(() *),NAT:] is non empty non trivial Relation-like non finite set
{(<*> ()),0} is non empty functional finite V38() non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{(<*> ())} is non empty trivial functional finite V38() 1 -element non with_pair V315() V316() V317() V318() V319() V320() V322() V323() V324() V325() V326() set
{{(<*> ()),0},{(<*> ())}} is non empty finite V38() set
the carrier' of () is non empty set
x is Element of the carrier' of ()
a is Element of the carrier' of ()
b is Element of the carrier' of ()
the carrier of () is non empty set
the ResultSort of () is Relation-like the carrier' of () -defined the carrier of () -valued Function-like quasi_total Element of bool [: the carrier' of (), the carrier of ():]
[: the carrier' of (), the carrier of ():] is non empty Relation-like set
bool [: the carrier' of (), the carrier of ():] is non empty set
the ResultSort of () . x is Element of the carrier of ()
x `1 is set
the ResultSort of () . a is Element of the carrier of ()
a `1 is set
the ResultSort of () . b is Element of the carrier of ()
b `1 is set
i is set
rng the ResultSort of () is Element of bool the carrier of ()
bool the carrier of () is non empty set
C is non empty non void V58() V259() () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total set
the carrier of C is non empty set
f1 is set
(C) " {{}} is set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
the carrier' of C is non empty set
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
rng the ResultSort of C is Element of bool the carrier of C
bool the carrier of C is non empty set
dom (C) is non empty Element of bool the carrier of C
(C) . f1 is set
(C) is (C,(C))
(C) is Element of the carrier of C
the ResultSort of C . (C) is Element of the carrier of C
(C) is (C,(C))
(C) is Element of the carrier of C
the ResultSort of C . (C) is Element of the carrier of C
C is ManySortedSign
the carrier of C is set
T is Relation-like the carrier of C -defined Function-like total set
f1 is set
T " {{}} is set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
the carrier' of C is set
[: the carrier' of C, the carrier of C:] is Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
rng the ResultSort of C is Element of bool the carrier of C
bool the carrier of C is non empty set
dom T is Element of bool the carrier of C
T . f1 is set
proj2 T is set
C is ManySortedSign
the carrier of C is set
the Relation-like non-empty the carrier of C -defined Function-like total (C) set is Relation-like non-empty the carrier of C -defined Function-like total (C) set
C is () ManySortedSign
the carrier of C is set
T is Relation-like the carrier of C -defined Function-like total set
T " {{}} is set
dom T is Element of bool the carrier of C
bool the carrier of C is non empty set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
the carrier' of C is set
[: the carrier' of C, the carrier of C:] is Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
rng the ResultSort of C is Element of bool the carrier of C
C is non empty DTConstrStr
Terminals C is set
the carrier of C is non empty set
{ b₁ where b₁ is Element of the carrier of C : for b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set holds not b₁ ==> b₂ } is set
bool the carrier of C is non empty set
NonTerminals C is set
{ b₁ where b₁ is Element of the carrier of C : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
(Terminals C) \/ (NonTerminals C) is set
NonTerminals C is set
{ b₁ where b₁ is Element of the carrier of C : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
(Terminals C) \/ (NonTerminals C) is set
C is non empty DTConstrStr
the carrier of C is non empty set
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Rules of C is Relation-like the carrier of C -defined the carrier of C * -valued Element of bool [: the carrier of C,( the carrier of C *):]
[: the carrier of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier of C,( the carrier of C *):] is non empty set
T is non empty DTConstrStr
the Rules of T is Relation-like the carrier of T -defined the carrier of T * -valued Element of bool [: the carrier of T,( the carrier of T *):]
the carrier of T is non empty set
the carrier of T * is non empty functional FinSequence-membered FinSequenceSet of the carrier of T
[: the carrier of T,( the carrier of T *):] is non empty Relation-like set
bool [: the carrier of T,( the carrier of T *):] is non empty set
(C) is Element of bool the carrier of C
bool the carrier of C is non empty set
{ b₁ where b₁ is Element of the carrier of C : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
(T) is Element of bool the carrier of T
bool the carrier of T is non empty set
{ b₁ where b₁ is Element of the carrier of T : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
(T) is Element of bool the carrier of T
{ b₁ where b₁ is Element of the carrier of T : for b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set holds not b₁ ==> b₂ } is set
the carrier of C /\ (T) is Element of bool the carrier of T
(C) is Element of bool the carrier of C
{ b₁ where b₁ is Element of the carrier of C : for b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set holds not b₁ ==> b₂ } is set
f1 is set
f2 is Element of the carrier of C
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f2 is Element of the carrier of C
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
[f2,x] is pair non empty set
{f2,x} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,x},{f2}} is non empty finite V38() set
a is Element of the carrier of T
f1 is set
f2 is Element of the carrier of C
a is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
[f2,a] is pair non empty set
{f2,a} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,a},{f2}} is non empty finite V38() set
x is Element of the carrier of T
b is Element of the carrier of T
(C) \/ (C) is Element of bool the carrier of C
(T) \/ (T) is Element of bool the carrier of T
C is non empty DTConstrStr
(C) is Element of bool the carrier of C
the carrier of C is non empty set
bool the carrier of C is non empty set
{ b₁ where b₁ is Element of the carrier of C : for b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set holds not b₁ ==> b₂ } is set
T is non empty DTConstrStr
(T) is Element of bool the carrier of T
the carrier of T is non empty set
bool the carrier of T is non empty set
{ b₁ where b₁ is Element of the carrier of T : for b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set holds not b₁ ==> b₂ } is set
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Rules of C is Relation-like the carrier of C -defined the carrier of C * -valued Element of bool [: the carrier of C,( the carrier of C *):]
[: the carrier of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier of C,( the carrier of C *):] is non empty set
the Rules of T is Relation-like the carrier of T -defined the carrier of T * -valued Element of bool [: the carrier of T,( the carrier of T *):]
the carrier of T * is non empty functional FinSequence-membered FinSequenceSet of the carrier of T
[: the carrier of T,( the carrier of T *):] is non empty Relation-like set
bool [: the carrier of T,( the carrier of T *):] is non empty set
TS C is functional constituted-DTrees Element of bool (FinTrees the carrier of C)
FinTrees the carrier of C is non empty functional constituted-DTrees DTree-set of the carrier of C
bool (FinTrees the carrier of C) is non empty set
TS T is functional constituted-DTrees Element of bool (FinTrees the carrier of T)
FinTrees the carrier of T is non empty functional constituted-DTrees DTree-set of the carrier of T
bool (FinTrees the carrier of T) is non empty set
(T) is Element of bool the carrier of T
{ b₁ where b₁ is Element of the carrier of T : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
(T) \/ (T) is Element of bool the carrier of T
f1 is Element of the carrier of C
root-tree f1 is non empty Relation-like the carrier of C -valued Function-like DecoratedTree-like Element of FinTrees the carrier of C
f2 is Element of the carrier of T
root-tree f2 is non empty Relation-like the carrier of T -valued Function-like DecoratedTree-like Element of FinTrees the carrier of T
f1 is Element of the carrier of C
f2 is Relation-like NAT -defined FinTrees the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() FinSequence of TS C
roots f2 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of C
rng f2 is functional finite constituted-DTrees Element of bool (FinTrees the carrier of C)
f1 -tree f2 is non empty Relation-like the carrier of C -valued Function-like DecoratedTree-like Element of FinTrees the carrier of C
[:NAT, the carrier of C:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of C:] is non empty non trivial non finite set
[f1,(roots f2)] is pair non empty Element of [: the carrier of C,(bool [:NAT, the carrier of C:]):]
[: the carrier of C,(bool [:NAT, the carrier of C:]):] is non empty non trivial Relation-like non finite set
{f1,(roots f2)} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,(roots f2)},{f1}} is non empty finite V38() set
x is set
a is Element of the carrier of T
x is Relation-like NAT -defined FinTrees the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() FinSequence of TS T
roots x is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
f1 is set
f2 is non empty Relation-like the carrier of C -valued Function-like DecoratedTree-like Element of FinTrees the carrier of C
C is ManySortedSign
the carrier of C is set
T is Relation-like the carrier of C -defined Function-like total set
f1 is Relation-like the carrier of C -defined Function-like total set
T " {{}} is set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
the carrier' of C is set
[: the carrier' of C, the carrier of C:] is Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
rng the ResultSort of C is Element of bool the carrier of C
bool the carrier of C is non empty set
f2 is set
f1 " {{}} is set
dom f1 is Element of bool the carrier of C
f1 . f2 is set
dom T is Element of bool the carrier of C
T . f2 is set
C is set
T is Relation-like C -defined Function-like total set
f1 is Relation-like C -defined Function-like total set
coprod T is Relation-like C -defined Function-like total set
Union (coprod T) is set
proj2 (coprod T) is set
union (proj2 (coprod T)) is set
coprod f1 is Relation-like C -defined Function-like total set
Union (coprod f1) is set
proj2 (coprod f1) is set
union (proj2 (coprod f1)) is set
dom f1 is Element of bool C
bool C is non empty set
f2 is set
f2 `2 is set
dom T is Element of bool C
f2 `1 is set
T . (f2 `2) is set
[(f2 `1),(f2 `2)] is pair non empty set
{(f2 `1),(f2 `2)} is non empty finite set
{(f2 `1)} is non empty trivial finite 1 -element set
{{(f2 `1),(f2 `2)},{(f2 `1)}} is non empty finite V38() set
f1 . (f2 `2) is set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like the carrier of C -defined Function-like total set
f1 is non empty Relation-like the carrier of C -defined Function-like total set
DTConMSA T is non empty strict DTConstrStr
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod T is non empty Relation-like the carrier of C -defined Function-like total set
Union (coprod T) is set
proj2 (coprod T) is non empty set
union (proj2 (coprod T)) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) is non empty set
REL T is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(REL T) #) is non empty strict DTConstrStr
the carrier of (DTConMSA T) is non empty set
DTConMSA f1 is non empty strict DTConstrStr
coprod f1 is non empty Relation-like the carrier of C -defined Function-like total set
Union (coprod f1) is set
proj2 (coprod f1) is non empty set
union (proj2 (coprod f1)) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1)) is non empty set
REL f1 is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1)) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(REL f1) #) is non empty strict DTConstrStr
the carrier of (DTConMSA f1) is non empty set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
T is non empty Relation-like the carrier of C -defined Function-like total set
DTConMSA T is non empty strict DTConstrStr
coprod T is non empty Relation-like the carrier of C -defined Function-like total set
Union (coprod T) is set
proj2 (coprod T) is non empty set
union (proj2 (coprod T)) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) is non empty set
REL T is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(REL T) #) is non empty strict DTConstrStr
((DTConMSA T)) is Element of bool the carrier of (DTConMSA T)
the carrier of (DTConMSA T) is non empty set
bool the carrier of (DTConMSA T) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA T) : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
((DTConMSA T)) is Element of bool the carrier of (DTConMSA T)
{ b₁ where b₁ is Element of the carrier of (DTConMSA T) : for b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set holds not b₁ ==> b₂ } is set
x is set
a is set
[x,a] is pair non empty set
{x,a} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,a},{x}} is non empty finite V38() set
b is Element of the carrier' of C
[b, the carrier of C] is pair non empty set
{b, the carrier of C} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b, the carrier of C},{b}} is non empty finite V38() set
the_arity_of b is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . b is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of b) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Seg (len (the_arity_of b)) is finite len (the_arity_of b) -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b₁ & b₁ <= len (the_arity_of b) ) } is set
z is set
(the_arity_of b) . z is set
T . ((the_arity_of b) . z) is set
coprod (((the_arity_of b) . z),T) is set
dom (the_arity_of b) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
rng (the_arity_of b) is finite Element of bool the carrier of C
bool the carrier of C is non empty set
x1 is set
[x1,((the_arity_of b) . z)] is pair non empty set
{x1,((the_arity_of b) . z)} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,((the_arity_of b) . z)},{x1}} is non empty finite V38() set
x2 is pair non empty set
dom (coprod T) is non empty Element of bool the carrier of C
(coprod T) . ((the_arity_of b) . z) is set
x2 is Element of the carrier of C
x1 is Element of the carrier' of C
the_result_sort_of x1 is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . x1 is Element of the carrier of C
[x1, the carrier of C] is pair non empty set
{x1, the carrier of C} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1, the carrier of C},{x1}} is non empty finite V38() set
x2 is pair non empty set
z is Relation-like Function-like set
proj1 z is set
x2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
proj2 x2 is finite set
x1 is set
dom x2 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
x2 is set
x2 . x2 is set
x1 is Relation-like NAT -defined [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))
x2 is Relation-like NAT -defined [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) -valued Function-like finite FinSequence-like FinSubsequence-like Element of ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *
len x2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
p is set
dom x2 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
x2 . p is set
(the_arity_of b) . p is set
T . ((the_arity_of b) . p) is set
coprod (((the_arity_of b) . p),T) is set
dom (the_arity_of b) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
rng (the_arity_of b) is finite Element of bool the carrier of C
bool the carrier of C is non empty set
dom (coprod T) is non empty Element of bool the carrier of C
(coprod T) . ((the_arity_of b) . p) is set
c is Element of the carrier' of C
[c, the carrier of C] is pair non empty set
{c, the carrier of C} is non empty finite set
{c} is non empty trivial finite 1 -element set
{{c, the carrier of C},{c}} is non empty finite V38() set
the_result_sort_of c is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . c is Element of the carrier of C
c is Element of the carrier' of C
[c, the carrier of C] is pair non empty set
{c, the carrier of C} is non empty finite set
{c} is non empty trivial finite 1 -element set
{{c, the carrier of C},{c}} is non empty finite V38() set
the_result_sort_of c is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . c is Element of the carrier of C
a is Element of the carrier' of C
[a, the carrier of C] is pair non empty set
{a, the carrier of C} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a, the carrier of C},{a}} is non empty finite V38() set
the_result_sort_of a is Element of the carrier of C
the ResultSort of C . a is Element of the carrier of C
c is Element of the carrier' of C
[c, the carrier of C] is pair non empty set
{c, the carrier of C} is non empty finite set
{c} is non empty trivial finite 1 -element set
{{c, the carrier of C},{c}} is non empty finite V38() set
the_result_sort_of c is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . c is Element of the carrier of C
i is Element of the carrier of (DTConMSA T)
[i,x2] is pair non empty Element of [: the carrier of (DTConMSA T),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):]
[: the carrier of (DTConMSA T),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty Relation-like set
{i,x2} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,x2},{i}} is non empty finite V38() set
x is set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like the carrier of C -defined Function-like total set
f1 is non empty Relation-like the carrier of C -defined Function-like total set
DTConMSA T is non empty strict DTConstrStr
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod T is non empty Relation-like the carrier of C -defined Function-like total set
Union (coprod T) is set
proj2 (coprod T) is non empty set
union (proj2 (coprod T)) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) is non empty set
REL T is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(REL T) #) is non empty strict DTConstrStr
((DTConMSA T)) is Element of bool the carrier of (DTConMSA T)
the carrier of (DTConMSA T) is non empty set
bool the carrier of (DTConMSA T) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA T) : for b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set holds not b₁ ==> b₂ } is set
DTConMSA f1 is non empty strict DTConstrStr
coprod f1 is non empty Relation-like the carrier of C -defined Function-like total set
Union (coprod f1) is set
proj2 (coprod f1) is non empty set
union (proj2 (coprod f1)) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1)) is non empty set
REL f1 is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1)) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(REL f1) #) is non empty strict DTConstrStr
((DTConMSA f1)) is Element of bool the carrier of (DTConMSA f1)
the carrier of (DTConMSA f1) is non empty set
bool the carrier of (DTConMSA f1) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA f1) : for b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set holds not b₁ ==> b₂ } is set
the carrier of (DTConMSA T) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (DTConMSA T)
the Rules of (DTConMSA T) is Relation-like the carrier of (DTConMSA T) -defined the carrier of (DTConMSA T) * -valued Element of bool [: the carrier of (DTConMSA T),( the carrier of (DTConMSA T) *):]
[: the carrier of (DTConMSA T),( the carrier of (DTConMSA T) *):] is non empty Relation-like set
bool [: the carrier of (DTConMSA T),( the carrier of (DTConMSA T) *):] is non empty set
the Rules of (DTConMSA f1) is Relation-like the carrier of (DTConMSA f1) -defined the carrier of (DTConMSA f1) * -valued Element of bool [: the carrier of (DTConMSA f1),( the carrier of (DTConMSA f1) *):]
the carrier of (DTConMSA f1) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (DTConMSA f1)
[: the carrier of (DTConMSA f1),( the carrier of (DTConMSA f1) *):] is non empty Relation-like set
bool [: the carrier of (DTConMSA f1),( the carrier of (DTConMSA f1) *):] is non empty set
TS (DTConMSA T) is functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA T))
FinTrees the carrier of (DTConMSA T) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA T)
bool (FinTrees the carrier of (DTConMSA T)) is non empty set
TS (DTConMSA f1) is functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA f1))
FinTrees the carrier of (DTConMSA f1) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA f1)
bool (FinTrees the carrier of (DTConMSA f1)) is non empty set
a is set
b is set
[a,b] is pair non empty set
{a,b} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,b},{a}} is non empty finite V38() set
i is Element of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))
z is Relation-like NAT -defined [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) -valued Function-like finite FinSequence-like FinSubsequence-like Element of ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *
x1 is Element of the carrier' of C
[x1, the carrier of C] is pair non empty set
{x1, the carrier of C} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1, the carrier of C},{x1}} is non empty finite V38() set
pi1 is Element of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))
x2 is Relation-like NAT -defined [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1)) -valued Function-like finite FinSequence-like FinSubsequence-like Element of ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *
len x2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
the_arity_of x1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . x1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of x1) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
x2 is set
dom x2 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
x2 . x2 is set
z . x2 is set
(the_arity_of x1) . x2 is set
p is Element of the carrier' of C
[p, the carrier of C] is pair non empty set
{p, the carrier of C} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p, the carrier of C},{p}} is non empty finite V38() set
the_result_sort_of p is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . p is Element of the carrier of C
Seg (len x2) is finite len x2 -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b₁ & b₁ <= len x2 ) } is set
dom (the_arity_of x1) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
coprod (((the_arity_of x1) . x2),T) is set
T . ((the_arity_of x1) . x2) is set
f1 . ((the_arity_of x1) . x2) is set
coprod (((the_arity_of x1) . x2),f1) is set
p is set
[p,((the_arity_of x1) . x2)] is pair non empty set
{p,((the_arity_of x1) . x2)} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p,((the_arity_of x1) . x2)},{p}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
DTConMSA (C) is non empty strict DTConstrStr
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod (C) is non empty Relation-like the carrier of C -defined Function-like total set
Union (coprod (C)) is set
proj2 (coprod (C)) is non empty set
union (proj2 (coprod (C))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C))) is non empty set
REL (C) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))),(REL (C)) #) is non empty strict DTConstrStr
((DTConMSA (C))) is Element of bool the carrier of (DTConMSA (C))
the carrier of (DTConMSA (C)) is non empty set
bool the carrier of (DTConMSA (C)) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA (C)) : for b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set holds not b₁ ==> b₂ } is set
(C) is Element of the carrier of C
T is set
dom (C) is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
(C) . () is set
(C) . () is set
(C) . () is set
T `2 is set
T `1 is set
(C) . (T `2) is set
f2 is Element of ()
x is Element of ()
[x,(C)] is pair non empty Element of [:(), the carrier of C:]
[:(), the carrier of C:] is non empty Relation-like set
{x,(C)} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,(C)},{x}} is non empty finite V38() set
f2 is Element of ()
[f2,(C)] is pair non empty Element of [:(), the carrier of C:]
{f2,(C)} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,(C)},{f2}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
DTConMSA (C) is non empty strict DTConstrStr
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod (C) is non empty Relation-like the carrier of C -defined Function-like total set
Union (coprod (C)) is set
proj2 (coprod (C)) is non empty set
union (proj2 (coprod (C))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C))) is non empty set
REL (C) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (C)))),(REL (C)) #) is non empty strict DTConstrStr
((DTConMSA (C))) is Element of bool the carrier of (DTConMSA (C))
the carrier of (DTConMSA (C)) is non empty set
bool the carrier of (DTConMSA (C)) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of (DTConMSA (C)) : ex b<sub>2</sub> being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b<sub>1</sub> ==> b<sub>2</sub> } is set
(C) is (C,(C))
(C) is Element of the carrier of C
[(C), the carrier of C] is pair non empty set
{(C), the carrier of C} is non empty finite set
{(C)} is non empty trivial finite 1 -element set
{{(C), the carrier of C},{(C)}} is non empty finite V38() set
(C) is (C,(C))
(C) is Element of the carrier of C
[(C), the carrier of C] is pair non empty set
{(C), the carrier of C} is non empty finite set
{(C)} is non empty trivial finite 1 -element set
{{(C), the carrier of C},{(C)}} is non empty finite V38() set
T is set
f2 is set
x is set
[f2,x] is pair non empty set
{f2,x} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,x},{f2}} is non empty finite V38() set
a is Element of the carrier' of C
f2 is (C) Element of the carrier' of C
[f2, the carrier of C] is pair non empty set
{f2, the carrier of C} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2, the carrier of C},{f2}} is non empty finite V38() set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined the carrier of C -defined bool NAT -valued Function-like constant total total quasi_total (C) Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
T is non empty Relation-like the carrier of C -defined Function-like total (C) set
Free (C,T) is strict MSAlgebra over C
the Sorts of (Free (C,T)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,T)) is set
proj2 the Sorts of (Free (C,T)) is non empty set
union (proj2 the Sorts of (Free (C,T))) is set
T \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined the carrier of C -defined Function-like total total (C) set
DTConMSA (T \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod (T \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined the carrier of C -defined Function-like total total (C) set
Union (coprod (T \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod (T \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod (T \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0})))) is non empty set
REL (T \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(REL (T \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))
C -Terms (T \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))) is non empty set
C -Terms (T,(T \/ ( the carrier of C --> {0}))) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA (T \/ ( the carrier of C --> {0})))
FreeMSA (T \/ ( the carrier of C --> {0})) is strict non-empty V172(C) MSAlgebra over C
FreeSort (T \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() (C) set
FreeOper (T \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier' of C -defined Function-like total ManySortedFunction of the Arity of C * ((FreeSort (T \/ ( the carrier of C --> {0}))) #), the ResultSort of C * (FreeSort (T \/ ( the carrier of C --> {0})))
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
(FreeSort (T \/ ( the carrier of C --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of C * -defined Function-like total set
the Arity of C * ((FreeSort (T \/ ( the carrier of C --> {0}))) #) is Relation-like non-empty the carrier' of C -defined Function-like set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C * (FreeSort (T \/ ( the carrier of C --> {0}))) is Relation-like non-empty the carrier' of C -defined Function-like set
MSAlgebra(# (FreeSort (T \/ ( the carrier of C --> {0}))),(FreeOper (T \/ ( the carrier of C --> {0}))) #) is strict MSAlgebra over C
the Sorts of (FreeMSA (T \/ ( the carrier of C --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() (C) set
a is set
dom the Sorts of (Free (C,T)) is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
b is set
the Sorts of (Free (C,T)) . b is set
i is Element of the carrier of C
the Sorts of (Free (C,T)) . i is set
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (T \/ ( the carrier of C --> {0})) : ( the_sort_of b<sub>1</sub> = i & variables_in b<sub>1</sub> c= T ) } is set
pi1 is non empty Relation-like the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (T \/ ( the carrier of C --> {0}))
the_sort_of pi1 is Element of the carrier of C
variables_in pi1 is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of T \/ ( the carrier of C --> {0})
C variables_in pi1 is non empty Relation-like the carrier of C -defined Function-like total set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined the carrier of C -defined bool NAT -valued Function-like constant total total quasi_total (C) Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
T is non empty Relation-like the carrier of C -defined Function-like total (C) set
T \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined the carrier of C -defined Function-like total total (C) set
DTConMSA (T \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod (T \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined the carrier of C -defined Function-like total total (C) set
Union (coprod (T \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod (T \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod (T \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0})))) is non empty set
REL (T \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(REL (T \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))
C -Terms (T \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))) is non empty set
Free (C,T) is strict MSAlgebra over C
the Sorts of (Free (C,T)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,T)) is set
proj2 the Sorts of (Free (C,T)) is non empty set
union (proj2 the Sorts of (Free (C,T))) is set
C -Terms (T,(T \/ ( the carrier of C --> {0}))) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA (T \/ ( the carrier of C --> {0})))
FreeMSA (T \/ ( the carrier of C --> {0})) is strict non-empty V172(C) MSAlgebra over C
FreeSort (T \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() (C) set
FreeOper (T \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier' of C -defined Function-like total ManySortedFunction of the Arity of C * ((FreeSort (T \/ ( the carrier of C --> {0}))) #), the ResultSort of C * (FreeSort (T \/ ( the carrier of C --> {0})))
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
(FreeSort (T \/ ( the carrier of C --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of C * -defined Function-like total set
the Arity of C * ((FreeSort (T \/ ( the carrier of C --> {0}))) #) is Relation-like non-empty the carrier' of C -defined Function-like set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C * (FreeSort (T \/ ( the carrier of C --> {0}))) is Relation-like non-empty the carrier' of C -defined Function-like set
MSAlgebra(# (FreeSort (T \/ ( the carrier of C --> {0}))),(FreeOper (T \/ ( the carrier of C --> {0}))) #) is strict MSAlgebra over C
the Sorts of (FreeMSA (T \/ ( the carrier of C --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() (C) set
a is non empty Relation-like the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (T \/ ( the carrier of C --> {0}))
the_sort_of a is Element of the carrier of C
the Sorts of (Free (C,T)) . (the_sort_of a) is set
dom the Sorts of (Free (C,T)) is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
b is set
the Sorts of (Free (C,T)) . b is set
i is Element of the carrier of C
the Sorts of (Free (C,T)) . i is set
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (T \/ ( the carrier of C --> {0})) : ( the_sort_of b<sub>1</sub> = i & variables_in b<sub>1</sub> c= T ) } is set
pi1 is non empty Relation-like the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (T \/ ( the carrier of C --> {0}))
the_sort_of pi1 is Element of the carrier of C
variables_in pi1 is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of T \/ ( the carrier of C --> {0})
C variables_in pi1 is non empty Relation-like the carrier of C -defined Function-like total set
C is non empty DTConstrStr
the carrier of C is non empty set
T is Element of the carrier of C
f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
[T,f1] is pair non empty set
{T,f1} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T,f1},{T}} is non empty finite V38() set
the Rules of C is Relation-like the carrier of C -defined the carrier of C * -valued Element of bool [: the carrier of C,( the carrier of C *):]
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
[: the carrier of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier of C,( the carrier of C *):] is non empty set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like the carrier of C -defined Function-like total set
DTConMSA T is non empty strict DTConstrStr
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod T is non empty Relation-like the carrier of C -defined Function-like total set
Union (coprod T) is set
proj2 (coprod T) is non empty set
union (proj2 (coprod T)) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) is non empty set
REL T is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(REL T) #) is non empty strict DTConstrStr
the carrier of (DTConMSA T) is non empty set
f1 is non empty Relation-like the carrier of C -defined Function-like total set
DTConMSA f1 is non empty strict DTConstrStr
coprod f1 is non empty Relation-like the carrier of C -defined Function-like total set
Union (coprod f1) is set
proj2 (coprod f1) is non empty set
union (proj2 (coprod f1)) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1)) is non empty set
REL f1 is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1)) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod f1))),(REL f1) #) is non empty strict DTConstrStr
the carrier of (DTConMSA f1) is non empty set
dom f1 is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
a is Element of the carrier of (DTConMSA T)
b is Element of the carrier of (DTConMSA f1)
i is Relation-like NAT -defined the carrier of (DTConMSA T) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA T)
pi1 is Relation-like NAT -defined the carrier of (DTConMSA f1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA f1)
[:NAT, the carrier of (DTConMSA T):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (DTConMSA T):] is non empty non trivial non finite set
[a,i] is pair non empty Element of [: the carrier of (DTConMSA T),(bool [:NAT, the carrier of (DTConMSA T):]):]
[: the carrier of (DTConMSA T),(bool [:NAT, the carrier of (DTConMSA T):]):] is non empty non trivial Relation-like non finite set
{a,i} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,i},{a}} is non empty finite V38() set
z is Element of the carrier' of C
[z, the carrier of C] is pair non empty set
{z, the carrier of C} is non empty finite set
{z} is non empty trivial finite 1 -element set
{{z, the carrier of C},{z}} is non empty finite V38() set
len pi1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
the_arity_of z is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . z is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of z) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
x2 is set
dom pi1 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
pi1 . x2 is set
(the_arity_of z) . x2 is set
x1 is Element of the carrier' of C
[x1, the carrier of C] is pair non empty set
{x1, the carrier of C} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1, the carrier of C},{x1}} is non empty finite V38() set
the_result_sort_of x1 is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . x1 is Element of the carrier of C
dom (the_arity_of z) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
rng (the_arity_of z) is finite Element of bool the carrier of C
(pi1 . x2) `2 is set
(pi1 . x2) `1 is set
f1 . ((pi1 . x2) `2) is set
[((pi1 . x2) `1),((pi1 . x2) `2)] is pair non empty set
{((pi1 . x2) `1),((pi1 . x2) `2)} is non empty finite set
{((pi1 . x2) `1)} is non empty trivial finite 1 -element set
{{((pi1 . x2) `1),((pi1 . x2) `2)},{((pi1 . x2) `1)}} is non empty finite V38() set
rng i is finite Element of bool the carrier of (DTConMSA T)
bool the carrier of (DTConMSA T) is non empty set
x1 is Element of the carrier of C
coprod (x1,T) is set
T . x1 is set
x2 is set
[x2,x1] is pair non empty set
{x2,x1} is non empty finite set
{x2} is non empty trivial finite 1 -element set
{{x2,x1},{x2}} is non empty finite V38() set
coprod (((the_arity_of z) . x2),f1) is set
[:NAT, the carrier of (DTConMSA f1):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (DTConMSA f1):] is non empty non trivial non finite set
[b,pi1] is pair non empty Element of [: the carrier of (DTConMSA f1),(bool [:NAT, the carrier of (DTConMSA f1):]):]
[: the carrier of (DTConMSA f1),(bool [:NAT, the carrier of (DTConMSA f1):]):] is non empty non trivial Relation-like non finite set
{b,pi1} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,pi1},{b}} is non empty finite V38() set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like the carrier of C -defined Function-like total (C) set
Free (C,T) is strict MSAlgebra over C
the Sorts of (Free (C,T)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,T)) is set
proj2 the Sorts of (Free (C,T)) is non empty set
union (proj2 the Sorts of (Free (C,T))) is set
DTConMSA T is non empty strict DTConstrStr
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite 1 -element set
[: the carrier' of C,{ the carrier of C}:] is non empty Relation-like set
coprod T is non empty Relation-like the carrier of C -defined Function-like total set
Union (coprod T) is set
proj2 (coprod T) is non empty set
union (proj2 (coprod T)) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) is non empty set
REL T is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T)) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod T))),(REL T) #) is non empty strict DTConstrStr
TS (DTConMSA T) is functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA T))
the carrier of (DTConMSA T) is non empty set
FinTrees the carrier of (DTConMSA T) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA T)
bool (FinTrees the carrier of (DTConMSA T)) is non empty set
the carrier of C --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of C -defined the carrier of C -defined bool NAT -valued Function-like constant total total quasi_total (C) Element of bool [: the carrier of C,(bool NAT):]
[: the carrier of C,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of C,(bool NAT):] is non empty non trivial non finite set
T \/ ( the carrier of C --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined the carrier of C -defined Function-like total total (C) set
C -Terms (T,(T \/ ( the carrier of C --> {0}))) is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA (T \/ ( the carrier of C --> {0})))
FreeMSA (T \/ ( the carrier of C --> {0})) is strict non-empty V172(C) MSAlgebra over C
FreeSort (T \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() (C) set
FreeOper (T \/ ( the carrier of C --> {0})) is non empty Relation-like the carrier' of C -defined Function-like total ManySortedFunction of the Arity of C * ((FreeSort (T \/ ( the carrier of C --> {0}))) #), the ResultSort of C * (FreeSort (T \/ ( the carrier of C --> {0})))
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
(FreeSort (T \/ ( the carrier of C --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of C * -defined Function-like total set
the Arity of C * ((FreeSort (T \/ ( the carrier of C --> {0}))) #) is Relation-like non-empty the carrier' of C -defined Function-like set
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C * (FreeSort (T \/ ( the carrier of C --> {0}))) is Relation-like non-empty the carrier' of C -defined Function-like set
MSAlgebra(# (FreeSort (T \/ ( the carrier of C --> {0}))),(FreeOper (T \/ ( the carrier of C --> {0}))) #) is strict MSAlgebra over C
the Sorts of (FreeMSA (T \/ ( the carrier of C --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total V159() (C) set
dom the Sorts of (Free (C,T)) is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
b is Element of the carrier of C
(T \/ ( the carrier of C --> {0})) . b is non empty set
[:((T \/ ( the carrier of C --> {0})) . b), the carrier of C:] is non empty Relation-like set
i is Element of (T \/ ( the carrier of C --> {0})) . b
[i,b] is pair non empty Element of [:((T \/ ( the carrier of C --> {0})) . b), the carrier of C:]
{i,b} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,b},{i}} is non empty finite V38() set
root-tree [i,b] is non empty Relation-like [:((T \/ ( the carrier of C --> {0})) . b), the carrier of C:] -valued Function-like DecoratedTree-like Element of FinTrees [:((T \/ ( the carrier of C --> {0})) . b), the carrier of C:]
FinTrees [:((T \/ ( the carrier of C --> {0})) . b), the carrier of C:] is non empty functional constituted-DTrees DTree-set of [:((T \/ ( the carrier of C --> {0})) . b), the carrier of C:]
pi1 is set
the Sorts of (Free (C,T)) . pi1 is set
z is Element of the carrier of C
the Sorts of (Free (C,T)) . z is set
DTConMSA (T \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
coprod (T \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined the carrier of C -defined Function-like total total (C) set
Union (coprod (T \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod (T \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod (T \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0})))) is non empty set
REL (T \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(REL (T \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))
C -Terms (T \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))) is non empty set
{ b₁ where b₁ is non empty Relation-like the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (T \/ ( the carrier of C --> {0})) : ( the_sort_of b₁ = z & variables_in b₁ c= T ) } is set
x2 is non empty Relation-like the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (T \/ ( the carrier of C --> {0}))
the_sort_of x2 is Element of the carrier of C
variables_in x2 is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of T \/ ( the carrier of C --> {0})
C variables_in x2 is non empty Relation-like the carrier of C -defined Function-like total set
(variables_in x2) . b is finite set
{i} is non empty trivial finite 1 -element Element of bool ((T \/ ( the carrier of C --> {0})) . b)
bool ((T \/ ( the carrier of C --> {0})) . b) is non empty set
T . b is set
((DTConMSA T)) is Element of bool the carrier of (DTConMSA T)
bool the carrier of (DTConMSA T) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA T) : for b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set holds not b₁ ==> b₂ } is set
DTConMSA (T \/ ( the carrier of C --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
coprod (T \/ ( the carrier of C --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined the carrier of C -defined Function-like total total (C) set
Union (coprod (T \/ ( the carrier of C --> {0}))) is non empty set
proj2 (coprod (T \/ ( the carrier of C --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod (T \/ ( the carrier of C --> {0})))) is set
[: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0})))) is non empty set
REL (T \/ ( the carrier of C --> {0})) is Relation-like [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0})))) -defined ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) * -valued Element of bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):]
([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))
[:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of C,{ the carrier of C}:] \/ (Union (coprod (T \/ ( the carrier of C --> {0}))))),(REL (T \/ ( the carrier of C --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))
C -Terms (T \/ ( the carrier of C --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))))
bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))) is non empty set
b is Element of the carrier' of C
Sym (b,(T \/ ( the carrier of C --> {0}))) is Element of NonTerminals (DTConMSA (T \/ ( the carrier of C --> {0})))
NonTerminals (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty Element of bool the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))
bool the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
[b, the carrier of C] is pair non empty set
{b, the carrier of C} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b, the carrier of C},{b}} is non empty finite V38() set
i is Relation-like NAT -defined FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding ArgumentSeq of Sym (b,(T \/ ( the carrier of C --> {0})))
rng i is functional finite constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))))
[b, the carrier of C] -tree i is non empty Relation-like Function-like DecoratedTree-like set
pi1 is set
the Sorts of (Free (C,T)) . pi1 is set
z is Element of the carrier of C
the Sorts of (Free (C,T)) . z is set
{ b₁ where b₁ is non empty Relation-like the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (T \/ ( the carrier of C --> {0})) : ( the_sort_of b₁ = z & variables_in b₁ c= T ) } is set
x2 is non empty Relation-like the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (T \/ ( the carrier of C --> {0}))
the_sort_of x2 is Element of the carrier of C
variables_in x2 is non empty Relation-like the carrier of C -defined Function-like total ManySortedSubset of T \/ ( the carrier of C --> {0})
C variables_in x2 is non empty Relation-like the carrier of C -defined Function-like total set
x2 . {} is set
the_result_sort_of b is Element of the carrier of C
the ResultSort of C . b is Element of the carrier of C
x1 is set
((DTConMSA T)) is Element of bool the carrier of (DTConMSA T)
bool the carrier of (DTConMSA T) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA T) : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
roots i is Relation-like NAT -defined the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))
x2 is Element of the carrier of (DTConMSA T)
x1 is Relation-like NAT -defined FinTrees the carrier of (DTConMSA T) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() FinSequence of TS (DTConMSA T)
roots x1 is Relation-like NAT -defined the carrier of (DTConMSA T) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA T)
((DTConMSA T)) is Element of bool the carrier of (DTConMSA T)
bool the carrier of (DTConMSA T) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA T) : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
((DTConMSA T)) is Element of bool the carrier of (DTConMSA T)
{ b₁ where b₁ is Element of the carrier of (DTConMSA T) : for b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set holds not b₁ ==> b₂ } is set
b is Element of the carrier of (DTConMSA T)
root-tree b is non empty Relation-like the carrier of (DTConMSA T) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (DTConMSA T)
b `2 is set
dom T is non empty Element of bool the carrier of C
b `1 is set
T . (b `2) is set
[(b `1),(b `2)] is pair non empty set
{(b `1),(b `2)} is non empty finite set
{(b `1)} is non empty trivial finite 1 -element set
{{(b `1),(b `2)},{(b `1)}} is non empty finite V38() set
the Sorts of (Free (C,T)) . (b `2) is set
b is Element of the carrier of (DTConMSA T)
i is Relation-like NAT -defined FinTrees the carrier of (DTConMSA T) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() FinSequence of TS (DTConMSA T)
roots i is Relation-like NAT -defined the carrier of (DTConMSA T) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA T)
rng i is functional finite constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA T))
b -tree i is non empty Relation-like the carrier of (DTConMSA T) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (DTConMSA T)
pi1 is set
z is set
[pi1,z] is pair non empty set
{pi1,z} is non empty finite set
{pi1} is non empty trivial finite 1 -element set
{{pi1,z},{pi1}} is non empty finite V38() set
x1 is set
TS (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))))
x1 is set
x1 is Relation-like NAT -defined FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding FinSequence of TS (DTConMSA (T \/ ( the carrier of C --> {0})))
x2 is Element of the carrier' of C
Sym (x2,(T \/ ( the carrier of C --> {0}))) is Element of NonTerminals (DTConMSA (T \/ ( the carrier of C --> {0})))
NonTerminals (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty Element of bool the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))
bool the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
[x2, the carrier of C] is pair non empty set
{x2, the carrier of C} is non empty finite set
{x2} is non empty trivial finite 1 -element set
{{x2, the carrier of C},{x2}} is non empty finite V38() set
roots x1 is Relation-like NAT -defined the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA (T \/ ( the carrier of C --> {0})))
x2 is Relation-like NAT -defined FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding FinSequence of C -Terms (T \/ ( the carrier of C --> {0}))
p is Relation-like NAT -defined FinTrees the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding ArgumentSeq of Sym (x2,(T \/ ( the carrier of C --> {0})))
(Sym (x2,(T \/ ( the carrier of C --> {0})))) -tree p is non empty Relation-like the carrier of (DTConMSA (T \/ ( the carrier of C --> {0}))) -valued Function-like finite DecoratedTree-like Element of C -Terms (T \/ ( the carrier of C --> {0}))
the_result_sort_of x2 is Element of the carrier of C
the ResultSort of C . x2 is Element of the carrier of C
the Sorts of (Free (C,T)) . (the_result_sort_of x2) is set
b is set
i is set
the Sorts of (Free (C,T)) . i is set
pi1 is Element of the carrier of C
the Sorts of (Free (C,T)) . pi1 is set
b is set
i is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA T))
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like the carrier of C -defined Function-like total set
Free (C,T) is strict MSAlgebra over C
the Sorts of (Free (C,T)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,T)) is set
proj2 the Sorts of (Free (C,T)) is non empty set
union (proj2 the Sorts of (Free (C,T))) is set
[:(Union the Sorts of (Free (C,T))),(Union the Sorts of (Free (C,T))):] is Relation-like set
bool [:(Union the Sorts of (Free (C,T))),(Union the Sorts of (Free (C,T))):] is non empty set
id (Union the Sorts of (Free (C,T))) is Relation-like Union the Sorts of (Free (C,T)) -defined Union the Sorts of (Free (C,T)) -valued Function-like one-to-one total V99() V101() V102() V106() V350() Element of bool [:(Union the Sorts of (Free (C,T))),(Union the Sorts of (Free (C,T))):]
dom (id (Union the Sorts of (Free (C,T)))) is Element of bool (Union the Sorts of (Free (C,T)))
bool (Union the Sorts of (Free (C,T))) is non empty set
rng (id (Union the Sorts of (Free (C,T)))) is Element of bool (Union the Sorts of (Free (C,T)))
f2 is Relation-like Union the Sorts of (Free (C,T)) -defined Union the Sorts of (Free (C,T)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,T))),(Union the Sorts of (Free (C,T))):]
x is Element of the carrier of C
the Sorts of (Free (C,T)) . x is set
f2 .: ( the Sorts of (Free (C,T)) . x) is Element of bool (Union the Sorts of (Free (C,T)))
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like the carrier of C -defined Function-like total set
Free (C,T) is strict MSAlgebra over C
the Sorts of (Free (C,T)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,T)) is set
proj2 the Sorts of (Free (C,T)) is non empty set
union (proj2 the Sorts of (Free (C,T))) is set
[:(Union the Sorts of (Free (C,T))),(Union the Sorts of (Free (C,T))):] is Relation-like set
bool [:(Union the Sorts of (Free (C,T))),(Union the Sorts of (Free (C,T))):] is non empty set
dom the Sorts of (Free (C,T)) is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
f1 is Relation-like Union the Sorts of (Free (C,T)) -defined Union the Sorts of (Free (C,T)) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (C,T))),(Union the Sorts of (Free (C,T))):]
dom f1 is Element of bool (Union the Sorts of (Free (C,T)))
bool (Union the Sorts of (Free (C,T))) is non empty set
f2 is Element of the carrier of C
the Sorts of (Free (C,T)) . f2 is set
f1 .: ( the Sorts of (Free (C,T)) . f2) is Element of bool (Union the Sorts of (Free (C,T)))
x is set
f1 . x is set
f2 is Element of the carrier of C
the Sorts of (Free (C,T)) . f2 is set
f1 .: ( the Sorts of (Free (C,T)) . f2) is Element of bool (Union the Sorts of (Free (C,T)))
x is set
a is set
f1 . a is set
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like the carrier of C -defined Function-like total set
Free (C,T) is strict MSAlgebra over C
the Sorts of (Free (C,T)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,T)) is set
proj2 the Sorts of (Free (C,T)) is non empty set
union (proj2 the Sorts of (Free (C,T))) is set
f2 is Relation-like Union the Sorts of (Free (C,T)) -defined Union the Sorts of (Free (C,T)) -valued Function-like quasi_total (C,T)
x is Element of the carrier of C
the Sorts of (Free (C,T)) . x is set
a is Relation-like NAT -defined the Sorts of (Free (C,T)) . x -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the Sorts of (Free (C,T)) . x
f2 * a is Relation-like NAT -defined Union the Sorts of (Free (C,T)) -valued Function-like finite Element of bool [:NAT,(Union the Sorts of (Free (C,T))):]
[:NAT,(Union the Sorts of (Free (C,T))):] is Relation-like set
bool [:NAT,(Union the Sorts of (Free (C,T))):] is non empty set
card (f2 * a) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of omega
len a is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
dom the Sorts of (Free (C,T)) is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
dom f2 is Element of bool (Union the Sorts of (Free (C,T)))
bool (Union the Sorts of (Free (C,T))) is non empty set
rng a is finite Element of bool ( the Sorts of (Free (C,T)) . x)
bool ( the Sorts of (Free (C,T)) . x) is non empty set
dom (f2 * a) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
dom a is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
Seg (len a) is finite len a -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b₁ & b₁ <= len a ) } is set
rng (f2 * a) is finite Element of bool (Union the Sorts of (Free (C,T)))
b is set
i is set
(f2 * a) . i is set
a . i is set
f2 . (a . i) is set
b is Relation-like NAT -defined the Sorts of (Free (C,T)) . x -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the Sorts of (Free (C,T)) . x
len b is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
C is non empty non void V58() V259() ManySortedSign
the carrier of C is non empty set
T is non empty Relation-like the carrier of C -defined Function-like total set
Free (C,T) is strict MSAlgebra over C
the Sorts of (Free (C,T)) is non empty Relation-like the carrier of C -defined Function-like total set
Union the Sorts of (Free (C,T)) is set
proj2 the Sorts of (Free (C,T)) is non empty set
union (proj2 the Sorts of (Free (C,T))) is set
F₁() is non empty non void V58() V259() () () ManySortedSign
(F₁()) is non empty Relation-like non empty-yielding the carrier of F₁() -defined Function-like total (F₁()) set
the carrier of F₁() is non empty set
Free (F₁(),(F₁())) is strict non-empty non empty MSAlgebra over F₁()
the Sorts of (Free (F₁(),(F₁()))) is non empty Relation-like non-empty non empty-yielding the carrier of F₁() -defined Function-like total (F₁()) set
Union the Sorts of (Free (F₁(),(F₁()))) is non empty set
proj2 the Sorts of (Free (F₁(),(F₁()))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (F₁(),(F₁())))) is set
(F₁()) is Element of the carrier of F₁()
the carrier' of F₁() is non empty set
(F₁()) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (F₁(),(F₁()))))
bool (Union the Sorts of (Free (F₁(),(F₁())))) is non empty set
the Sorts of (Free (F₁(),(F₁()))) . (F₁()) is non empty set
(F₁()) is Element of the carrier of F₁()
(F₁()) is Element of the carrier of F₁()
(F₁()) is (F₁(),(F₁()))
(F₁()) is (F₁(),(F₁()))
the carrier of F₁() --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of F₁() -defined the carrier of F₁() -defined bool NAT -valued Function-like constant total total quasi_total (F₁()) Element of bool [: the carrier of F₁(),(bool NAT):]
[: the carrier of F₁(),(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of F₁(),(bool NAT):] is non empty non trivial non finite set
(F₁()) \/ ( the carrier of F₁() --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of F₁() -defined the carrier of F₁() -defined Function-like total total (F₁()) set
DTConMSA (F₁()) is non empty strict DTConstrStr
{ the carrier of F₁()} is non empty trivial finite 1 -element set
[: the carrier' of F₁(),{ the carrier of F₁()}:] is non empty Relation-like set
coprod (F₁()) is non empty Relation-like the carrier of F₁() -defined Function-like total set
Union (coprod (F₁())) is set
proj2 (coprod (F₁())) is non empty set
union (proj2 (coprod (F₁()))) is set
[: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod (F₁()))) is non empty set
REL (F₁()) is Relation-like [: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod (F₁()))) -defined ([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod (F₁())))) * -valued Element of bool [:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod (F₁())))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod (F₁())))) *):]
([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod (F₁())))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod (F₁())))
[:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod (F₁())))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod (F₁())))) *):] is non empty Relation-like set
bool [:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod (F₁())))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod (F₁())))) *):] is non empty set
DTConstrStr(# ([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod (F₁())))),(REL (F₁())) #) is non empty strict DTConstrStr
the carrier of (DTConMSA (F₁())) is non empty set
TS (DTConMSA (F₁())) is functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA (F₁())))
FinTrees the carrier of (DTConMSA (F₁())) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA (F₁()))
bool (FinTrees the carrier of (DTConMSA (F₁()))) is non empty set
[:(TS (DTConMSA (F₁()))),(Union the Sorts of (Free (F₁(),(F₁())))):] is Relation-like set
bool [:(TS (DTConMSA (F₁()))),(Union the Sorts of (Free (F₁(),(F₁())))):] is non empty set
((DTConMSA (F₁()))) is Element of bool the carrier of (DTConMSA (F₁()))
bool the carrier of (DTConMSA (F₁())) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA (F₁())) : for b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set holds not b₁ ==> b₂ } is set
b is Relation-like TS (DTConMSA (F₁())) -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like quasi_total Element of bool [:(TS (DTConMSA (F₁()))),(Union the Sorts of (Free (F₁(),(F₁())))):]
[:(Union the Sorts of (Free (F₁(),(F₁())))),(Union the Sorts of (Free (F₁(),(F₁())))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (F₁(),(F₁())))),(Union the Sorts of (Free (F₁(),(F₁())))):] is non empty set
i is Relation-like Union the Sorts of (Free (F₁(),(F₁()))) -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like quasi_total Element of bool [:(Union the Sorts of (Free (F₁(),(F₁())))),(Union the Sorts of (Free (F₁(),(F₁())))):]
pi1 is Element of the carrier of F₁()
the Sorts of (Free (F₁(),(F₁()))) . pi1 is non empty set
i .: ( the Sorts of (Free (F₁(),(F₁()))) . pi1) is Element of bool (Union the Sorts of (Free (F₁(),(F₁()))))
z is set
x2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
i . x2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
x1 is Element of ()
(x1,F₁()) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F₁(),(F₁())) (F₁(),(F₁()))
[x1,()] is pair non empty set
{x1,()} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,()},{x1}} is non empty finite V38() set
root-tree [x1,()] is non empty Relation-like Function-like DecoratedTree-like set
i . (x1,F₁()) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
p is Element of the carrier of F₁()
the Sorts of (Free (F₁(),(F₁()))) . p is non empty set
[x1,(F₁())] is pair non empty Element of [:(), the carrier of F₁():]
[:(), the carrier of F₁():] is non empty Relation-like set
{x1,(F₁())} is non empty finite set
{{x1,(F₁())},{x1}} is non empty finite V38() set
c is Element of the carrier of (DTConMSA (F₁()))
c `1 is set
F<sub>2</sub>((c `1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
F₂(x1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
x1 is (F₁()) Element of the carrier' of F₁()
the_arity_of x1 is Relation-like NAT -defined the carrier of F₁() -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F₁() *
the carrier of F₁() * is non empty functional FinSequence-membered FinSequenceSet of the carrier of F₁()
the Arity of F₁() is Relation-like the carrier' of F₁() -defined the carrier of F₁() * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of F₁(),( the carrier of F₁() *):]
[: the carrier' of F₁(),( the carrier of F₁() *):] is non empty Relation-like set
bool [: the carrier' of F₁(),( the carrier of F₁() *):] is non empty set
the Arity of F₁() . x1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F₁() *
len (the_arity_of x1) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
x2 is Relation-like NAT -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (F₁())
len x2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
rng x2 is finite Element of bool (Union the Sorts of (Free (F₁(),(F₁()))))
(F₁(),x1,x2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F₁(),(F₁())) Element of Union the Sorts of (Free (F₁(),(F₁())))
i . (F₁(),x1,x2) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
[x1, the carrier of F₁()] is pair non empty set
{x1, the carrier of F₁()} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1, the carrier of F₁()},{x1}} is non empty finite V38() set
a is Element of the carrier of F₁()
the Sorts of (Free (F₁(),(F₁()))) . a is non empty set
((DTConMSA (F₁()))) is Element of bool the carrier of (DTConMSA (F₁()))
{ b₁ where b₁ is Element of the carrier of (DTConMSA (F₁())) : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
nt is Element of the carrier of (DTConMSA (F₁()))
nt is Relation-like NAT -defined FinTrees the carrier of (DTConMSA (F₁())) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() FinSequence of TS (DTConMSA (F₁()))
nt -tree nt is non empty Relation-like the carrier of (DTConMSA (F₁())) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (DTConMSA (F₁()))
DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
coprod ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of F₁() -defined the carrier of F₁() -defined Function-like total total (F₁()) set
Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty set
proj2 (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod ((F₁()) \/ ( the carrier of F₁() --> {0})))) is set
[: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0})))) is non empty set
REL ((F₁()) \/ ( the carrier of F₁() --> {0})) is Relation-like [: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0})))) -defined ([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) * -valued Element of bool [:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) *):]
([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))
[:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(REL ((F₁()) \/ ( the carrier of F₁() --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
F₁() -Terms ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))) is non empty set
F₁() -Terms ((F₁()),((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty Relation-like the carrier of F₁() -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
FreeMSA ((F₁()) \/ ( the carrier of F₁() --> {0})) is strict non-empty V172(F₁()) MSAlgebra over F₁()
FreeSort ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of F₁() -defined Function-like total V159() (F₁()) set
FreeOper ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty Relation-like the carrier' of F₁() -defined Function-like total ManySortedFunction of the Arity of F₁() * ((FreeSort ((F₁()) \/ ( the carrier of F₁() --> {0}))) #), the ResultSort of F₁() * (FreeSort ((F₁()) \/ ( the carrier of F₁() --> {0})))
(FreeSort ((F₁()) \/ ( the carrier of F₁() --> {0}))) # is non empty Relation-like non-empty non empty-yielding the carrier of F₁() * -defined Function-like total set
the Arity of F₁() * ((FreeSort ((F₁()) \/ ( the carrier of F₁() --> {0}))) #) is Relation-like non-empty the carrier' of F₁() -defined Function-like set
the ResultSort of F₁() is Relation-like the carrier' of F₁() -defined the carrier of F₁() -valued Function-like quasi_total Element of bool [: the carrier' of F₁(), the carrier of F₁():]
[: the carrier' of F₁(), the carrier of F₁():] is non empty Relation-like set
bool [: the carrier' of F₁(), the carrier of F₁():] is non empty set
the ResultSort of F₁() * (FreeSort ((F₁()) \/ ( the carrier of F₁() --> {0}))) is Relation-like non-empty the carrier' of F₁() -defined Function-like set
MSAlgebra(# (FreeSort ((F₁()) \/ ( the carrier of F₁() --> {0}))),(FreeOper ((F₁()) \/ ( the carrier of F₁() --> {0}))) #) is strict MSAlgebra over F₁()
the Sorts of (FreeMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty Relation-like non-empty non empty-yielding the carrier of F₁() -defined Function-like total V159() (F₁()) set
the Sorts of (FreeMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) . a is non empty set
ts is non empty Relation-like the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) -valued Function-like finite DecoratedTree-like Element of F₁() -Terms ((F₁()) \/ ( the carrier of F₁() --> {0}))
(FreeSort ((F₁()) \/ ( the carrier of F₁() --> {0}))) . a is non empty set
FreeSort (((F₁()) \/ ( the carrier of F₁() --> {0})),a) is non empty functional constituted-DTrees Element of bool (TS (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))))
TS (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))))
bool (TS (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))) is non empty set
((F₁()) \/ ( the carrier of F₁() --> {0})) . a is non empty set
{ b₁ where b₁ is non empty Relation-like the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) -valued Function-like DecoratedTree-like Element of TS (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) : ( ex b₂ being set st
( b₂ in ((F₁()) \/ ( the carrier of F₁() --> {0})) . a & b₁ = root-tree [b₂,a] ) or ex b₂ being Element of the carrier' of F₁() st
( [b₂, the carrier of F₁()] = b₁ . {} & the_result_sort_of b₂ = a ) ) } is set
the_sort_of ts is Element of the carrier of F₁()
nt `1 is set
dom i is Element of bool (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))))
i * x2 is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) *
(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
rng (i * x2) is finite Element of bool (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))))
r is set
dom (i * x2) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
nt is set
(i * x2) . nt is set
dom x2 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
x2 . nt is set
ts is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
i . ts is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
nt is set
r is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (F<sub>1</sub>())
len r is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
nt is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding FinSequence of F<sub>1</sub>() -Terms ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))
Sym (x1,((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is Element of NonTerminals (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))
NonTerminals (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is non empty Element of bool the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))
bool the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) : ex b<sub>2</sub> being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b<sub>1</sub> ==> b<sub>2</sub> } is set
the_result_sort_of x1 is Element of the carrier of F<sub>1</sub>()
the ResultSort of F<sub>1</sub>() . x1 is Element of the carrier of F<sub>1</sub>()
roots nt is Relation-like NAT -defined the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))
roots nt is Relation-like NAT -defined the carrier of (DTConMSA (F<sub>1</sub>())) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA (F<sub>1</sub>()))
i * nt is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite Element of bool [:NAT,(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))):]
[:NAT,(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))):] is non empty non trivial Relation-like non finite set
bool [:NAT,(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))):] is non empty non trivial non finite set
(i * nt) . 1 is set
(i * nt) . 2 is set
F<sub>5</sub>(((i * nt) . 1),((i * nt) . 2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>3</sub>(((i * nt) . 1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>4</sub>((nt `1),(i * nt)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
IFEQ ((nt `1),(),F<sub>3</sub>(((i * nt) . 1)),F<sub>4</sub>((nt `1),(i * nt))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
IFEQ ((nt `1),(),F<sub>5</sub>(((i * nt) . 1),((i * nt) . 2)),(IFEQ ((nt `1),(),F₃(((i * nt) . 1)),F₄((nt `1),(i * nt))))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>4</sub>(x1,(i * nt)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
IFEQ (x1,(),F<sub>3</sub>(((i * nt) . 1)),F<sub>4</sub>(x1,(i * nt))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
x1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
i . x1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
(F<sub>1</sub>(),(F<sub>1</sub>()),x1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
i . (F<sub>1</sub>(),(F<sub>1</sub>()),x1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) . (F<sub>1</sub>()) is non empty set
p is Element of the carrier of F<sub>1</sub>()
the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) . p is non empty set
<*x1*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) *
(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
[1,x1] is pair non empty set
{1,x1} is non empty finite V38() non with_pair set
{{1,x1},{1}} is non empty finite V38() set
{[1,x1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
rng <*x1*> is non empty trivial finite 1 -element non with_pair Element of bool (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))))
{x1} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))))
[(F<sub>1</sub>()), the carrier of F<sub>1</sub>()] is pair non empty set
{(F<sub>1</sub>()), the carrier of F<sub>1</sub>()} is non empty finite set
{(F<sub>1</sub>())} is non empty trivial finite 1 -element set
{{(F<sub>1</sub>()), the carrier of F<sub>1</sub>()},{(F<sub>1</sub>())}} is non empty finite V38() set
((DTConMSA (F<sub>1</sub>()))) is Element of bool the carrier of (DTConMSA (F<sub>1</sub>()))
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of (DTConMSA (F<sub>1</sub>())) : ex b<sub>2</sub> being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b<sub>1</sub> ==> b<sub>2</sub> } is set
a is Relation-like NAT -defined the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) . (F<sub>1</sub>()) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) . (F<sub>1</sub>())
r is Element of the carrier of (DTConMSA (F<sub>1</sub>()))
nt is Relation-like NAT -defined FinTrees the carrier of (DTConMSA (F<sub>1</sub>())) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() FinSequence of TS (DTConMSA (F<sub>1</sub>()))
r -tree nt is non empty Relation-like the carrier of (DTConMSA (F<sub>1</sub>())) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (DTConMSA (F<sub>1</sub>()))
r `1 is set
dom i is Element of bool (Union the Sorts of (Free (F₁(),(F₁()))))
i * a is Relation-like NAT -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like finite Element of bool [:NAT,(Union the Sorts of (Free (F₁(),(F₁())))):]
[:NAT,(Union the Sorts of (Free (F₁(),(F₁())))):] is non empty non trivial Relation-like non finite set
bool [:NAT,(Union the Sorts of (Free (F₁(),(F₁())))):] is non empty non trivial non finite set
x2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (F₁(),(F₁()))
<*x2*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (F₁(),(F₁())))) *
[1,x2] is pair non empty set
{1,x2} is non empty finite V38() non with_pair set
{{1,x2},{1}} is non empty finite V38() set
{[1,x2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
rng a is finite Element of bool ( the Sorts of (Free (F₁(),(F₁()))) . (F₁()))
bool ( the Sorts of (Free (F₁(),(F₁()))) . (F₁())) is non empty set
F₁() -Terms ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))))
DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
coprod ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of F₁() -defined the carrier of F₁() -defined Function-like total total (F₁()) set
Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty set
proj2 (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod ((F₁()) \/ ( the carrier of F₁() --> {0})))) is set
[: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0})))) is non empty set
REL ((F₁()) \/ ( the carrier of F₁() --> {0})) is Relation-like [: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0})))) -defined ([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) * -valued Element of bool [:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) *):]
([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))
[:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(REL ((F₁()) \/ ( the carrier of F₁() --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
bool (FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))) is non empty set
ts is set
ts is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding FinSequence of F₁() -Terms ((F₁()) \/ ( the carrier of F₁() --> {0}))
Sym ((F₁()),((F₁()) \/ ( the carrier of F₁() --> {0}))) is Element of NonTerminals (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
NonTerminals (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty Element of bool the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
bool the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
roots ts is Relation-like NAT -defined the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
roots nt is Relation-like NAT -defined the carrier of (DTConMSA (F₁())) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA (F₁()))
i * nt is Relation-like NAT -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like finite Element of bool [:NAT,(Union the Sorts of (Free (F₁(),(F₁())))):]
(i * nt) . 1 is set
(i * nt) . 2 is set
F₅(((i * nt) . 1),((i * nt) . 2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
F₃(((i * nt) . 1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
F₄((r `1),(i * nt)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
IFEQ ((r `1),(),F₃(((i * nt) . 1)),F₄((r `1),(i * nt))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
IFEQ ((r `1),(),F₅(((i * nt) . 1),((i * nt) . 2)),(IFEQ ((r `1),(),F<sub>3</sub>(((i * nt) . 1)),F<sub>4</sub>((r `1),(i * nt))))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
F₄((F₁()),(i * nt)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
IFEQ ((F₁()),(),F₃(((i * nt) . 1)),F₄((F₁()),(i * nt))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
F₃(x2) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
x1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (F₁(),(F₁()))
i . x1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
x2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (F₁(),(F₁()))
i . x2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
(F₁(),(F₁()),x1,x2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F₁(),(F₁())) Element of Union the Sorts of (Free (F₁(),(F₁())))
i . (F₁(),(F₁()),x1,x2) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
the Sorts of (Free (F₁(),(F₁()))) . (F₁()) is non empty set
the Sorts of (Free (F₁(),(F₁()))) . (F₁()) is non empty set
a is Element of the carrier of F₁()
the Sorts of (Free (F₁(),(F₁()))) . a is non empty set
<*x1,x2*> is non empty Relation-like NAT -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (F₁(),(F₁())))) *
(Union the Sorts of (Free (F₁(),(F₁())))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (F₁(),(F₁())))
<*x1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x1] is pair non empty set
{1,x1} is non empty finite V38() non with_pair set
{{1,x1},{1}} is non empty finite V38() set
{[1,x1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x2] is pair non empty set
{1,x2} is non empty finite V38() non with_pair set
{{1,x2},{1}} is non empty finite V38() set
{[1,x2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x1*> ^ <*x2*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(F₁()), the carrier of F₁()] is pair non empty set
{(F₁()), the carrier of F₁()} is non empty finite set
{(F₁())} is non empty trivial finite 1 -element set
{{(F₁()), the carrier of F₁()},{(F₁())}} is non empty finite V38() set
((DTConMSA (F₁()))) is Element of bool the carrier of (DTConMSA (F₁()))
{ b₁ where b₁ is Element of the carrier of (DTConMSA (F₁())) : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
nt is Relation-like NAT -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of Union the Sorts of (Free (F₁(),(F₁())))
nt is Element of the carrier of (DTConMSA (F₁()))
ts is Relation-like NAT -defined FinTrees the carrier of (DTConMSA (F₁())) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() FinSequence of TS (DTConMSA (F₁()))
nt -tree ts is non empty Relation-like the carrier of (DTConMSA (F₁())) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (DTConMSA (F₁()))
nt `1 is set
i * nt is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) *
p is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
c is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
<*p,c*> is non empty Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) *
<*p*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,p] is pair non empty set
{1,p} is non empty finite V38() non with_pair set
{{1,p},{1}} is non empty finite V38() set
{[1,p]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*c*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,c] is pair non empty set
{1,c} is non empty finite V38() non with_pair set
{{1,c},{1}} is non empty finite V38() set
{[1,c]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*p*> ^ <*c*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
rng nt is finite Element of bool (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))))
F<sub>1</sub>() -Terms ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))))
DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() -defined Function-like total total (F<sub>1</sub>()) set
Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is non empty set
proj2 (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))) is set
[: the carrier' of F<sub>1</sub>(),{ the carrier of F<sub>1</sub>()}:] \/ (Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))) is non empty set
REL ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})) is Relation-like [: the carrier' of F<sub>1</sub>(),{ the carrier of F<sub>1</sub>()}:] \/ (Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))) -defined ([: the carrier' of F<sub>1</sub>(),{ the carrier of F<sub>1</sub>()}:] \/ (Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))))) * -valued Element of bool [:([: the carrier' of F<sub>1</sub>(),{ the carrier of F<sub>1</sub>()}:] \/ (Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))))),(([: the carrier' of F<sub>1</sub>(),{ the carrier of F<sub>1</sub>()}:] \/ (Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))))) *):]
([: the carrier' of F<sub>1</sub>(),{ the carrier of F<sub>1</sub>()}:] \/ (Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of F<sub>1</sub>(),{ the carrier of F<sub>1</sub>()}:] \/ (Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))))
[:([: the carrier' of F<sub>1</sub>(),{ the carrier of F<sub>1</sub>()}:] \/ (Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))))),(([: the carrier' of F<sub>1</sub>(),{ the carrier of F<sub>1</sub>()}:] \/ (Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of F<sub>1</sub>(),{ the carrier of F<sub>1</sub>()}:] \/ (Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))))),(([: the carrier' of F<sub>1</sub>(),{ the carrier of F<sub>1</sub>()}:] \/ (Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of F<sub>1</sub>(),{ the carrier of F<sub>1</sub>()}:] \/ (Union (coprod ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))))),(REL ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))
bool (FinTrees the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))) is non empty set
r is set
r is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding FinSequence of F<sub>1</sub>() -Terms ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))
Sym ((F<sub>1</sub>()),((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is Element of NonTerminals (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))
NonTerminals (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is non empty Element of bool the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))
bool the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) : ex b<sub>2</sub> being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b<sub>1</sub> ==> b<sub>2</sub> } is set
roots r is Relation-like NAT -defined the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))
roots ts is Relation-like NAT -defined the carrier of (DTConMSA (F<sub>1</sub>())) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA (F<sub>1</sub>()))
i * ts is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite Element of bool [:NAT,(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))):]
[:NAT,(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))):] is non empty non trivial Relation-like non finite set
bool [:NAT,(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))):] is non empty non trivial non finite set
(i * ts) . 1 is set
(i * ts) . 2 is set
F<sub>5</sub>(((i * ts) . 1),((i * ts) . 2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>3</sub>(((i * ts) . 1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>4</sub>((nt `1),(i * ts)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
IFEQ ((nt `1),(),F<sub>3</sub>(((i * ts) . 1)),F<sub>4</sub>((nt `1),(i * ts))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
IFEQ ((nt `1),(),F<sub>5</sub>(((i * ts) . 1),((i * ts) . 2)),(IFEQ ((nt `1),(),F₃(((i * ts) . 1)),F₄((nt `1),(i * ts))))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>5</sub>(p,((i * ts) . 2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>5</sub>(p,c) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
pi1 is Relation-like Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like quasi_total (F<sub>1</sub>(),(F<sub>1</sub>()))
z is Element of ()
(F<sub>1</sub>()) . (F<sub>1</sub>()) is set
x2 is Element of (F<sub>1</sub>()) . (F<sub>1</sub>())
[x2,(F<sub>1</sub>())] is pair non empty set
{x2,(F<sub>1</sub>())} is non empty finite set
{x2} is non empty trivial finite 1 -element set
{{x2,(F<sub>1</sub>())},{x2}} is non empty finite V38() set
x1 is Element of the carrier of (DTConMSA (F<sub>1</sub>()))
(z,F<sub>1</sub>()) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) (F<sub>1</sub>(),(F<sub>1</sub>()))
[z,()] is pair non empty set
{z,()} is non empty finite set
{z} is non empty trivial finite 1 -element set
{{z,()},{z}} is non empty finite V38() set
root-tree [z,()] is non empty Relation-like Function-like DecoratedTree-like set
pi1 . (z,F<sub>1</sub>()) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
x1 `1 is set
F₂((x1 `1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>2</sub>(z) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
x2 is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (F<sub>1</sub>())
len x2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
z is (F<sub>1</sub>()) Element of the carrier' of F<sub>1</sub>()
the_arity_of z is Relation-like NAT -defined the carrier of F<sub>1</sub>() -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
the carrier of F<sub>1</sub>() * is non empty functional FinSequence-membered FinSequenceSet of the carrier of F<sub>1</sub>()
the Arity of F<sub>1</sub>() is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):]
[: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty Relation-like set
bool [: the carrier' of F<sub>1</sub>(),( the carrier of F<sub>1</sub>() *):] is non empty set
the Arity of F<sub>1</sub>() . z is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F<sub>1</sub>() *
len (the_arity_of z) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
x1 is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (F<sub>1</sub>())
pi1 * x2 is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) *
(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
(F<sub>1</sub>(),z,x2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
[z, the carrier of F<sub>1</sub>()] is pair non empty set
{z, the carrier of F<sub>1</sub>()} is non empty finite set
{z} is non empty trivial finite 1 -element set
{{z, the carrier of F<sub>1</sub>()},{z}} is non empty finite V38() set
((DTConMSA (F<sub>1</sub>()))) is Element of bool the carrier of (DTConMSA (F<sub>1</sub>()))
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of (DTConMSA (F<sub>1</sub>())) : ex b<sub>2</sub> being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b<sub>1</sub> ==> b<sub>2</sub> } is set
c is Element of the carrier of (DTConMSA (F<sub>1</sub>()))
a is Relation-like NAT -defined FinTrees the carrier of (DTConMSA (F<sub>1</sub>())) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() FinSequence of TS (DTConMSA (F<sub>1</sub>()))
c -tree a is non empty Relation-like the carrier of (DTConMSA (F<sub>1</sub>())) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (DTConMSA (F<sub>1</sub>()))
c `1 is set
rng x2 is finite Element of bool (Union the Sorts of (Free (F₁(),(F₁()))))
F₁() -Terms ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))))
DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
coprod ((F₁()) \/ ( the carrier of F₁() --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of F₁() -defined the carrier of F₁() -defined Function-like total total (F₁()) set
Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty set
proj2 (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty with_non-empty_elements set
union (proj2 (coprod ((F₁()) \/ ( the carrier of F₁() --> {0})))) is set
[: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0})))) is non empty set
REL ((F₁()) \/ ( the carrier of F₁() --> {0})) is Relation-like [: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0})))) -defined ([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) * -valued Element of bool [:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) *):]
([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))
[:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))) *):] is non empty set
DTConstrStr(# ([: the carrier' of F₁(),{ the carrier of F₁()}:] \/ (Union (coprod ((F₁()) \/ ( the carrier of F₁() --> {0}))))),(REL ((F₁()) \/ ( the carrier of F₁() --> {0}))) #) is non empty strict DTConstrStr
the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty set
FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
bool (FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))) is non empty set
nt is set
nt is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding FinSequence of F₁() -Terms ((F₁()) \/ ( the carrier of F₁() --> {0}))
Sym (z,((F₁()) \/ ( the carrier of F₁() --> {0}))) is Element of NonTerminals (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
NonTerminals (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty Element of bool the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
bool the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) is non empty set
{ b₁ where b₁ is Element of the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) : ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
roots nt is Relation-like NAT -defined the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
roots a is Relation-like NAT -defined the carrier of (DTConMSA (F₁())) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA (F₁()))
pi1 . (F₁(),z,x2) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
pi1 * a is Relation-like NAT -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like finite Element of bool [:NAT,(Union the Sorts of (Free (F₁(),(F₁())))):]
[:NAT,(Union the Sorts of (Free (F₁(),(F₁())))):] is non empty non trivial Relation-like non finite set
bool [:NAT,(Union the Sorts of (Free (F₁(),(F₁())))):] is non empty non trivial non finite set
(pi1 * a) . 1 is set
(pi1 * a) . 2 is set
F₅(((pi1 * a) . 1),((pi1 * a) . 2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
F₃(((pi1 * a) . 1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
F₄((c `1),(pi1 * a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
IFEQ ((c `1),(),F₃(((pi1 * a) . 1)),F₄((c `1),(pi1 * a))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
IFEQ ((c `1),(),F₅(((pi1 * a) . 1),((pi1 * a) . 2)),(IFEQ ((c `1),(),F<sub>3</sub>(((pi1 * a) . 1)),F<sub>4</sub>((c `1),(pi1 * a))))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
F₄(z,(pi1 * a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
IFEQ (z,(),F₃(((pi1 * a) . 1)),F₄(z,(pi1 * a))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
F₄(z,x1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
z is non pair non empty Relation-like Function-like finite DecoratedTree-like (F₁(),(F₁()))
the Sorts of (Free (F₁(),(F₁()))) . (F₁()) is non empty set
pi1 . z is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
<*z*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (F₁(),(F₁())))) *
[1,z] is pair non empty set
{1,z} is non empty finite V38() non with_pair set
{{1,z},{1}} is non empty finite V38() set
{[1,z]} is non empty trivial Relation-like Function-like constant finite 1 -element set
rng <*z*> is non empty trivial finite 1 -element non with_pair Element of bool (Union the Sorts of (Free (F₁(),(F₁()))))
{z} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (F₁(),(F₁()))))
(F₁(),(F₁()),z) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F₁(),(F₁())) Element of Union the Sorts of (Free (F₁(),(F₁())))
[(F₁()), the carrier of F₁()] is pair non empty set
{(F₁()), the carrier of F₁()} is non empty finite set
{(F₁())} is non empty trivial finite 1 -element set
{{(F₁()), the carrier of F₁()},{(F₁())}} is non empty finite V38() set
x2 is Relation-like NAT -defined the Sorts of (Free (F₁(),(F₁()))) . (F₁()) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the Sorts of (Free (F₁(),(F₁()))) . (F₁())
nt is Element of the carrier of (DTConMSA (F₁()))
nt is Relation-like NAT -defined FinTrees the carrier of (DTConMSA (F₁())) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() FinSequence of TS (DTConMSA (F₁()))
nt -tree nt is non empty Relation-like the carrier of (DTConMSA (F₁())) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (DTConMSA (F₁()))
nt `1 is set
dom pi1 is Element of bool (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))))
pi1 * x2 is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite Element of bool [:NAT,(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))):]
x2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
<*x2*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) *
[1,x2] is pair non empty set
{1,x2} is non empty finite V38() non with_pair set
{{1,x2},{1}} is non empty finite V38() set
{[1,x2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
rng x2 is finite Element of bool ( the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) . (F<sub>1</sub>()))
bool ( the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) . (F<sub>1</sub>())) is non empty set
ts is set
ts is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding FinSequence of F<sub>1</sub>() -Terms ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))
Sym ((F<sub>1</sub>()),((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) is Element of NonTerminals (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))
roots ts is Relation-like NAT -defined the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA ((F<sub>1</sub>()) \/ ( the carrier of F<sub>1</sub>() --> {0})))
roots nt is Relation-like NAT -defined the carrier of (DTConMSA (F<sub>1</sub>())) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA (F<sub>1</sub>()))
pi1 . (F<sub>1</sub>(),(F<sub>1</sub>()),z) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
pi1 * nt is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite Element of bool [:NAT,(Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))):]
(pi1 * nt) . 1 is set
(pi1 * nt) . 2 is set
F<sub>5</sub>(((pi1 * nt) . 1),((pi1 * nt) . 2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>3</sub>(((pi1 * nt) . 1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>4</sub>((nt `1),(pi1 * nt)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
IFEQ ((nt `1),(),F<sub>3</sub>(((pi1 * nt) . 1)),F<sub>4</sub>((nt `1),(pi1 * nt))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
IFEQ ((nt `1),(),F<sub>5</sub>(((pi1 * nt) . 1),((pi1 * nt) . 2)),(IFEQ ((nt `1),(),F₃(((pi1 * nt) . 1)),F₄((nt `1),(pi1 * nt))))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>4</sub>((F<sub>1</sub>()),(pi1 * nt)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
IFEQ ((F<sub>1</sub>()),(),F<sub>3</sub>(((pi1 * nt) . 1)),F<sub>4</sub>((F<sub>1</sub>()),(pi1 * nt))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>3</sub>((pi1 . z)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
z is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
pi1 . z is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
x2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>()))
(F<sub>1</sub>(),(F<sub>1</sub>()),z,x2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (F<sub>1</sub>(),(F<sub>1</sub>())) Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
pi1 . (F<sub>1</sub>(),(F<sub>1</sub>()),z,x2) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
pi1 . x2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
F<sub>5</sub>((pi1 . z),(pi1 . x2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) . (F<sub>1</sub>()) is non empty set
<*z,x2*> is non empty Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))) *
<*z*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,z] is pair non empty set
{1,z} is non empty finite V38() non with_pair set
{{1,z},{1}} is non empty finite V38() set
{[1,z]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x2] is pair non empty set
{1,x2} is non empty finite V38() non with_pair set
{{1,x2},{1}} is non empty finite V38() set
{[1,x2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*z*> ^ <*x2*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(F<sub>1</sub>()), the carrier of F<sub>1</sub>()] is pair non empty set
{(F<sub>1</sub>()), the carrier of F<sub>1</sub>()} is non empty finite set
{(F<sub>1</sub>())} is non empty trivial finite 1 -element set
{{(F<sub>1</sub>()), the carrier of F<sub>1</sub>()},{(F<sub>1</sub>())}} is non empty finite V38() set
p is Relation-like NAT -defined Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
nt is Element of the carrier of (DTConMSA (F<sub>1</sub>()))
ts is Relation-like NAT -defined FinTrees the carrier of (DTConMSA (F<sub>1</sub>())) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() FinSequence of TS (DTConMSA (F<sub>1</sub>()))
nt -tree ts is non empty Relation-like the carrier of (DTConMSA (F<sub>1</sub>())) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (DTConMSA (F<sub>1</sub>()))
nt `1 is set
pi1 * p is Relation-like NAT -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (F₁(),(F₁())))) *
x1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (F₁(),(F₁()))
x2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (F₁(),(F₁()))
<*x1,x2*> is non empty Relation-like NAT -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (F₁(),(F₁())))) *
<*x1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x1] is pair non empty set
{1,x1} is non empty finite V38() non with_pair set
{{1,x1},{1}} is non empty finite V38() set
{[1,x1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x2] is pair non empty set
{1,x2} is non empty finite V38() non with_pair set
{{1,x2},{1}} is non empty finite V38() set
{[1,x2]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x1*> ^ <*x2*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
rng p is finite Element of bool (Union the Sorts of (Free (F₁(),(F₁()))))
r is set
r is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V115() DTree-yielding FinSequence of F₁() -Terms ((F₁()) \/ ( the carrier of F₁() --> {0}))
Sym ((F₁()),((F₁()) \/ ( the carrier of F₁() --> {0}))) is Element of NonTerminals (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
roots r is Relation-like NAT -defined the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA ((F₁()) \/ ( the carrier of F₁() --> {0})))
roots ts is Relation-like NAT -defined the carrier of (DTConMSA (F₁())) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (DTConMSA (F₁()))
pi1 * ts is Relation-like NAT -defined Union the Sorts of (Free (F₁(),(F₁()))) -valued Function-like finite Element of bool [:NAT,(Union the Sorts of (Free (F₁(),(F₁())))):]
(pi1 * ts) . 1 is set
(pi1 * ts) . 2 is set
F₅(((pi1 * ts) . 1),((pi1 * ts) . 2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
F₃(((pi1 * ts) . 1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
F₄((nt `1),(pi1 * ts)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
IFEQ ((nt `1),(),F₃(((pi1 * ts) . 1)),F₄((nt `1),(pi1 * ts))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F<sub>1</sub>(),(F<sub>1</sub>())))
IFEQ ((nt `1),(),F₅(((pi1 * ts) . 1),((pi1 * ts) . 2)),(IFEQ ((nt `1),(),F<sub>3</sub>(((pi1 * ts) . 1)),F<sub>4</sub>((nt `1),(pi1 * ts))))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
F₅(x1,((pi1 * ts) . 2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (F₁(),(F₁())))
C is set
T is set
f1 is set
f2 is Element of C
x is Element of C
IFIN (T,f1,f2,x) is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f2 is Element of ()
dom T is Element of bool ()
T . f2 is Relation-like Function-like set
f1 is non pair empty proper Relation-like non-empty empty-yielding () -defined (C) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of bool [:(),(C):]
dom f1 is non pair empty proper 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of bool NAT
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
{} ((),(C)) is non pair empty proper Relation-like non-empty empty-yielding () -defined NAT -defined (C) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() (C) Element of bool [:(),(C):]
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is Element of bool ()
{ [b₁,(b₁,C)] where b₁ is Element of () : b₁ in T } is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
f2 is Element of ()
(f2,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[f2,()] is pair non empty set
{f2,()} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,()},{f2}} is non empty finite V38() set
root-tree [f2,()] is non empty Relation-like Function-like DecoratedTree-like set
x is non empty Relation-like Function-like DecoratedTree-like Element of (C)
a is non empty Relation-like Function-like DecoratedTree-like Element of (C)
f2 is Relation-like () -defined (C) -valued Function-like quasi_total Function-yielding V115() Element of bool [:(),(C):]
x is set
a is Element of ()
(a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[a,()] is pair non empty set
{a,()} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,()},{a}} is non empty finite V38() set
root-tree [a,()] is non empty Relation-like Function-like DecoratedTree-like set
[a,(a,C)] is pair non empty Element of [:(),(Union the Sorts of (Free (C,(C)))):]
[:(),(Union the Sorts of (Free (C,(C)))):] is non empty Relation-like set
{a,(a,C)} is non empty finite set
{{a,(a,C)},{a}} is non empty finite V38() set
f2 . a is non empty Relation-like Function-like DecoratedTree-like Element of (C)
dom f2 is Element of bool ()
C is non empty non void V58() V259() () () ManySortedSign
T is Element of bool ()
(C,T) is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
{ [b₁,(b₁,C)] where b₁ is Element of () : b₁ in T } is set
dom (C,T) is Element of bool ()
f2 is set
(C,T) . f2 is Relation-like Function-like set
[f2,((C,T) . f2)] is pair non empty set
{f2,((C,T) . f2)} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,((C,T) . f2)},{f2}} is non empty finite V38() set
x is Element of ()
(x,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[x,()] is pair non empty set
{x,()} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,()},{x}} is non empty finite V38() set
root-tree [x,()] is non empty Relation-like Function-like DecoratedTree-like set
[x,(x,C)] is pair non empty Element of [:(),(Union the Sorts of (Free (C,(C)))):]
[:(),(Union the Sorts of (Free (C,(C)))):] is non empty Relation-like set
{x,(x,C)} is non empty finite set
{{x,(x,C)},{x}} is non empty finite V38() set
f2 is set
x is Element of ()
(x,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[x,()] is pair non empty set
{x,()} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,()},{x}} is non empty finite V38() set
root-tree [x,()] is non empty Relation-like Function-like DecoratedTree-like set
[x,(x,C)] is pair non empty Element of [:(),(Union the Sorts of (Free (C,(C)))):]
[:(),(Union the Sorts of (Free (C,(C)))):] is non empty Relation-like set
{x,(x,C)} is non empty finite set
{{x,(x,C)},{x}} is non empty finite V38() set
f2 is Element of ()
(C,T) . f2 is Relation-like Function-like set
(f2,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[f2,()] is pair non empty set
{f2,()} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,()},{f2}} is non empty finite V38() set
root-tree [f2,()] is non empty Relation-like Function-like DecoratedTree-like set
[f2,(f2,C)] is pair non empty Element of [:(),(Union the Sorts of (Free (C,(C)))):]
{f2,(f2,C)} is non empty finite set
{{f2,(f2,C)},{f2}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
T is Element of bool ()
(C,T) is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
{ [b₁,(b₁,C)] where b₁ is Element of () : b₁ in T } is set
dom (C,T) is Element of bool ()
f2 is Element of ()
(C,T) . f2 is Relation-like Function-like set
x is Element of ()
(x,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[x,()] is pair non empty set
{x,()} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,()},{x}} is non empty finite V38() set
root-tree [x,()] is non empty Relation-like Function-like DecoratedTree-like set
f2 is set
proj1 (C,T) is set
x is set
(C,T) . f2 is Relation-like Function-like set
(C,T) . x is Relation-like Function-like set
a is Element of ()
(C,T) . a is Relation-like Function-like set
(a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[a,()] is pair non empty set
{a,()} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,()},{a}} is non empty finite V38() set
root-tree [a,()] is non empty Relation-like Function-like DecoratedTree-like set
b is Element of ()
(C,T) . b is Relation-like Function-like set
(b,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[b,()] is pair non empty set
{b,()} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,()},{b}} is non empty finite V38() set
root-tree [b,()] is non empty Relation-like Function-like DecoratedTree-like set
C is non empty non void V58() V259() () () ManySortedSign
T is non pair empty proper 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of bool ()
(C,T) is Relation-like () -defined (C) -valued Function-like one-to-one Function-yielding V115() (C) Element of bool [:(),(C):]
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
{ [b₁,(b₁,C)] where b₁ is Element of () : b₁ in T } is set
dom (C,T) is Element of bool ()
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
dom T is Element of bool ()
the carrier' of C is non empty set
(C) is Element of the carrier of C
(C) is (C,(C))
(C) is Element of the carrier of C
(C) is (C,(C))
f1 is Element of ()
T /. f1 is non empty Relation-like Function-like DecoratedTree-like Element of (C)
(f1,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[f1,()] is pair non empty set
{f1,()} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,()},{f1}} is non empty finite V38() set
root-tree [f1,()] is non empty Relation-like Function-like DecoratedTree-like set
((Union the Sorts of (Free (C,(C)))),f1,(dom T),(T /. f1),(f1,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f1 is (C) Element of the carrier' of C
the_arity_of f1 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f1) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
the_result_sort_of f1 is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . f1 is Element of the carrier of C
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f1 is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C))
f2 is Element of ()
(f2,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[f2,()] is pair non empty set
{f2,()} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,()},{f2}} is non empty finite V38() set
root-tree [f2,()] is non empty Relation-like Function-like DecoratedTree-like set
f1 . (f2,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
T /. f2 is non empty Relation-like Function-like DecoratedTree-like Element of (C)
((Union the Sorts of (Free (C,(C)))),f2,(dom T),(T /. f2),(f2,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
T . f2 is Relation-like Function-like set
x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len x is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f2 is (C) Element of the carrier' of C
the_arity_of f2 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f2) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
a is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
f1 * x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
(C,f2,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f1 . (C,f2,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
b is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f1 . (C,(C),b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f1 . b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),(f1 . b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),i,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f1 . (C,(C),i,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f1 . i is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f1 . pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),(f1 . i),(f1 . pi1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f1 is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C))
f2 is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C))
dom f1 is Element of bool (Union the Sorts of (Free (C,(C))))
dom f2 is Element of bool (Union the Sorts of (Free (C,(C))))
a is Element of ()
(a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[a,()] is pair non empty set
{a,()} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,()},{a}} is non empty finite V38() set
root-tree [a,()] is non empty Relation-like Function-like DecoratedTree-like set
f1 . (a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 . (a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
T . a is Relation-like Function-like set
a is (C) Element of the carrier' of C
the_arity_of a is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . a is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of a) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
b is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len b is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
rng b is finite Element of bool (Union the Sorts of (Free (C,(C))))
(C,a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f1 . (C,a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 . (C,a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f1 * b is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
rng (f1 * b) is finite Element of bool (Union the Sorts of (Free (C,(C))))
f1 .: (rng b) is finite Element of bool (Union the Sorts of (Free (C,(C))))
f2 * b is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
rng (f2 * b) is finite Element of bool (Union the Sorts of (Free (C,(C))))
f2 .: (rng b) is finite Element of bool (Union the Sorts of (Free (C,(C))))
f1 .: (C) is Element of bool (Union the Sorts of (Free (C,(C))))
f2 .: (C) is Element of bool (Union the Sorts of (Free (C,(C))))
i is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
dom i is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
dom b is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
pi1 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
dom pi1 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
z is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
i . z is set
b . z is set
f1 . (b . z) is set
pi1 . z is set
f2 . (b . z) is set
(C,a,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f1 . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f1 . (C,(C),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 . (C,(C),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),(f2 . a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f1 . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
b is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f1 . b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 . b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
f1 . (C,(C),a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 . (C,(C),a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),(f2 . a),(f2 . b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f1 . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C))
the carrier' of C is non empty set
f1 is Element of the carrier' of C
[f1, the carrier of C] is pair non empty set
{f1, the carrier of C} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1, the carrier of C},{f1}} is non empty finite V38() set
f2 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of Union the Sorts of (Free (C,(C)))
[f1, the carrier of C] -tree f2 is non empty Relation-like Function-like DecoratedTree-like set
x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of Union the Sorts of (Free (C,(C)))
(C,T) * f2 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite Element of bool [:NAT,(Union the Sorts of (Free (C,(C)))):]
[:NAT,(Union the Sorts of (Free (C,(C)))):] is non empty non trivial Relation-like non finite set
bool [:NAT,(Union the Sorts of (Free (C,(C)))):] is non empty non trivial non finite set
(C,T) . ([f1, the carrier of C] -tree f2) is set
[f1, the carrier of C] -tree x is non empty Relation-like Function-like DecoratedTree-like set
(C,T) * f2 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
dom (C,T) is Element of bool (Union the Sorts of (Free (C,(C))))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
a . {} is set
b is (C) Element of the carrier' of C
[b, the carrier of C] is pair non empty set
{b, the carrier of C} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b, the carrier of C},{b}} is non empty finite V38() set
[b, the carrier of C] -tree f2 is non empty Relation-like Function-like DecoratedTree-like set
len f2 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
the_arity_of b is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . b is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of b) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C) * is non empty functional FinSequence-membered FinSequenceSet of (C)
i is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
(C,T) * i is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
pi1 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len pi1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,b,i) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,T) . (C,b,i) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,b,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is Element of the carrier of C
(C) is Element of the carrier of C
(C) is (C,(C))
b is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),b,i) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
the Sorts of (Free (C,(C))) . (C) is non empty set
(C,T) . b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
the Sorts of (Free (C,(C))) . (C) is non empty set
(C,T) . i is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
[(C), the carrier of C] is pair non empty set
{(C), the carrier of C} is non empty finite set
{(C)} is non empty trivial finite 1 -element set
{{(C), the carrier of C},{(C)}} is non empty finite V38() set
<*b,i*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
<*b*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,b] is pair non empty set
{1,b} is non empty finite V38() non with_pair set
{{1,b},{1}} is non empty finite V38() set
{[1,b]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*i*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,i] is pair non empty set
{1,i} is non empty finite V38() non with_pair set
{{1,i},{1}} is non empty finite V38() set
{[1,i]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*b*> ^ <*i*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(C), the carrier of C] -tree <*b,i*> is non empty Relation-like Function-like DecoratedTree-like set
pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
z is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
<*pi1,z*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
<*pi1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,pi1] is pair non empty set
{1,pi1} is non empty finite V38() non with_pair set
{{1,pi1},{1}} is non empty finite V38() set
{[1,pi1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*z*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,z] is pair non empty set
{1,z} is non empty finite V38() non with_pair set
{{1,z},{1}} is non empty finite V38() set
{[1,z]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*pi1*> ^ <*z*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
(C,(C),pi1,z) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is Element of the carrier of C
(C) is (C,(C))
b is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
the Sorts of (Free (C,(C))) . (C) is non empty set
(C,T) . b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
[(C), the carrier of C] is pair non empty set
{(C), the carrier of C} is non empty finite set
{(C)} is non empty trivial finite 1 -element set
{{(C), the carrier of C},{(C)}} is non empty finite V38() set
<*b*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
[1,b] is pair non empty set
{1,b} is non empty finite V38() non with_pair set
{{1,b},{1}} is non empty finite V38() set
{[1,b]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(C), the carrier of C] -tree <*b*> is non empty Relation-like Function-like DecoratedTree-like set
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
<*i*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
[1,i] is pair non empty set
{1,i} is non empty finite V38() non with_pair set
{{1,i},{1}} is non empty finite V38() set
{[1,i]} is non empty trivial Relation-like Function-like constant finite 1 -element set
(C,(C),i) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) . f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
proj2 f1 is finite set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
f1 * (C,T) is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite set
dom (C,T) is Element of bool (Union the Sorts of (Free (C,(C))))
dom (f1 * (C,T)) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
dom f1 is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
len f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
Seg (len f1) is finite len f1 -element V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT : ( 1 <= b₁ & b₁ <= len f1 ) } is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
(C,T,f1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) * f1 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
rng f1 is finite Element of bool (Union the Sorts of (Free (C,(C))))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) * f1 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
rng f1 is finite Element of bool (Union the Sorts of (Free (C,(C))))
f2 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
f1 is Element of ()
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
dom T is Element of bool ()
(f1,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[f1,()] is pair non empty set
{f1,()} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,()},{f1}} is non empty finite V38() set
root-tree [f1,()] is non empty Relation-like Function-like DecoratedTree-like set
(C,T,(f1,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . (f1,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
f1 is Element of ()
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
dom T is Element of bool ()
(f1,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[f1,()] is pair non empty set
{f1,()} is non empty finite set
{f1} is non empty trivial finite 1 -element set
{{f1,()},{f1}} is non empty finite V38() set
root-tree [f1,()] is non empty Relation-like Function-like DecoratedTree-like set
(C,T,(f1,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . (f1,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
T . f1 is Relation-like Function-like set
C is non empty non void V58() V259() () () ManySortedSign
the carrier' of C is non empty set
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
f1 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len f1 is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
T is (C) Element of the carrier' of C
the_arity_of T is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
f2 is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C,T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,f2,(C,T,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f2) . (C,T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2,f1) is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
(C,f2) * f1 is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
(C,T,(C,f2,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
f1 is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C) is (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,(C),T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f1) . (C,(C),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) . T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),(C,f1,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is Element of the carrier of C
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
f2 is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C) is (C,(C))
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f1,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,f2,(C,(C),f1,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f2) . (C,(C),f1,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) . f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) . T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),(C,f2,f1),(C,f2,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 is Element of bool ()
(C,f2) is Relation-like () -defined (C) -valued Function-like one-to-one Function-yielding V115() (C) Element of bool [:(),(C):]
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
{ [b₁,(b₁,C)] where b₁ is Element of () : b₁ in f2 } is set
(C,(C,f2),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2)) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,(C,f2)) . T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
a is Element of ()
(a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[a,()] is pair non empty set
{a,()} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,()},{a}} is non empty finite V38() set
root-tree [a,()] is non empty Relation-like Function-like DecoratedTree-like set
(C,(C,f2),(a,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2)) . (a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
dom (C,f2) is Element of bool ()
(C,f2) . a is Relation-like Function-like set
the carrier' of C is non empty set
a is (C) Element of the carrier' of C
the_arity_of a is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . a is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of a) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
b is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len b is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
rng b is finite Element of bool (Union the Sorts of (Free (C,(C))))
(C,a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2),(C,a,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2)) . (C,a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2),b) is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
(C,(C,f2)) * b is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
len (C,(C,f2),b) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
dom (C,(C,f2),b) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
dom b is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
i is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
b . i is set
(C,(C,f2),b) . i is set
pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C,f2),pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2)) . pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C) is Element of the carrier of C
(C) is (C,(C))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C,f2),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2)) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2),(C,(C),a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2)) . (C,(C),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C) is Element of the carrier of C
(C) is (C,(C))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C,f2),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2)) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
b is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C,f2),b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2)) . b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2),(C,(C),a,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2)) . (C,(C),a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
id (Union the Sorts of (Free (C,(C)))) is non empty Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like one-to-one total V99() V101() V102() V106() V350() Element of bool [:(Union the Sorts of (Free (C,(C)))),(Union the Sorts of (Free (C,(C)))):]
[:(Union the Sorts of (Free (C,(C)))),(Union the Sorts of (Free (C,(C)))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(Union the Sorts of (Free (C,(C)))):] is non empty set
T is Element of bool ()
(C,T) is Relation-like () -defined (C) -valued Function-like one-to-one Function-yielding V115() (C) Element of bool [:(),(C):]
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
{ [b₁,(b₁,C)] where b₁ is Element of () : b₁ in T } is set
(C,(C,T)) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
dom (C,(C,T)) is Element of bool (Union the Sorts of (Free (C,(C))))
f2 is set
(C,(C,T)) . f2 is set
x is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,T),x) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,T)) . x is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f1 is non pair empty proper Relation-like non-empty empty-yielding () -defined (C) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() (C) Element of bool [:(),(C):]
(C,f1,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f1) . T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
{} () is non pair empty proper 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 V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() Element of bool ()
(C,({} ())) is non pair empty proper Relation-like non-empty empty-yielding () -defined (C) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() (C) Element of bool [:(),(C):]
{ [b₁,(b₁,C)] where b₁ is Element of () : b₁ in {} () } is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
id (Union the Sorts of (Free (C,(C)))) is non empty Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like one-to-one total V99() V101() V102() V106() V350() Element of bool [:(Union the Sorts of (Free (C,(C)))),(Union the Sorts of (Free (C,(C)))):]
[:(Union the Sorts of (Free (C,(C)))),(Union the Sorts of (Free (C,(C)))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (C,(C)))),(Union the Sorts of (Free (C,(C)))):] is non empty set
T is non pair empty proper Relation-like non-empty empty-yielding () -defined (C) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V32() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V100() V103() V106() Function-yielding V115() ext-real constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding non with_pair V315() V316() V317() V318() V319() V320() V321() V324() V325() V326() V327() V328() (C) Element of bool [:(),(C):]
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
dom (C,T) is Element of bool (Union the Sorts of (Free (C,(C))))
f1 is set
(C,T) . f1 is set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) . f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
(C) is Element of the carrier of C
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
the Sorts of (Free (C,(C))) . (C) is non empty set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
(C) is Element of the carrier of C
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
the carrier' of C is non empty set
f2 is (C) Element of the carrier' of C
the_result_sort_of f2 is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . f2 is Element of the carrier of C
the_arity_of f2 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f2) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len x is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f2,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len x is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f2,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,T,x) is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
(C,T) * x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
len (C,T,x) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f2,(C,T,x)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
(C) is Element of the carrier of C
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C) is (C,(C))
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,(C),(C,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,T,(C,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,T) . (C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),(C,T,(C,f1))) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,(C,T,(C,f1))) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
(C) is Element of the carrier of C
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,T,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,T) . f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,T,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,T) . f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is Element of the carrier of C
the carrier of C is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f1 is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C,f1,(C,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f1) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f1) . (C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f1) . T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f1,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,f1) . f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C) is (C,(C))
(C,(C),f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,(C),f2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) . (C,(C),f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C) (C) (C,(C))
(C,(C),x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is (C,(C))
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,f1,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f1) . f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),(C,f1,f2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
(C) is Element of the carrier of C
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
the Sorts of (Free (C,(C))) . (C) is non empty set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
(C) is Element of the carrier of C
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . f1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
the carrier' of C is non empty set
f2 is (C) Element of the carrier' of C
the_result_sort_of f2 is Element of the carrier of C
the ResultSort of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the ResultSort of C . f2 is Element of the carrier of C
the_arity_of f2 is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . f2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of f2) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len x is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f2,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len x is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f2,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,T,x) is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
(C,T) * x is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
len (C,T,x) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f2,(C,T,x)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is Relation-like () -defined (C) -valued Function-like one-to-one Function-yielding V115() (C) Element of bool [:(),(C):]
dom T is Element of bool ()
rng T is functional constituted-DTrees Element of bool (C)
bool (C) is non empty set
{ b₁ where b₁ is Element of () : (b₁,C) in rng T } is set
f2 is set
[f2,()] is pair non empty set
{f2,()} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,()},{f2}} is non empty finite V38() set
root-tree [f2,()] is non empty Relation-like Function-like DecoratedTree-like set
a is Element of ()
(a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[a,()] is pair non empty set
{a,()} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,()},{a}} is non empty finite V38() set
root-tree [a,()] is non empty Relation-like Function-like DecoratedTree-like set
x is Element of ()
(x,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[x,()] is pair non empty set
{x,()} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,()},{x}} is non empty finite V38() set
root-tree [x,()] is non empty Relation-like Function-like DecoratedTree-like set
a is Element of ()
(a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[a,()] is pair non empty set
{a,()} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,()},{a}} is non empty finite V38() set
root-tree [a,()] is non empty Relation-like Function-like DecoratedTree-like set
a is set
T . a is Relation-like Function-like set
b is Element of ()
(b,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[b,()] is pair non empty set
{b,()} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,()},{b}} is non empty finite V38() set
root-tree [b,()] is non empty Relation-like Function-like DecoratedTree-like set
f2 is Relation-like Function-like set
proj1 f2 is set
x is set
a is Element of ()
(a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[a,()] is pair non empty set
{a,()} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,()},{a}} is non empty finite V38() set
root-tree [a,()] is non empty Relation-like Function-like DecoratedTree-like set
proj2 f2 is set
x is set
a is set
f2 . a is set
b is Element of ()
(b,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[b,()] is pair non empty set
{b,()} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,()},{b}} is non empty finite V38() set
root-tree [b,()] is non empty Relation-like Function-like DecoratedTree-like set
f2 . b is set
i is set
T . i is Relation-like Function-like set
[i,()] is pair non empty set
{i,()} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,()},{i}} is non empty finite V38() set
root-tree [i,()] is non empty Relation-like Function-like DecoratedTree-like set
pi1 is Element of ()
(pi1,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[pi1,()] is pair non empty set
{pi1,()} is non empty finite set
{pi1} is non empty trivial finite 1 -element set
{{pi1,()},{pi1}} is non empty finite V38() set
root-tree [pi1,()] is non empty Relation-like Function-like DecoratedTree-like set
x is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
a is Element of ()
dom x is Element of bool ()
x . a is Relation-like Function-like set
(a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[a,()] is pair non empty set
{a,()} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,()},{a}} is non empty finite V38() set
root-tree [a,()] is non empty Relation-like Function-like DecoratedTree-like set
b is set
T . b is Relation-like Function-like set
[b,()] is pair non empty set
{b,()} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,()},{b}} is non empty finite V38() set
root-tree [b,()] is non empty Relation-like Function-like DecoratedTree-like set
i is Element of ()
(i,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[i,()] is pair non empty set
{i,()} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,()},{i}} is non empty finite V38() set
root-tree [i,()] is non empty Relation-like Function-like DecoratedTree-like set
a is set
proj1 x is set
b is set
x . a is Relation-like Function-like set
x . b is Relation-like Function-like set
dom x is Element of bool ()
i is Element of ()
(i,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[i,()] is pair non empty set
{i,()} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,()},{i}} is non empty finite V38() set
root-tree [i,()] is non empty Relation-like Function-like DecoratedTree-like set
x . i is Relation-like Function-like set
z is set
T . z is Relation-like Function-like set
[z,()] is pair non empty set
{z,()} is non empty finite set
{z} is non empty trivial finite 1 -element set
{{z,()},{z}} is non empty finite V38() set
root-tree [z,()] is non empty Relation-like Function-like DecoratedTree-like set
pi1 is Element of ()
(pi1,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[pi1,()] is pair non empty set
{pi1,()} is non empty finite set
{pi1} is non empty trivial finite 1 -element set
{{pi1,()},{pi1}} is non empty finite V38() set
root-tree [pi1,()] is non empty Relation-like Function-like DecoratedTree-like set
x2 is set
T . x2 is Relation-like Function-like set
[x2,()] is pair non empty set
{x2,()} is non empty finite set
{x2} is non empty trivial finite 1 -element set
{{x2,()},{x2}} is non empty finite V38() set
root-tree [x2,()] is non empty Relation-like Function-like DecoratedTree-like set
x1 is Element of ()
(x1,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[x1,()] is pair non empty set
{x1,()} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,()},{x1}} is non empty finite V38() set
root-tree [x1,()] is non empty Relation-like Function-like DecoratedTree-like set
x2 is Element of ()
(x2,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[x2,()] is pair non empty set
{x2,()} is non empty finite set
{x2} is non empty trivial finite 1 -element set
{{x2,()},{x2}} is non empty finite V38() set
root-tree [x2,()] is non empty Relation-like Function-like DecoratedTree-like set
a is Relation-like () -defined (C) -valued Function-like one-to-one Function-yielding V115() (C) Element of bool [:(),(C):]
dom a is Element of bool ()
b is Element of ()
T . b is Relation-like Function-like set
i is Element of ()
(i,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[i,()] is pair non empty set
{i,()} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,()},{i}} is non empty finite V38() set
root-tree [i,()] is non empty Relation-like Function-like DecoratedTree-like set
a . i is Relation-like Function-like set
(b,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[b,()] is pair non empty set
{b,()} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,()},{b}} is non empty finite V38() set
root-tree [b,()] is non empty Relation-like Function-like DecoratedTree-like set
pi1 is set
T . pi1 is Relation-like Function-like set
[pi1,()] is pair non empty set
{pi1,()} is non empty finite set
{pi1} is non empty trivial finite 1 -element set
{{pi1,()},{pi1}} is non empty finite V38() set
root-tree [pi1,()] is non empty Relation-like Function-like DecoratedTree-like set
pi1 is set
T . pi1 is Relation-like Function-like set
[pi1,()] is pair non empty set
{pi1,()} is non empty finite set
{pi1} is non empty trivial finite 1 -element set
{{pi1,()},{pi1}} is non empty finite V38() set
root-tree [pi1,()] is non empty Relation-like Function-like DecoratedTree-like set
z is Element of ()
(z,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[z,()] is pair non empty set
{z,()} is non empty finite set
{z} is non empty trivial finite 1 -element set
{{z,()},{z}} is non empty finite V38() set
root-tree [z,()] is non empty Relation-like Function-like DecoratedTree-like set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is Relation-like () -defined (C) -valued Function-like one-to-one Function-yielding V115() (C) Element of bool [:(),(C):]
dom T is Element of bool ()
f1 is Relation-like () -defined (C) -valued Function-like one-to-one Function-yielding V115() (C) Element of bool [:(),(C):]
dom f1 is Element of bool ()
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) is finite Element of bool ()
C variables_in f2 is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in f2) . (C) is finite set
(C,T,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,f2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f1) . (C,T,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
x is Element of ()
(x,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[x,()] is pair non empty set
{x,()} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,()},{x}} is non empty finite V38() set
root-tree [x,()] is non empty Relation-like Function-like DecoratedTree-like set
(C,(x,C)) is finite Element of bool ()
C variables_in (x,C) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (x,C)) . (C) is finite set
(C,T,(x,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) . (x,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,(x,C))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) . (C,T,(x,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
{x} is non empty trivial finite 1 -element Element of bool ()
T . x is Relation-like Function-like set
a is Element of ()
(a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[a,()] is pair non empty set
{a,()} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,()},{a}} is non empty finite V38() set
root-tree [a,()] is non empty Relation-like Function-like DecoratedTree-like set
f1 . a is Relation-like Function-like set
(C,T,(x,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
the carrier' of C is non empty set
x is (C) Element of the carrier' of C
the_arity_of x is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of x) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
a is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len a is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
rng a is finite Element of bool (Union the Sorts of (Free (C,(C))))
(C,x,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,(C,x,a)) is finite Element of bool ()
C variables_in (C,x,a) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,x,a)) . (C) is finite set
(C,T,(C,x,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) . (C,x,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,(C,x,a))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) . (C,T,(C,x,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
[x, the carrier of C] is pair non empty set
{x, the carrier of C} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x, the carrier of C},{x}} is non empty finite V38() set
[x, the carrier of C] -tree a is non empty Relation-like Function-like DecoratedTree-like set
{ (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in rng a } is set
union { (C,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ in rng a } is set
(C,T,a) is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
(C,T) * a is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
len (C,T,a) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,f1,(C,T,a)) is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
(C,f1) * (C,T,a) is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
len (C,f1,(C,T,a)) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
dom (C,T,a) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
dom a is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
dom (C,f1,(C,T,a)) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
b is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
(C,T,a) . b is set
a . b is set
(C,T) . (a . b) is set
i is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,i) is finite Element of bool ()
C variables_in i is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in i) . (C) is finite set
(C,f1,(C,T,a)) . b is set
(C,T,i) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) . i is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,i)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f1) . (C,T,i) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,T,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is Element of the carrier of C
(C) is (C,(C))
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,x) is finite Element of bool ()
C variables_in x is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in x) . (C) is finite set
(C,T,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) . x is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,x)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) . (C,T,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,(C,(C),x)) is finite Element of bool ()
C variables_in (C,(C),x) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,(C),x)) . (C) is finite set
(C,T,(C,(C),x)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) . (C,(C),x) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,(C,(C),x))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) . (C,T,(C,(C),x)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*x*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
[1,x] is pair non empty set
{1,x} is non empty finite V38() non with_pair set
{{1,x},{1}} is non empty finite V38() set
{[1,x]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(), the carrier of C] -tree <*x*> is non empty Relation-like Function-like DecoratedTree-like set
(C,T,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),(C,T,x)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,(C),(C,T,x))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) . (C,(C),(C,T,x)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C) is Element of the carrier of C
(C) is (C,(C))
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,x) is finite Element of bool ()
C variables_in x is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in x) . (C) is finite set
(C,T,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) . x is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,x)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) . (C,T,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,a) is finite Element of bool ()
C variables_in a is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in a) . (C) is finite set
(C,T,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) . (C,T,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),x,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,(C,(C),x,a)) is finite Element of bool ()
C variables_in (C,(C),x,a) is non empty Relation-like the carrier of C -defined Function-like total set
(C variables_in (C,(C),x,a)) . (C) is finite set
(C,T,(C,(C),x,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,T) . (C,(C),x,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,(C,(C),x,a))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) . (C,T,(C,(C),x,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
[(), the carrier of C] is pair non empty set
{(), the carrier of C} is non empty finite set
{()} is non empty trivial finite 1 -element set
{{(), the carrier of C},{()}} is non empty finite V38() set
<*x,a*> is non empty Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
<*x*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x] is pair non empty set
{1,x} is non empty finite V38() non with_pair set
{{1,x},{1}} is non empty finite V38() set
{[1,x]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*a*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,a] is pair non empty set
{1,a} is non empty finite V38() non with_pair set
{{1,a},{1}} is non empty finite V38() set
{[1,a]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x*> ^ <*a*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[(), the carrier of C] -tree <*x,a*> is non empty Relation-like Function-like DecoratedTree-like set
(C variables_in x) \/ (C variables_in a) is non empty Relation-like the carrier of C -defined Function-like total set
((C variables_in x) \/ (C variables_in a)) . () is set
(C,x) \/ (C,a) is finite Element of bool ()
(C,T,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),(C,T,x),(C,T,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,(C),(C,T,x),(C,T,a))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1) . (C,(C),(C,T,x),(C,T,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is functional constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } is set
x is set
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is functional constituted-DTrees Element of bool (C)
(C,T,f1) is functional constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } is set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
{f2} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
(C,T,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
{(C,T,f2)} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
x is set
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
x is set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is functional constituted-DTrees Element of bool (C)
f2 is functional constituted-DTrees Element of bool (C)
f1 \/ f2 is functional constituted-DTrees Element of bool (C)
(C,T,(f1 \/ f2)) is functional constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 \/ f2 } is set
(C,T,f1) is functional constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } is set
(C,T,f2) is functional constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f2 } is set
(C,T,f1) \/ (C,T,f2) is functional constituted-DTrees Element of bool (C)
x is set
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
x is set
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
b is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) . b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is functional constituted-DTrees Element of bool (C)
f2 is functional constituted-DTrees Element of bool (C)
(C,T,f1) is functional constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } is set
(C,T,f2) is functional constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f2 } is set
f1 \/ f2 is functional constituted-DTrees Element of bool (C)
(C,T,f1) \/ (C,T,f2) is functional constituted-DTrees Element of bool (C)
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is functional finite constituted-DTrees Element of bool (C)
(C,T,f1) is functional constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in f1 } is set
{ H₂(b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C))) : b₁ in f1 } is set
f2 is set
x is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,x) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . x is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is pair non empty (C)
(C,f1) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C,T,(C,f1)) is functional finite constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in (C,f1) } is set
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
(C,T,(C,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . (C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,T,(C,f1)),(C,T,(C,f1))) is pair non empty (C)
{(C,T,(C,f1)),(C,T,(C,f1))} is non empty finite V38() set
{(C,T,(C,f1))} is non empty trivial finite V38() 1 -element set
{{(C,T,(C,f1)),(C,T,(C,f1))},{(C,T,(C,f1))}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
f2 is non empty non void V58() V259() () () ManySortedSign
(f2) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (f2,(f2))))
(f2) is non empty Relation-like non empty-yielding the carrier of f2 -defined Function-like total (f2) set
the carrier of f2 is non empty set
Free (f2,(f2)) is strict non-empty non empty MSAlgebra over f2
the Sorts of (Free (f2,(f2))) is non empty Relation-like non-empty non empty-yielding the carrier of f2 -defined Function-like total (f2) set
Union the Sorts of (Free (f2,(f2))) is non empty set
proj2 the Sorts of (Free (f2,(f2))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (f2,(f2)))) is set
bool (Union the Sorts of (Free (f2,(f2)))) is non empty set
(f2) is Element of the carrier of f2
the Sorts of (Free (f2,(f2))) . (f2) is non empty set
[:(),(f2):] is non empty Relation-like set
bool [:(),(f2):] is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is pair non empty (C)
(C,T,f1) is pair non empty (C)
(C,f1) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C,T,(C,f1)) is functional finite constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in (C,f1) } is set
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
(C,T,(C,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . (C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,T,(C,f1)),(C,T,(C,f1))) is pair non empty (C)
{(C,T,(C,f1)),(C,T,(C,f1))} is non empty finite V38() set
{(C,T,(C,f1))} is non empty trivial finite V38() 1 -element set
{{(C,T,(C,f1)),(C,T,(C,f1))},{(C,T,(C,f1))}} is non empty finite V38() set
(C,(C,T,f1)) is functional finite constituted-DTrees Element of bool (C)
x is Relation-like () -defined (f2) -valued Function-like Function-yielding V115() Element of bool [:(),(f2):]
a is pair non empty (f2)
(f2,x,a) is pair non empty (f2)
(f2,a) is functional finite constituted-DTrees Element of bool (f2)
(f2) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (f2,(f2))))
(f2) is Element of the carrier of f2
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2,(f2)) : b₁ is (f2) } is set
bool (f2) is non empty set
(f2,x,(f2,a)) is functional finite constituted-DTrees Element of bool (f2)
{ (f2,x,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2) (f2,(f2)) : b₁ in (f2,a) } is set
(f2,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2) (f2,(f2))
(f2) is Element of the carrier of f2
(f2,x,(f2,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2) (f2,(f2))
(f2,x) is Relation-like Union the Sorts of (Free (f2,(f2))) -defined Union the Sorts of (Free (f2,(f2))) -valued Function-like quasi_total (f2,(f2)) (f2,(f2))
(f2,x) . (f2,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (f2,(f2)))
(f2,(f2,x,(f2,a)),(f2,x,(f2,a))) is pair non empty (f2)
{(f2,x,(f2,a)),(f2,x,(f2,a))} is non empty finite V38() set
{(f2,x,(f2,a))} is non empty trivial finite V38() 1 -element set
{{(f2,x,(f2,a)),(f2,x,(f2,a))},{(f2,x,(f2,a))}} is non empty finite V38() set
(f2,(f2,x,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (f2) (f2,(f2))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
(C) is Element of the carrier of C
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is pair non empty (C)
(C,T,f1) is pair non empty (C)
(C,f1) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C,T,(C,f1)) is functional finite constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in (C,f1) } is set
(C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
(C,T,(C,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . (C,f1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,T,(C,f1)),(C,T,(C,f1))) is pair non empty (C)
{(C,T,(C,f1)),(C,T,(C,f1))} is non empty finite V38() set
{(C,T,(C,f1))} is non empty trivial finite V38() 1 -element set
{{(C,T,(C,f1)),(C,T,(C,f1))},{(C,T,(C,f1))}} is non empty finite V38() set
f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f1,f2) is pair non empty (C)
{f2} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
{f2} \/ (C,f1) is non empty finite set
[({f2} \/ (C,f1)),(C,f1)] is pair non empty set
{({f2} \/ (C,f1)),(C,f1)} is non empty finite V38() set
{({f2} \/ (C,f1))} is non empty trivial finite V38() 1 -element set
{{({f2} \/ (C,f1)),(C,f1)},{({f2} \/ (C,f1))}} is non empty finite V38() set
(C,T,(C,f1,f2)) is pair non empty (C)
(C,(C,f1,f2)) is functional finite constituted-DTrees Element of bool (C)
(C,T,(C,(C,f1,f2))) is functional finite constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in (C,(C,f1,f2)) } is set
(C,(C,f1,f2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T,(C,(C,f1,f2))) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) . (C,(C,f1,f2)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,T,(C,(C,f1,f2))),(C,T,(C,(C,f1,f2)))) is pair non empty (C)
{(C,T,(C,(C,f1,f2))),(C,T,(C,(C,f1,f2)))} is non empty finite V38() set
{(C,T,(C,(C,f1,f2)))} is non empty trivial finite V38() 1 -element set
{{(C,T,(C,(C,f1,f2))),(C,T,(C,(C,f1,f2)))},{(C,T,(C,(C,f1,f2)))}} is non empty finite V38() set
(C,T,f2) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,T) . f2 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,T,f1),(C,T,f2)) is pair non empty (C)
{(C,T,f2)} is non empty trivial functional finite V38() 1 -element non with_pair Element of bool (Union the Sorts of (Free (C,(C))))
(C,(C,T,f1)) is functional finite constituted-DTrees Element of bool (C)
{(C,T,f2)} \/ (C,(C,T,f1)) is non empty finite set
(C,(C,T,f1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
[({(C,T,f2)} \/ (C,(C,T,f1))),(C,(C,T,f1))] is pair non empty set
{({(C,T,f2)} \/ (C,(C,T,f1))),(C,(C,T,f1))} is non empty finite V38() set
{({(C,T,f2)} \/ (C,(C,T,f1)))} is non empty trivial finite V38() 1 -element set
{{({(C,T,f2)} \/ (C,(C,T,f1))),(C,(C,T,f1))},{({(C,T,f2)} \/ (C,(C,T,f1)))}} is non empty finite V38() set
[(C,T,(C,(C,f1,f2))),(C,T,(C,f1))] is pair non empty Element of [:(bool (C)),(Union the Sorts of (Free (C,(C)))):]
[:(bool (C)),(Union the Sorts of (Free (C,(C)))):] is non empty Relation-like set
{(C,T,(C,(C,f1,f2))),(C,T,(C,f1))} is non empty finite V38() set
{{(C,T,(C,(C,f1,f2))),(C,T,(C,f1))},{(C,T,(C,(C,f1,f2)))}} is non empty finite V38() set
x is functional constituted-DTrees Element of bool (C)
x \/ (C,f1) is functional constituted-DTrees Element of bool (C)
(C,T,(x \/ (C,f1))) is functional constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in x \/ (C,f1) } is set
[(C,T,(x \/ (C,f1))),(C,T,(C,f1))] is pair non empty Element of [:(bool (C)),(Union the Sorts of (Free (C,(C)))):]
{(C,T,(x \/ (C,f1))),(C,T,(C,f1))} is non empty finite set
{(C,T,(x \/ (C,f1)))} is non empty trivial finite 1 -element set
{{(C,T,(x \/ (C,f1))),(C,T,(C,f1))},{(C,T,(x \/ (C,f1)))}} is non empty finite V38() set
(C,T,x) is functional constituted-DTrees Element of bool (C)
{ (C,T,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in x } is set
(C,T,x) \/ (C,T,(C,f1)) is functional constituted-DTrees Element of bool (C)
[((C,T,x) \/ (C,T,(C,f1))),(C,T,(C,f1))] is pair non empty Element of [:(bool (C)),(Union the Sorts of (Free (C,(C)))):]
{((C,T,x) \/ (C,T,(C,f1))),(C,T,(C,f1))} is non empty finite set
{((C,T,x) \/ (C,T,(C,f1)))} is non empty trivial finite 1 -element set
{{((C,T,x) \/ (C,T,(C,f1))),(C,T,(C,f1))},{((C,T,x) \/ (C,T,(C,f1)))}} is non empty finite V38() set
{(C,T,f2)} \/ (C,T,(C,f1)) is non empty finite set
[({(C,T,f2)} \/ (C,T,(C,f1))),(C,T,(C,f1))] is pair non empty set
{({(C,T,f2)} \/ (C,T,(C,f1))),(C,T,(C,f1))} is non empty finite V38() set
{({(C,T,f2)} \/ (C,T,(C,f1)))} is non empty trivial finite V38() 1 -element set
{{({(C,T,f2)} \/ (C,T,(C,f1))),(C,T,(C,f1))},{({(C,T,f2)} \/ (C,T,(C,f1)))}} is non empty finite V38() set
[({(C,T,f2)} \/ (C,(C,T,f1))),(C,T,(C,f1))] is pair non empty set
{({(C,T,f2)} \/ (C,(C,T,f1))),(C,T,(C,f1))} is non empty finite V38() set
{{({(C,T,f2)} \/ (C,(C,T,f1))),(C,T,(C,f1))},{({(C,T,f2)} \/ (C,(C,T,f1)))}} is non empty finite V38() set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
dom T is Element of bool ()
f1 is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
dom f1 is Element of bool ()
(dom T) \/ (dom f1) is Element of bool ()
f2 is Relation-like Function-like set
proj1 f2 is set
proj2 f2 is set
x is set
a is set
f2 . a is set
In (a,()) is Element of ()
((In (a,())),C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[(In (a,())),()] is pair non empty set
{(In (a,())),()} is non empty finite set
{(In (a,()))} is non empty trivial finite 1 -element set
{{(In (a,())),()},{(In (a,()))}} is non empty finite V38() set
root-tree [(In (a,())),()] is non empty Relation-like Function-like DecoratedTree-like set
(C,T,((In (a,())),C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . ((In (a,())),C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,((In (a,())),C))) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f1) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f1) . (C,T,((In (a,())),C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
x is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
dom x is Element of bool ()
a is Element of ()
x . a is Relation-like Function-like set
(a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[a,()] is pair non empty set
{a,()} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,()},{a}} is non empty finite V38() set
root-tree [a,()] is non empty Relation-like Function-like DecoratedTree-like set
(C,T,(a,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . (a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,(a,C))) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f1) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f1) . (C,T,(a,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
In (a,()) is Element of ()
((In (a,())),C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[(In (a,())),()] is pair non empty set
{(In (a,())),()} is non empty finite set
{(In (a,()))} is non empty trivial finite 1 -element set
{{(In (a,())),()},{(In (a,()))}} is non empty finite V38() set
root-tree [(In (a,())),()] is non empty Relation-like Function-like DecoratedTree-like set
(C,T,((In (a,())),C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) . ((In (a,())),C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,((In (a,())),C))) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f1) . (C,T,((In (a,())),C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
f2 is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
dom f2 is Element of bool ()
x is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
dom x is Element of bool ()
a is Element of ()
f2 . a is Relation-like Function-like set
(a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[a,()] is pair non empty set
{a,()} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,()},{a}} is non empty finite V38() set
root-tree [a,()] is non empty Relation-like Function-like DecoratedTree-like set
(C,T,(a,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . (a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,(a,C))) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f1) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f1) . (C,T,(a,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
x . a is Relation-like Function-like set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is Relation-like () -defined (C) -valued Function-like Function-yielding V115() (C) Element of bool [:(),(C):]
f1 is Relation-like () -defined (C) -valued Function-like Function-yielding V115() (C) Element of bool [:(),(C):]
(C,T,f1) is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f2 is Element of ()
dom (C,T,f1) is Element of bool ()
(C,T,f1) . f2 is Relation-like Function-like set
(f2,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[f2,()] is pair non empty set
{f2,()} is non empty finite set
{f2} is non empty trivial finite 1 -element set
{{f2,()},{f2}} is non empty finite V38() set
root-tree [f2,()] is non empty Relation-like Function-like DecoratedTree-like set
(C,T,(f2,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,T) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,T) . (f2,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,(C,T,(f2,C))) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f1) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f1) . (C,T,(f2,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
dom T is Element of bool ()
dom f1 is Element of bool ()
(dom T) \/ (dom f1) is Element of bool ()
T . f2 is Relation-like Function-like set
x is Element of ()
(x,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[x,()] is pair non empty set
{x,()} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,()},{x}} is non empty finite V38() set
root-tree [x,()] is non empty Relation-like Function-like DecoratedTree-like set
f1 . x is Relation-like Function-like set
f1 . f2 is Relation-like Function-like set
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
x is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f2 is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C,f2,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f2) . T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,f2,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,x) . (C,f2,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2,x) is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C,(C,f2,x),T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x)) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,(C,f2,x)) . T is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
dom (C,f2,x) is Element of bool ()
dom f2 is Element of bool ()
dom x is Element of bool ()
(dom f2) \/ (dom x) is Element of bool ()
a is Element of ()
(a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) (C,(C))
[a,()] is pair non empty set
{a,()} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,()},{a}} is non empty finite V38() set
root-tree [a,()] is non empty Relation-like Function-like DecoratedTree-like set
(C,f2,(a,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) . (a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,f2,(a,C))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x) . (C,f2,(a,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x),(a,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x)) . (a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x),(a,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f2,x) . a is Relation-like Function-like set
(C,f2,(a,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,x,(a,C)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,x) . (a,C) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
the carrier' of C is non empty set
a is (C) Element of the carrier' of C
the_arity_of a is Relation-like NAT -defined the carrier of C -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
the carrier of C * is non empty functional FinSequence-membered FinSequenceSet of the carrier of C
the Arity of C is Relation-like the carrier' of C -defined the carrier of C * -valued Function-like quasi_total Function-yielding V115() Element of bool [: the carrier' of C,( the carrier of C *):]
[: the carrier' of C,( the carrier of C *):] is non empty Relation-like set
bool [: the carrier' of C,( the carrier of C *):] is non empty set
the Arity of C . a is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of C *
len (the_arity_of a) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
b is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
len b is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
rng b is finite Element of bool (Union the Sorts of (Free (C,(C))))
(C,a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,f2,(C,a,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) . (C,a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,f2,(C,a,b))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x) . (C,f2,(C,a,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x),(C,a,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x)) . (C,a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2,b) is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
(C,f2) * b is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
(Union the Sorts of (Free (C,(C)))) * is non empty functional FinSequence-membered FinSequenceSet of Union the Sorts of (Free (C,(C)))
len (C,f2,b) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,(C,f2,x),b) is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
(C,(C,f2,x)) * b is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
len (C,(C,f2,x),b) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
(C,x,(C,f2,b)) is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of (C)
(C,x) * (C,f2,b) is Relation-like NAT -defined Union the Sorts of (Free (C,(C))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Element of (Union the Sorts of (Free (C,(C)))) *
len (C,x,(C,f2,b)) is non pair epsilon-transitive epsilon-connected ordinal natural V32() V33() finite cardinal ext-real V315() V316() V317() V318() V319() V320() V324() V325() V326() V328() V329() Element of NAT
dom (C,f2,b) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
dom b is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
dom (C,(C,f2,x),b) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
dom (C,x,(C,f2,b)) is finite V315() V316() V317() V318() V319() V320() V324() V325() V326() Element of bool NAT
i is non pair epsilon-transitive epsilon-connected ordinal natural V32() finite cardinal ext-real V328() set
(C,x,(C,f2,b)) . i is set
(C,f2,b) . i is set
(C,x) . ((C,f2,b) . i) is set
b . i is set
pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f2,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f2) . pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,f2,pi1)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,x) . (C,f2,pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x),pi1) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C,f2,x)) . pi1 is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x),b) . i is set
(C,a,(C,f2,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,a,(C,f2,b))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x) . (C,a,(C,f2,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,a,(C,(C,f2,x),b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is Element of the carrier of C
(C) is (C,(C))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f2,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,f2,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x) . (C,f2,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x)) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,f2,(C,(C),a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) . (C,(C),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,f2,(C,(C),a))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x) . (C,f2,(C,(C),a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x),(C,(C),a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x)) . (C,(C),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),(C,f2,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,(C),(C,f2,a))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x) . (C,(C),(C,f2,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),(C,(C,f2,x),a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C) is Element of the carrier of C
(C) is (C,(C))
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f2,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,f2,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x) . (C,f2,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x)) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
b is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f2,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) . b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,f2,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x) . (C,f2,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x),b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x)) . b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C),a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,f2,(C,(C),a,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2) . (C,(C),a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,f2,(C,(C),a,b))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x) . (C,f2,(C,(C),a,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x),(C,(C),a,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x)) . (C,(C),a,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,f2,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),(C,f2,a),(C,f2,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
(C,x,(C,(C),(C,f2,a),(C,f2,b))) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,x) . (C,(C),(C,f2,a),(C,f2,b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,x),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C,f2,x),b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C))
(C,(C),(C,(C,f2,x),a),(C,(C,f2,x),b)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is functional constituted-DTrees Element of bool (C)
f2 is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C,f1,T) is functional constituted-DTrees Element of bool (C)
{ (C,f1,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in T } is set
(C,f2,(C,f1,T)) is functional constituted-DTrees Element of bool (C)
{ (C,f2,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in (C,f1,T) } is set
(C,f1,f2) is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C,(C,f1,f2),T) is functional constituted-DTrees Element of bool (C)
{ (C,(C,f1,f2),b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in T } is set
x is set
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f2,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f2) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f2) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
b is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f1,b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f1) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f1) . b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f1,f2),b) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,f1,f2)) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,(C,f1,f2)) . b is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
x is set
a is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,f1,f2),a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,f1,f2)) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,(C,f1,f2)) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f1,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f1) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f1) . a is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,f2,(C,f1,a)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f2) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f2) . (C,f1,a) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
C is non empty non void V58() V259() () () ManySortedSign
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is non empty Relation-like non empty-yielding the carrier of C -defined Function-like total (C) set
the carrier of C is non empty set
Free (C,(C)) is strict non-empty non empty MSAlgebra over C
the Sorts of (Free (C,(C))) is non empty Relation-like non-empty non empty-yielding the carrier of C -defined Function-like total (C) set
Union the Sorts of (Free (C,(C))) is non empty set
proj2 the Sorts of (Free (C,(C))) is non empty with_non-empty_elements set
union (proj2 the Sorts of (Free (C,(C)))) is set
bool (Union the Sorts of (Free (C,(C)))) is non empty set
(C) is Element of the carrier of C
the Sorts of (Free (C,(C))) . (C) is non empty set
[:(),(C):] is non empty Relation-like set
bool [:(),(C):] is non empty set
T is pair non empty (C)
f2 is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
f1 is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C,f1,T) is pair non empty (C)
(C,T) is functional finite constituted-DTrees Element of bool (C)
(C) is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (C,(C))))
(C) is Element of the carrier of C
{ b₁ where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C,(C)) : b₁ is (C) } is set
bool (C) is non empty set
(C,f1,(C,T)) is functional finite constituted-DTrees Element of bool (C)
{ (C,f1,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in (C,T) } is set
(C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C) is Element of the carrier of C
(C,f1,(C,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f1) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f1) . (C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f1,(C,T)),(C,f1,(C,T))) is pair non empty (C)
{(C,f1,(C,T)),(C,f1,(C,T))} is non empty finite V38() set
{(C,f1,(C,T))} is non empty trivial finite V38() 1 -element set
{{(C,f1,(C,T)),(C,f1,(C,T))},{(C,f1,(C,T))}} is non empty finite V38() set
(C,f2,(C,f1,T)) is pair non empty (C)
(C,(C,f1,T)) is functional finite constituted-DTrees Element of bool (C)
(C,f2,(C,(C,f1,T))) is functional finite constituted-DTrees Element of bool (C)
{ (C,f2,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in (C,(C,f1,T)) } is set
(C,(C,f1,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f2,(C,(C,f1,T))) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f2) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,f2) . (C,(C,f1,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,f2,(C,(C,f1,T))),(C,f2,(C,(C,f1,T)))) is pair non empty (C)
{(C,f2,(C,(C,f1,T))),(C,f2,(C,(C,f1,T)))} is non empty finite V38() set
{(C,f2,(C,(C,f1,T)))} is non empty trivial finite V38() 1 -element set
{{(C,f2,(C,(C,f1,T))),(C,f2,(C,(C,f1,T)))},{(C,f2,(C,(C,f1,T)))}} is non empty finite V38() set
(C,f1,f2) is Relation-like () -defined (C) -valued Function-like Function-yielding V115() Element of bool [:(),(C):]
(C,(C,f1,f2),T) is pair non empty (C)
(C,(C,f1,f2),(C,T)) is functional finite constituted-DTrees Element of bool (C)
{ (C,(C,f1,f2),b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in (C,T) } is set
(C,(C,f1,f2),(C,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,(C,f1,f2)) is Relation-like Union the Sorts of (Free (C,(C))) -defined Union the Sorts of (Free (C,(C))) -valued Function-like quasi_total (C,(C)) (C,(C))
(C,(C,f1,f2)) . (C,T) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,(C,f1,f2),(C,T)),(C,(C,f1,f2),(C,T))) is pair non empty (C)
{(C,(C,f1,f2),(C,T)),(C,(C,f1,f2),(C,T))} is non empty finite V38() set
{(C,(C,f1,f2),(C,T))} is non empty trivial finite V38() 1 -element set
{{(C,(C,f1,f2),(C,T)),(C,(C,f1,f2),(C,T))},{(C,(C,f1,f2),(C,T))}} is non empty finite V38() set
(C,f2,(C,f1,(C,T))) is functional finite constituted-DTrees Element of bool (C)
{ (C,f2,b₁) where b₁ is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C)) : b₁ in (C,f1,(C,T)) } is set
(C,(C,f2,(C,f1,(C,T))),(C,f2,(C,(C,f1,T)))) is pair non empty (C)
{(C,f2,(C,f1,(C,T))),(C,f2,(C,(C,f1,T)))} is non empty finite V38() set
{(C,f2,(C,f1,(C,T)))} is non empty trivial finite V38() 1 -element set
{{(C,f2,(C,f1,(C,T))),(C,f2,(C,(C,f1,T)))},{(C,f2,(C,f1,(C,T)))}} is non empty finite V38() set
(C,(C,(C,f1,f2),(C,T)),(C,f2,(C,(C,f1,T)))) is pair non empty (C)
{(C,(C,f1,f2),(C,T)),(C,f2,(C,(C,f1,T)))} is non empty finite V38() set
{{(C,(C,f1,f2),(C,T)),(C,f2,(C,(C,f1,T)))},{(C,(C,f1,f2),(C,T))}} is non empty finite V38() set
(C,f2,(C,f1,(C,T))) is non pair non empty Relation-like Function-like finite DecoratedTree-like (C) (C,(C))
(C,f2) . (C,f1,(C,T)) is non pair non empty Relation-like Function-like finite DecoratedTree-like Element of Union the Sorts of (Free (C,(C)))
(C,(C,(C,f1,f2),(C,T)),(C,f2,(C,f1,(C,T)))) is pair non empty (C)
{(C,(C,f1,f2),(C,T)),(C,f2,(C,f1,(C,T)))} is non empty finite V38() set
{{(C,(C,f1,f2),(C,T)),(C,f2,(C,f1,(C,T)))},{(C,(C,f1,f2),(C,T))}} is non empty finite V38() set