:: CIRCTRM1 semantic presentation

REAL is set
NAT is V6() V7() V8() non empty non trivial non finite V33() V34() countable denumerable Element of bool REAL
bool REAL is set
NAT is V6() V7() V8() non empty non trivial non finite V33() V34() countable denumerable set
bool NAT is non trivial non finite set
bool NAT is non trivial non finite set
{} is Relation-like non-empty empty-yielding NAT -defined V6() V7() V8() V10() V11() V12() empty Function-like one-to-one constant functional finite finite-yielding V32() V33() V35( {} ) FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() Cardinal-yielding countable V154() ext-real V158() set
the Relation-like non-empty empty-yielding NAT -defined V6() V7() V8() V10() V11() V12() empty Function-like one-to-one constant functional finite finite-yielding V32() V33() V35( {} ) FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() Cardinal-yielding countable V154() ext-real V158() set is Relation-like non-empty empty-yielding NAT -defined V6() V7() V8() V10() V11() V12() empty Function-like one-to-one constant functional finite finite-yielding V32() V33() V35( {} ) FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() Cardinal-yielding countable V154() ext-real V158() set
1 is V6() V7() V8() V12() non empty finite V33() countable V154() ext-real V158() Element of NAT
{{},1} is non empty finite V32() countable set
Trees is non empty constituted-Trees set
bool Trees is set
FinTrees is non empty constituted-Trees constituted-FinTrees Element of bool Trees
K314() is non empty V112() L13()
the carrier of K314() is non empty set
FinTrees the carrier of K314() is non empty functional constituted-DTrees DTree-set of the carrier of K314()
K313(K314()) is functional constituted-DTrees Element of bool (FinTrees the carrier of K314())
bool (FinTrees the carrier of K314()) is set
[:K313(K314()),NAT:] is Relation-like set
bool [:K313(K314()),NAT:] is set
[:NAT,K313(K314()):] is Relation-like set
bool [:NAT,K313(K314()):] is set
K404() is set
2 is V6() V7() V8() V12() non empty finite V33() countable V154() ext-real V158() Element of NAT
K123(2,K404()) is M8(K404())
[:K123(2,K404()),K404():] is Relation-like set
bool [:K123(2,K404()),K404():] is set
3 is V6() V7() V8() V12() non empty finite V33() countable V154() ext-real V158() Element of NAT
K123(3,K404()) is M8(K404())
[:K123(3,K404()),K404():] is Relation-like set
bool [:K123(3,K404()),K404():] is set
K425() is Relation-like K123(2,K404()) -defined K404() -valued Function-like V25(K123(2,K404()),K404()) Element of bool [:K123(2,K404()),K404():]
0 is Relation-like non-empty empty-yielding NAT -defined V6() V7() V8() V10() V11() V12() empty Function-like one-to-one constant functional finite finite-yielding V32() V33() V35( {} ) FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() Cardinal-yielding countable V154() ext-real V158() Element of NAT
<*> NAT is Relation-like non-empty empty-yielding NAT -defined NAT -valued V6() V7() V8() V10() V11() V12() empty Function-like one-to-one constant functional finite finite-yielding V32() V33() V35( {} ) FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() Cardinal-yielding countable V154() ext-real V158() FinSequence of NAT
elementary_tree 0 is non empty Tree-like set
height (elementary_tree 0) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is non-empty MSAlgebra over S
the Sorts of A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total Variables of A
K334(S,V) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,V) is non empty set
FinTrees the carrier of K334(S,V) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,V)
S -Terms V is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,V))
bool (FinTrees the carrier of K334(S,V)) is set
the Sorts of A \/ V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
K334(S,( the Sorts of A \/ V)) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,( the Sorts of A \/ V)) is non empty set
FinTrees the carrier of K334(S,( the Sorts of A \/ V)) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,( the Sorts of A \/ V))
S -Terms ( the Sorts of A \/ V) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,( the Sorts of A \/ V)))
bool (FinTrees the carrier of K334(S,( the Sorts of A \/ V))) is set
X is Element of the carrier of S
V . X is non empty set
G is Element of V . X
[G,X] is pair set
{G,X} is non empty finite countable set
{G} is non empty trivial finite V35(1) countable set
{{G,X},{G}} is non empty finite V32() countable set
root-tree [G,X] is Relation-like trivial Function-like constant finite DecoratedTree-like finite-order finite-branching countable set
C is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
the_sort_of C is Element of the carrier of S
f is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
the_sort_of f is Element of the carrier of S
the carrier' of S is non empty set
X is Element of the carrier' of S
Sym (X,V) is Element of K316(K334(S,V))
K316(K334(S,V)) is non empty Element of bool the carrier of K334(S,V)
bool the carrier of K334(S,V) is set
[X, the carrier of S] is pair set
{X, the carrier of S} is non empty finite countable set
{X} is non empty trivial finite V35(1) countable set
{{X, the carrier of S},{X}} is non empty finite V32() countable set
G is Relation-like NAT -defined FinTrees the carrier of K334(S,V) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable ArgumentSeq of Sym (X,V)
proj2 G is finite countable set
[X, the carrier of S] -tree G is Relation-like Function-like DecoratedTree-like set
C is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
the_sort_of C is Element of the carrier of S
f is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
the_sort_of f is Element of the carrier of S
C . {} is set
the_result_sort_of X is Element of the carrier of S
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S . X is Element of the carrier of S
G is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
X is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
the_sort_of G is Element of the carrier of S
the_sort_of X is Element of the carrier of S
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the ResultSort of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V)) Element of bool [: the carrier' of (S,A,V), the carrier of (S,A,V):]
the carrier' of (S,A,V) is set
the carrier of (S,A,V) is non empty set
[: the carrier' of (S,A,V), the carrier of (S,A,V):] is Relation-like set
bool [: the carrier' of (S,A,V), the carrier of (S,A,V):] is set
id the carrier' of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier' of (S,A,V) -valued Function-like one-to-one total Element of bool [: the carrier' of (S,A,V), the carrier' of (S,A,V):]
[: the carrier' of (S,A,V), the carrier' of (S,A,V):] is Relation-like set
bool [: the carrier' of (S,A,V), the carrier' of (S,A,V):] is set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
C is non empty non void V68() V153() ManySortedSign
the carrier of C is non empty set
f is Relation-like non-empty non empty-yielding the carrier of C -defined non empty Function-like total set
C -Terms f is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(C,f))
K334(C,f) is non empty V112() V116() V117() V118() L13()
the carrier of K334(C,f) is non empty set
FinTrees the carrier of K334(C,f) is non empty functional constituted-DTrees DTree-set of the carrier of K334(C,f)
bool (FinTrees the carrier of K334(C,f)) is set
bool (C -Terms f) is set
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
X is Relation-like Function-like DecoratedTree-like Element of V
G is Relation-like Function-like DecoratedTree-like Element of V
G . {} is set
g is non empty functional constituted-DTrees Element of bool (C -Terms f)
the carrier' of C is non empty set
{ the carrier of C} is non empty trivial finite V35(1) countable set
[: the carrier' of C,{ the carrier of C}:] is Relation-like set
(C,f,g) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees g is non empty functional constituted-DTrees set
[: the carrier' of C,{ the carrier of C}:] -Subtrees g is functional constituted-DTrees Element of bool (Subtrees g)
bool (Subtrees g) is set
[: the carrier' of C,{ the carrier of C}:] -ImmediateSubtrees g is Relation-like [: the carrier' of C,{ the carrier of C}:] -Subtrees g -defined (Subtrees g) * -valued Function-like V25([: the carrier' of C,{ the carrier of C}:] -Subtrees g,(Subtrees g) * ) Function-yielding V54() Element of bool [:([: the carrier' of C,{ the carrier of C}:] -Subtrees g),((Subtrees g) *):]
(Subtrees g) * is non empty functional FinSequence-membered M8( Subtrees g)
[:([: the carrier' of C,{ the carrier of C}:] -Subtrees g),((Subtrees g) *):] is Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] -Subtrees g),((Subtrees g) *):] is set
incl ([: the carrier' of C,{ the carrier of C}:] -Subtrees g) is Relation-like [: the carrier' of C,{ the carrier of C}:] -Subtrees g -defined Subtrees g -valued [: the carrier' of C,{ the carrier of C}:] -Subtrees g -valued Function-like one-to-one V25([: the carrier' of C,{ the carrier of C}:] -Subtrees g, Subtrees g) Function-yielding V54() Element of bool [:([: the carrier' of C,{ the carrier of C}:] -Subtrees g),(Subtrees g):]
[:([: the carrier' of C,{ the carrier of C}:] -Subtrees g),(Subtrees g):] is Relation-like set
bool [:([: the carrier' of C,{ the carrier of C}:] -Subtrees g),(Subtrees g):] is set
ManySortedSign(# (Subtrees g),([: the carrier' of C,{ the carrier of C}:] -Subtrees g),([: the carrier' of C,{ the carrier of C}:] -ImmediateSubtrees g),(incl ([: the carrier' of C,{ the carrier of C}:] -Subtrees g)) #) is non empty V68() strict V153() ManySortedSign
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
X is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable CompoundTerm of S,A
X . {} is set
X is Relation-like Function-like DecoratedTree-like Element of V
X . {} is set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
V is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,A,V) is non empty set
the carrier' of (S,A,V) is set
G is Element of the carrier of (S,A,V)
C is Relation-like Function-like DecoratedTree-like Element of V
proj1 C is non empty Tree-like set
f is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of proj1 C
C | f is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
G is set
C is Relation-like Function-like DecoratedTree-like Element of V
proj1 C is non empty Tree-like set
f is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of proj1 C
C | f is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
Leaves (proj1 C) is Element of bool (proj1 C)
bool (proj1 C) is set
C . f is Element of the carrier of K334(S,A)
proj1 (C | f) is non empty finite Tree-like finite-order finite-branching countable set
(proj1 C) | f is non empty Tree-like set
f is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of proj1 (C | f)
f ^ f is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
g is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
g . f is set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,A,V) is non empty set
the carrier' of (S,A,V) is set
X is Element of the carrier of (S,A,V)
C is Relation-like Function-like DecoratedTree-like Element of V
proj1 C is non empty Tree-like set
f is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of proj1 C
C | f is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
g is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable CompoundTerm of S,A
g . {} is set
f ^ (<*> NAT) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(proj1 C) | f is non empty Tree-like set
C . f is Element of the carrier of K334(S,A)
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
V is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,V) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,V) is non empty set
X is Element of the carrier' of (S,A,V)
the_arity_of X is Relation-like NAT -defined the carrier of (S,A,V) -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of (S,A,V) *
the carrier of (S,A,V) is non empty set
the carrier of (S,A,V) * is non empty functional FinSequence-membered M8( the carrier of (S,A,V))
the Arity of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) * -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):]
[: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is Relation-like set
bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is set
the Arity of (S,A,V) . X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of (S,A,V) *
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,A,V) is non empty set
X is Element of the carrier of (S,A,V)
G is Element of the carrier of (S,A,V)
C is Element of the carrier of (S,A,V)
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,A,V) is non empty set
X is Relation-like Function-like finite countable Element of the carrier of (S,A,V)
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
V is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,V) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,V) is non empty set
X is Element of the carrier' of (S,A,V)
G is Element of the carrier' of (S,A,V)
C is Element of the carrier' of (S,A,V)
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
V is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,V) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,V) is non empty set
X is Relation-like Function-like finite countable Element of the carrier' of (S,A,V)
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the Arity of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) * -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):]
the carrier' of (S,A,V) is set
the carrier of (S,A,V) is non empty set
the carrier of (S,A,V) * is non empty functional FinSequence-membered M8( the carrier of (S,A,V))
[: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is Relation-like set
bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is set
X is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,X) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
the Arity of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) * -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):]
the carrier' of (S,A,X) is set
the carrier of (S,A,X) is non empty set
the carrier of (S,A,X) * is non empty functional FinSequence-membered M8( the carrier of (S,A,X))
[: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is Relation-like set
bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is set
the ResultSort of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V)) Element of bool [: the carrier' of (S,A,V), the carrier of (S,A,V):]
[: the carrier' of (S,A,V), the carrier of (S,A,V):] is Relation-like set
bool [: the carrier' of (S,A,V), the carrier of (S,A,V):] is set
the ResultSort of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X)) Element of bool [: the carrier' of (S,A,X), the carrier of (S,A,X):]
[: the carrier' of (S,A,X), the carrier of (S,A,X):] is Relation-like set
bool [: the carrier' of (S,A,X), the carrier of (S,A,X):] is set
proj1 ([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V) is set
id ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one total Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V):] is set
proj1 (id ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) is set
proj1 ([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X) is set
id ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one total Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X):] is set
proj1 (id ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) is set
C is set
proj1 the Arity of (S,A,V) is set
proj1 the Arity of (S,A,X) is set
(proj1 the Arity of (S,A,V)) /\ (proj1 the Arity of (S,A,X)) is set
([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V) . C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
the Arity of (S,A,V) . C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
the Arity of (S,A,X) . C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
t is Relation-like Function-like DecoratedTree-like Element of V
t9 is Relation-like Function-like DecoratedTree-like Element of X
f is Relation-like Function-like DecoratedTree-like Element of Subtrees V
f . {} is set
g is Relation-like NAT -defined Subtrees V -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable FinSequence of Subtrees V
(f . {}) -tree g is Relation-like Function-like DecoratedTree-like set
f is Relation-like NAT -defined Subtrees X -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable FinSequence of Subtrees X
(f . {}) -tree f is Relation-like Function-like DecoratedTree-like set
C is set
proj1 the ResultSort of (S,A,V) is set
proj1 the ResultSort of (S,A,X) is set
(proj1 the ResultSort of (S,A,V)) /\ (proj1 the ResultSort of (S,A,X)) is set
the ResultSort of (S,A,V) . C is set
the ResultSort of (S,A,X) . C is set
S is functional constituted-DTrees set
A is functional constituted-DTrees set
S \/ A is set
S is non empty functional constituted-DTrees set
A is non empty functional constituted-DTrees set
S \/ A is non empty functional constituted-DTrees set
Subtrees (S \/ A) is non empty functional constituted-DTrees set
Subtrees S is non empty functional constituted-DTrees set
Subtrees A is non empty functional constituted-DTrees set
(Subtrees S) \/ (Subtrees A) is non empty functional constituted-DTrees set
V is set
X is Relation-like Function-like DecoratedTree-like Element of S \/ A
proj1 X is non empty Tree-like set
G is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of proj1 X
X | G is Relation-like Function-like DecoratedTree-like set
V is set
X is Relation-like Function-like DecoratedTree-like Element of S
proj1 X is non empty Tree-like set
G is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of proj1 X
X | G is Relation-like Function-like DecoratedTree-like set
X is Relation-like Function-like DecoratedTree-like Element of A
proj1 X is non empty Tree-like set
G is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of proj1 X
X | G is Relation-like Function-like DecoratedTree-like set
S is non empty functional constituted-DTrees set
A is non empty functional constituted-DTrees set
S \/ A is non empty functional constituted-DTrees set
V is set
V -Subtrees (S \/ A) is functional constituted-DTrees Element of bool (Subtrees (S \/ A))
Subtrees (S \/ A) is non empty functional constituted-DTrees set
bool (Subtrees (S \/ A)) is set
V -Subtrees S is functional constituted-DTrees Element of bool (Subtrees S)
Subtrees S is non empty functional constituted-DTrees set
bool (Subtrees S) is set
V -Subtrees A is functional constituted-DTrees Element of bool (Subtrees A)
Subtrees A is non empty functional constituted-DTrees set
bool (Subtrees A) is set
(V -Subtrees S) \/ (V -Subtrees A) is functional constituted-DTrees set
X is set
G is Relation-like Function-like DecoratedTree-like Element of S \/ A
proj1 G is non empty Tree-like set
C is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of proj1 G
G | C is Relation-like Function-like DecoratedTree-like set
Leaves (proj1 G) is Element of bool (proj1 G)
bool (proj1 G) is set
G . C is set
X is set
G is Relation-like Function-like DecoratedTree-like Element of S
proj1 G is non empty Tree-like set
C is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of proj1 G
G | C is Relation-like Function-like DecoratedTree-like set
Leaves (proj1 G) is Element of bool (proj1 G)
bool (proj1 G) is set
G . C is set
G is Relation-like Function-like DecoratedTree-like Element of A
proj1 G is non empty Tree-like set
C is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of proj1 G
G | C is Relation-like Function-like DecoratedTree-like set
Leaves (proj1 G) is Element of bool (proj1 G)
bool (proj1 G) is set
G . C is set
S is non empty functional constituted-DTrees set
A is non empty functional constituted-DTrees set
S \/ A is non empty functional constituted-DTrees set
V is Relation-like Function-like DecoratedTree-like Element of S \/ A
V is set
V -ImmediateSubtrees (S \/ A) is Relation-like V -Subtrees (S \/ A) -defined (Subtrees (S \/ A)) * -valued Function-like V25(V -Subtrees (S \/ A),(Subtrees (S \/ A)) * ) Function-yielding V54() Element of bool [:(V -Subtrees (S \/ A)),((Subtrees (S \/ A)) *):]
V -Subtrees (S \/ A) is functional constituted-DTrees Element of bool (Subtrees (S \/ A))
Subtrees (S \/ A) is non empty functional constituted-DTrees set
bool (Subtrees (S \/ A)) is set
(Subtrees (S \/ A)) * is non empty functional FinSequence-membered M8( Subtrees (S \/ A))
[:(V -Subtrees (S \/ A)),((Subtrees (S \/ A)) *):] is Relation-like set
bool [:(V -Subtrees (S \/ A)),((Subtrees (S \/ A)) *):] is set
V -ImmediateSubtrees S is Relation-like V -Subtrees S -defined (Subtrees S) * -valued Function-like V25(V -Subtrees S,(Subtrees S) * ) Function-yielding V54() Element of bool [:(V -Subtrees S),((Subtrees S) *):]
V -Subtrees S is functional constituted-DTrees Element of bool (Subtrees S)
Subtrees S is non empty functional constituted-DTrees set
bool (Subtrees S) is set
(Subtrees S) * is non empty functional FinSequence-membered M8( Subtrees S)
[:(V -Subtrees S),((Subtrees S) *):] is Relation-like set
bool [:(V -Subtrees S),((Subtrees S) *):] is set
V -ImmediateSubtrees A is Relation-like V -Subtrees A -defined (Subtrees A) * -valued Function-like V25(V -Subtrees A,(Subtrees A) * ) Function-yielding V54() Element of bool [:(V -Subtrees A),((Subtrees A) *):]
V -Subtrees A is functional constituted-DTrees Element of bool (Subtrees A)
Subtrees A is non empty functional constituted-DTrees set
bool (Subtrees A) is set
(Subtrees A) * is non empty functional FinSequence-membered M8( Subtrees A)
[:(V -Subtrees A),((Subtrees A) *):] is Relation-like set
bool [:(V -Subtrees A),((Subtrees A) *):] is set
(V -ImmediateSubtrees S) +* (V -ImmediateSubtrees A) is Relation-like Function-like set
proj1 (V -ImmediateSubtrees (S \/ A)) is set
proj1 (V -ImmediateSubtrees S) is set
proj1 (V -ImmediateSubtrees A) is set
(V -Subtrees S) \/ (V -Subtrees A) is functional constituted-DTrees set
g is set
(proj1 (V -ImmediateSubtrees S)) \/ (proj1 (V -ImmediateSubtrees A)) is set
(V -ImmediateSubtrees (S \/ A)) . g is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
(V -ImmediateSubtrees A) . g is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
f is Relation-like Function-like DecoratedTree-like Element of Subtrees (S \/ A)
f . {} is set
t is Relation-like NAT -defined Subtrees (S \/ A) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable FinSequence of Subtrees (S \/ A)
(f . {}) -tree t is Relation-like Function-like DecoratedTree-like set
t9 is Relation-like NAT -defined Subtrees A -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable FinSequence of Subtrees A
(f . {}) -tree t9 is Relation-like Function-like DecoratedTree-like set
(V -ImmediateSubtrees S) . g is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
t9 is Relation-like NAT -defined Subtrees S -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable FinSequence of Subtrees S
(f . {}) -tree t9 is Relation-like Function-like DecoratedTree-like set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
X is non empty functional constituted-DTrees Element of bool (S -Terms A)
V \/ X is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,(V \/ X)) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees (V \/ X) is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X) is functional constituted-DTrees Element of bool (Subtrees (V \/ X))
bool (Subtrees (V \/ X)) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees (V \/ X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X) -defined (Subtrees (V \/ X)) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X),(Subtrees (V \/ X)) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),((Subtrees (V \/ X)) *):]
(Subtrees (V \/ X)) * is non empty functional FinSequence-membered M8( Subtrees (V \/ X))
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),((Subtrees (V \/ X)) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),((Subtrees (V \/ X)) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X) -defined Subtrees (V \/ X) -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X) -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X), Subtrees (V \/ X)) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),(Subtrees (V \/ X)):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),(Subtrees (V \/ X)):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),(Subtrees (V \/ X)):] is set
ManySortedSign(# (Subtrees (V \/ X)),([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees (V \/ X)),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X))) #) is non empty V68() strict V153() ManySortedSign
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
(S,A,X) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
(S,A,V) +* (S,A,X) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
(Subtrees V) \/ (Subtrees X) is non empty functional constituted-DTrees set
([: the carrier' of S,{ the carrier of S}:] -Subtrees V) \/ ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is functional constituted-DTrees set
f is Relation-like Function-like DecoratedTree-like Element of V
g is Relation-like Function-like DecoratedTree-like Element of X
([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V) +* ([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X) is Relation-like Function-like set
id ([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X) -defined [: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X) -valued Function-like one-to-one total Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)):] is set
id ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one total Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V):] is set
id ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one total Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X):] is set
(id ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) +* (id ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) is Relation-like ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) \/ ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) -defined Function-like total set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
InputVertices (S,A,V) is Element of bool the carrier of (S,A,V)
the carrier of (S,A,V) is non empty set
bool the carrier of (S,A,V) is set
the ResultSort of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V)) Element of bool [: the carrier' of (S,A,V), the carrier of (S,A,V):]
the carrier' of (S,A,V) is set
[: the carrier' of (S,A,V), the carrier of (S,A,V):] is Relation-like set
bool [: the carrier' of (S,A,V), the carrier of (S,A,V):] is set
K507( the carrier of (S,A,V), the ResultSort of (S,A,V)) is Element of bool the carrier of (S,A,V)
the carrier of (S,A,V) \ K507( the carrier of (S,A,V), the ResultSort of (S,A,V)) is Element of bool the carrier of (S,A,V)
proj2 the ResultSort of (S,A,V) is set
G is set
C is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
C . {} is set
f is Element of the carrier of S
A . f is non empty set
g is Element of A . f
[g,f] is pair set
{g,f} is non empty finite countable set
{g} is non empty trivial finite V35(1) countable set
{{g,f},{g}} is non empty finite V32() countable set
f is Element of the carrier of S
A . f is non empty set
g is Element of A . f
[g,f] is pair set
{g,f} is non empty finite countable set
{g} is non empty trivial finite V35(1) countable set
{{g,f},{g}} is non empty finite V32() countable set
f is Element of the carrier of S
A . f is non empty set
g is Element of A . f
[g,f] is pair set
{g,f} is non empty finite countable set
{g} is non empty trivial finite V35(1) countable set
{{g,f},{g}} is non empty finite V32() countable set
f is Element of the carrier of S
A . f is non empty set
t is Element of A . f
t9 is Element of A . f
[t9,f] is pair set
{t9,f} is non empty finite countable set
{t9} is non empty trivial finite V35(1) countable set
{{t9,f},{t9}} is non empty finite V32() countable set
root-tree [t9,f] is Relation-like trivial Function-like constant finite DecoratedTree-like finite-order finite-branching countable set
C is Element of the carrier of S
A . C is non empty set
f is Element of A . C
[f,C] is pair set
{f,C} is non empty finite countable set
{f} is non empty trivial finite V35(1) countable set
{{f,C},{f}} is non empty finite V32() countable set
root-tree [f,C] is Relation-like trivial Function-like constant finite DecoratedTree-like finite-order finite-branching countable set
g is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable CompoundTerm of S,A
g . {} is set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
V is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,V) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,V) is non empty set
X is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier' of (S,A,V)
X . {} is set
the_arity_of X is Relation-like NAT -defined the carrier of (S,A,V) -valued the carrier of (S,A,V) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding countable Element of the carrier of (S,A,V) *
the carrier of (S,A,V) is non empty set
the carrier of (S,A,V) * is non empty functional FinSequence-membered M8( the carrier of (S,A,V))
the Arity of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) * -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):]
[: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is Relation-like set
bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is set
the Arity of (S,A,V) . X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of (S,A,V) *
(X . {}) -tree (the_arity_of X) is Relation-like Function-like DecoratedTree-like set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
G is Relation-like Function-like DecoratedTree-like Element of V
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,A,V) is non empty set
X is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,V)
G is MSAlgebra over S
the Sorts of G is Relation-like the carrier of S -defined non empty Function-like total set
C is set
f is set
g is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
the_sort_of g is Element of the carrier of S
the Sorts of G . (the_sort_of g) is set
C is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
the_sort_of C is Element of the carrier of S
the Sorts of G . (the_sort_of C) is set
f is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
the_sort_of f is Element of the carrier of S
the Sorts of G . (the_sort_of f) is set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,A,V) is non empty set
X is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,V)
G is non-empty MSAlgebra over S
(S,A,V,X,G) is set
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
C is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
the_sort_of C is Element of the carrier of S
the Sorts of G . (the_sort_of C) is non empty set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,V) is set
X is Element of the carrier' of (S,A,V)
G is MSAlgebra over S
the Charact of G is Relation-like the carrier' of S -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of G #), the ResultSort of S * the Sorts of G
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of G is Relation-like the carrier of S -defined non empty Function-like total set
the Sorts of G # is Relation-like the carrier of S * -defined non empty Function-like total set
the Arity of S * ( the Sorts of G #) is Relation-like the carrier' of S -defined non empty Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of G is Relation-like the carrier' of S -defined non empty Function-like total set
C is Relation-like Function-like set
f is Relation-like Function-like set
g is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,g) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees g is non empty functional constituted-DTrees set
[: the carrier' of S,{ the carrier of S}:] -Subtrees g is functional constituted-DTrees Element of bool (Subtrees g)
bool (Subtrees g) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees g is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees g -defined (Subtrees g) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees g,(Subtrees g) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),((Subtrees g) *):]
(Subtrees g) * is non empty functional FinSequence-membered M8( Subtrees g)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),((Subtrees g) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),((Subtrees g) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees g) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees g -defined Subtrees g -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees g -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees g, Subtrees g) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),(Subtrees g):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),(Subtrees g):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),(Subtrees g):] is set
ManySortedSign(# (Subtrees g),([: the carrier' of S,{ the carrier of S}:] -Subtrees g),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees g),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees g)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,g) is non empty set
f is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier' of (S,A,g)
f . {} is set
(f . {}) `1 is set
the Charact of G . ((f . {}) `1) is Relation-like Function-like set
C is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,C) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees C is non empty functional constituted-DTrees set
[: the carrier' of S,{ the carrier of S}:] -Subtrees C is functional constituted-DTrees Element of bool (Subtrees C)
bool (Subtrees C) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees C is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees C -defined (Subtrees C) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees C,(Subtrees C) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees C),((Subtrees C) *):]
(Subtrees C) * is non empty functional FinSequence-membered M8( Subtrees C)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees C),((Subtrees C) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees C),((Subtrees C) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees C) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees C -defined Subtrees C -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees C -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees C, Subtrees C) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees C),(Subtrees C):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees C),(Subtrees C):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees C),(Subtrees C):] is set
ManySortedSign(# (Subtrees C),([: the carrier' of S,{ the carrier of S}:] -Subtrees C),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees C),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees C)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,C) is non empty set
f is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier' of (S,A,C)
f . {} is set
(f . {}) `1 is set
the Charact of G . ((f . {}) `1) is Relation-like Function-like set
g is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,g) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees g is non empty functional constituted-DTrees set
[: the carrier' of S,{ the carrier of S}:] -Subtrees g is functional constituted-DTrees Element of bool (Subtrees g)
bool (Subtrees g) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees g is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees g -defined (Subtrees g) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees g,(Subtrees g) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),((Subtrees g) *):]
(Subtrees g) * is non empty functional FinSequence-membered M8( Subtrees g)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),((Subtrees g) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),((Subtrees g) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees g) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees g -defined Subtrees g -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees g -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees g, Subtrees g) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),(Subtrees g):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),(Subtrees g):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),(Subtrees g):] is set
ManySortedSign(# (Subtrees g),([: the carrier' of S,{ the carrier of S}:] -Subtrees g),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees g),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees g)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,g) is non empty set
f is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier' of (S,A,g)
f . {} is set
(f . {}) `1 is set
the Charact of G . ((f . {}) `1) is Relation-like Function-like set
F₁() is non empty set
F₂() is Relation-like non-empty non empty-yielding F₁() -defined non empty Function-like total set
F₃() is Relation-like non-empty non empty-yielding F₁() -defined non empty Function-like total set
S is set
F₂() . S is set
F₃() . S is set
[:(F₂() . S),(F₃() . S):] is Relation-like set
bool [:(F₂() . S),(F₃() . S):] is set
A is Element of F₁()
F₂() . A is non empty set
F₃() . A is non empty set
V is set
X is Element of F₃() . A
V is Relation-like Function-like set
proj1 V is set
proj2 V is set
[:(F₂() . A),(F₃() . A):] is Relation-like set
bool [:(F₂() . A),(F₃() . A):] is set
S is Relation-like Function-like set
proj1 S is set
A is Relation-like F₁() -defined non empty Function-like total set
V is set
A . V is set
F₂() . V is set
F₃() . V is set
[:(F₂() . V),(F₃() . V):] is Relation-like set
bool [:(F₂() . V),(F₃() . V):] is set
X is Relation-like F₂() . V -defined F₃() . V -valued Function-like V25(F₂() . V,F₃() . V) Element of bool [:(F₂() . V),(F₃() . V):]
V is Relation-like F₁() -defined non empty Function-like total Function-yielding V54() ManySortedFunction of F₂(),F₃()
X is Element of F₁()
F₂() . X is non empty set
V . X is Relation-like Function-like set
G is Element of F₂() . X
(V . X) . G is set
F₃() . X is non empty set
[:(F₂() . X),(F₃() . X):] is Relation-like set
bool [:(F₂() . X),(F₃() . X):] is set
C is Relation-like F₂() . X -defined F₃() . X -valued Function-like V25(F₂() . X,F₃() . X) Element of bool [:(F₂() . X),(F₃() . X):]
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,A,V) is non empty set
X is MSAlgebra over S
G is Relation-like the carrier of (S,A,V) -defined non empty Function-like total set
C is Relation-like the carrier of (S,A,V) -defined non empty Function-like total set
f is set
G . f is set
g is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,V)
(S,A,V,g,X) is set
C . f is set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
X is non-empty MSAlgebra over S
(S,A,V,X) is Relation-like the carrier of (S,A,V) -defined non empty Function-like total set
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,A,V) is non empty set
G is set
(S,A,V,X) . G is set
C is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,V)
(S,A,V,X) . C is set
(S,A,V,C,X) is non empty set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
the carrier' of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
V is non-empty MSAlgebra over S
the Sorts of V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,X) is non empty set
(S,A,X,V) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the carrier of (S,A,X) is non empty set
G is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier' of (S,A,X)
G . {} is set
the_arity_of G is Relation-like NAT -defined the carrier of (S,A,X) -valued the carrier of (S,A,X) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding countable Element of the carrier of (S,A,X) *
the carrier of (S,A,X) * is non empty functional FinSequence-membered M8( the carrier of (S,A,X))
the Arity of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) * -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):]
[: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is Relation-like set
bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is set
the Arity of (S,A,X) . G is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of (S,A,X) *
(the_arity_of G) * (S,A,X,V) is Relation-like non-empty NAT -defined Function-like finite countable set
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
f is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable CompoundTerm of S,A
f . {} is set
g is Relation-like NAT -defined Subtrees X -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable FinSequence of Subtrees X
(f . {}) -tree g is Relation-like Function-like DecoratedTree-like set
f is Element of the carrier' of S
[f, the carrier of S] is pair set
{f, the carrier of S} is non empty finite countable set
{f} is non empty trivial finite V35(1) countable set
{{f, the carrier of S},{f}} is non empty finite V32() countable set
the_arity_of f is Relation-like NAT -defined the carrier of S -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of S *
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Arity of S . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of S *
(the_arity_of f) * the Sorts of V is Relation-like non-empty NAT -defined Function-like finite countable set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
Sym (f,A) is Element of K316(K334(S,A))
K316(K334(S,A)) is non empty Element of bool the carrier of K334(S,A)
bool the carrier of K334(S,A) is set
t is Relation-like NAT -defined FinTrees the carrier of K334(S,A) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable ArgumentSeq of Sym (f,A)
[f, the carrier of S] -tree t is Relation-like Function-like DecoratedTree-like set
len t is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
len (the_arity_of f) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
dom (the_arity_of f) is finite countable Element of bool NAT
Seg (len t) is finite V35( len t) countable Element of bool NAT
dom (the_arity_of G) is finite countable Element of bool NAT
proj2 (the_arity_of G) is finite countable set
proj2 (the_arity_of f) is finite countable set
proj1 (S,A,X,V) is non empty set
proj1 the Sorts of V is non empty set
proj1 ((the_arity_of G) * (S,A,X,V)) is finite countable set
proj1 ((the_arity_of f) * the Sorts of V) is finite countable set
t9 is set
g . t9 is Relation-like Function-like set
v is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
g . v is Relation-like Function-like set
(the_arity_of f) . t9 is set
(the_arity_of f) . v is set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
bool (FinTrees the carrier of K334(S,A)) is set
s is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,X)
vp is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
the_sort_of vp is Element of the carrier of S
c₁₄ is Element of the carrier of S
((the_arity_of G) * (S,A,X,V)) . t9 is set
(S,A,X,V) . s is non empty set
((the_arity_of f) * the Sorts of V) . t9 is set
the Sorts of V . c₁₄ is non empty set
(S,A,X,s,V) is non empty set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,V) is set
the Arity of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) * -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):]
the carrier of (S,A,V) is non empty set
the carrier of (S,A,V) * is non empty functional FinSequence-membered M8( the carrier of (S,A,V))
[: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is Relation-like set
bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is set
X is non-empty MSAlgebra over S
(S,A,V,X) is Relation-like non-empty non empty-yielding the carrier of (S,A,V) -defined non empty Function-like total set
(S,A,V,X) # is Relation-like the carrier of (S,A,V) * -defined non empty Function-like total set
the Arity of (S,A,V) * ((S,A,V,X) #) is Relation-like the carrier' of (S,A,V) -defined Function-like total set
the ResultSort of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V)) Element of bool [: the carrier' of (S,A,V), the carrier of (S,A,V):]
[: the carrier' of (S,A,V), the carrier of (S,A,V):] is Relation-like set
bool [: the carrier' of (S,A,V), the carrier of (S,A,V):] is set
the ResultSort of (S,A,V) * (S,A,V,X) is Relation-like non-empty the carrier' of (S,A,V) -defined Function-like total set
G is Relation-like the carrier' of (S,A,V) -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,V) * ((S,A,V,X) #), the ResultSort of (S,A,V) * (S,A,V,X)
C is Relation-like the carrier' of (S,A,V) -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,V) * ((S,A,V,X) #), the ResultSort of (S,A,V) * (S,A,V,X)
f is set
g is Element of the carrier' of (S,A,V)
G . g is Relation-like Function-like set
(S,A,V,g,X) is Relation-like Function-like set
G . f is Relation-like Function-like set
C . f is Relation-like Function-like set
G is set
C is Element of the carrier' of (S,A,V)
(S,A,V,C,X) is Relation-like Function-like set
f is set
g is set
G is Relation-like the carrier' of (S,A,V) -defined Function-like total set
proj1 G is set
C is set
G . C is set
f is Element of the carrier' of (S,A,V)
(S,A,V,f,X) is Relation-like Function-like set
C is Relation-like the carrier' of (S,A,V) -defined Function-like total Function-yielding V54() set
f is set
C . f is Relation-like Function-like set
( the Arity of (S,A,V) * ((S,A,V,X) #)) . f is set
( the ResultSort of (S,A,V) * (S,A,V,X)) . f is set
[:(( the Arity of (S,A,V) * ((S,A,V,X) #)) . f),(( the ResultSort of (S,A,V) * (S,A,V,X)) . f):] is Relation-like set
bool [:(( the Arity of (S,A,V) * ((S,A,V,X) #)) . f),(( the ResultSort of (S,A,V) * (S,A,V,X)) . f):] is set
g is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,g) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees g is non empty functional constituted-DTrees set
[: the carrier' of S,{ the carrier of S}:] -Subtrees g is functional constituted-DTrees Element of bool (Subtrees g)
bool (Subtrees g) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees g is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees g -defined (Subtrees g) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees g,(Subtrees g) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),((Subtrees g) *):]
(Subtrees g) * is non empty functional FinSequence-membered M8( Subtrees g)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),((Subtrees g) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),((Subtrees g) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees g) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees g -defined Subtrees g -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees g -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees g, Subtrees g) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),(Subtrees g):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),(Subtrees g):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees g),(Subtrees g):] is set
ManySortedSign(# (Subtrees g),([: the carrier' of S,{ the carrier of S}:] -Subtrees g),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees g),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees g)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,g) is non empty set
f is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier' of (S,A,g)
the_result_sort_of f is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,g)
the carrier of (S,A,g) is non empty set
the ResultSort of (S,A,g) is Relation-like the carrier' of (S,A,g) -defined the carrier of (S,A,g) -valued Function-like V25( the carrier' of (S,A,g), the carrier of (S,A,g)) Element of bool [: the carrier' of (S,A,g), the carrier of (S,A,g):]
[: the carrier' of (S,A,g), the carrier of (S,A,g):] is Relation-like set
bool [: the carrier' of (S,A,g), the carrier of (S,A,g):] is set
the ResultSort of (S,A,g) . f is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,g)
t9 is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable CompoundTerm of S,A
t9 . {} is set
v is set
s is set
[v,s] is pair set
{v,s} is non empty finite countable set
{v} is non empty trivial finite V35(1) countable set
{{v,s},{v}} is non empty finite V32() countable set
c₁₄ is Element of the carrier' of S
(t9 . {}) `1 is set
(S,A,g,f,X) is Relation-like Function-like set
the Charact of X is Relation-like the carrier' of S -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of X #), the ResultSort of S * the Sorts of X
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of X is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the Sorts of X # is Relation-like the carrier of S * -defined non empty Function-like total set
the Arity of S * ( the Sorts of X #) is Relation-like the carrier' of S -defined non empty Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of X is Relation-like non-empty non empty-yielding the carrier' of S -defined non empty Function-like total set
the Charact of X . c<sub>14</sub> is Relation-like Function-like set
vp is Element of the carrier' of (S,A,V)
(S,A,V,vp,X) is Relation-like Function-like set
( the ResultSort of S * the Sorts of X) . c<sub>14</sub> is non empty set
the_result_sort_of c<sub>14</sub> is Element of the carrier of S
the ResultSort of S . c<sub>14</sub> is Element of the carrier of S
the Sorts of X . (the_result_sort_of c<sub>14</sub>) is non empty set
the_sort_of t9 is Element of the carrier of S
the Sorts of X . (the_sort_of t9) is non empty set
( the ResultSort of (S,A,V) * (S,A,V,X)) . f is set
(S,A,V,X) . (the_result_sort_of f) is set
t is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,g)
(S,A,g,t,X) is non empty set
( the Arity of (S,A,V) * ((S,A,V,X) #)) . f is set
the_arity_of f is Relation-like NAT -defined the carrier of (S,A,g) -valued the carrier of (S,A,g) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding countable Element of the carrier of (S,A,g) *
the carrier of (S,A,g) * is non empty functional FinSequence-membered M8( the carrier of (S,A,g))
the Arity of (S,A,g) is Relation-like the carrier' of (S,A,g) -defined the carrier of (S,A,g) * -valued Function-like V25( the carrier' of (S,A,g), the carrier of (S,A,g) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,g),( the carrier of (S,A,g) *):]
[: the carrier' of (S,A,g),( the carrier of (S,A,g) *):] is Relation-like set
bool [: the carrier' of (S,A,g),( the carrier of (S,A,g) *):] is set
the Arity of (S,A,g) . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of (S,A,g) *
((S,A,V,X) #) . (the_arity_of f) is set
(S,A,g,X) is Relation-like non-empty non empty-yielding the carrier of (S,A,g) -defined non empty Function-like total set
(the_arity_of f) * (S,A,g,X) is Relation-like non-empty NAT -defined Function-like finite countable set
product ((the_arity_of f) * (S,A,g,X)) is non empty functional with_common_domain product-like set
the_arity_of c<sub>14</sub> is Relation-like NAT -defined the carrier of S -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of S *
the Arity of S . c<sub>14</sub> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of S *
(the_arity_of c<sub>14</sub>) * the Sorts of X is Relation-like non-empty NAT -defined Function-like finite countable set
product ((the_arity_of c<sub>14</sub>) * the Sorts of X) is non empty functional with_common_domain product-like set
( the Arity of S * ( the Sorts of X #)) . c<sub>14</sub> is set
( the Sorts of X #) . (the_arity_of c<sub>14</sub>) is set
f is Relation-like the carrier' of (S,A,V) -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,V) * ((S,A,V,X) #), the ResultSort of (S,A,V) * (S,A,V,X)
g is Element of the carrier' of (S,A,V)
f . g is Relation-like Function-like set
(S,A,V,g,X) is Relation-like Function-like set
f is Element of the carrier' of (S,A,V)
(S,A,V,f,X) is Relation-like Function-like set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,V) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
X is non-empty MSAlgebra over S
(S,A,V,X) is Relation-like non-empty non empty-yielding the carrier of (S,A,V) -defined non empty Function-like total set
the carrier of (S,A,V) is non empty set
(S,A,V,X) is Relation-like the carrier' of (S,A,V) -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,V) * ((S,A,V,X) #), the ResultSort of (S,A,V) * (S,A,V,X)
the carrier' of (S,A,V) is set
the Arity of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) * -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):]
the carrier of (S,A,V) * is non empty functional FinSequence-membered M8( the carrier of (S,A,V))
[: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is Relation-like set
bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is set
(S,A,V,X) # is Relation-like the carrier of (S,A,V) * -defined non empty Function-like total set
the Arity of (S,A,V) * ((S,A,V,X) #) is Relation-like the carrier' of (S,A,V) -defined Function-like total set
the ResultSort of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V)) Element of bool [: the carrier' of (S,A,V), the carrier of (S,A,V):]
[: the carrier' of (S,A,V), the carrier of (S,A,V):] is Relation-like set
bool [: the carrier' of (S,A,V), the carrier of (S,A,V):] is set
the ResultSort of (S,A,V) * (S,A,V,X) is Relation-like non-empty the carrier' of (S,A,V) -defined Function-like total set
MSAlgebra(# (S,A,V,X),(S,A,V,X) #) is strict MSAlgebra over (S,A,V)
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
X is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,X) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,A,X) is non empty set
V is non-empty MSAlgebra over S
(S,A,X,V) is strict non-empty MSAlgebra over (S,A,X)
(S,A,X,V) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
(S,A,X,V) is Relation-like the carrier' of (S,A,X) -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,X) * ((S,A,X,V) #), the ResultSort of (S,A,X) * (S,A,X,V)
the carrier' of (S,A,X) is set
the Arity of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) * -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):]
the carrier of (S,A,X) * is non empty functional FinSequence-membered M8( the carrier of (S,A,X))
[: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is Relation-like set
bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is set
(S,A,X,V) # is Relation-like the carrier of (S,A,X) * -defined non empty Function-like total set
the Arity of (S,A,X) * ((S,A,X,V) #) is Relation-like the carrier' of (S,A,X) -defined Function-like total set
the ResultSort of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X)) Element of bool [: the carrier' of (S,A,X), the carrier of (S,A,X):]
[: the carrier' of (S,A,X), the carrier of (S,A,X):] is Relation-like set
bool [: the carrier' of (S,A,X), the carrier of (S,A,X):] is set
the ResultSort of (S,A,X) * (S,A,X,V) is Relation-like non-empty the carrier' of (S,A,X) -defined Function-like total set
MSAlgebra(# (S,A,X,V),(S,A,X,V) #) is strict MSAlgebra over (S,A,X)
the Sorts of (S,A,X,V) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
G is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,X)
the Sorts of (S,A,X,V) . G is non empty set
(S,A,X,G,V) is non empty set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,X) is non empty set
G is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier' of (S,A,X)
V is non-empty finite-yielding MSAlgebra over S
(S,A,X,V) is strict non-empty MSAlgebra over (S,A,X)
(S,A,X,V) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the carrier of (S,A,X) is non empty set
(S,A,X,V) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,X) * ((S,A,X,V) #), the ResultSort of (S,A,X) * (S,A,X,V)
the Arity of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) * -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):]
the carrier of (S,A,X) * is non empty functional FinSequence-membered M8( the carrier of (S,A,X))
[: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is Relation-like set
bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is set
(S,A,X,V) # is Relation-like the carrier of (S,A,X) * -defined non empty Function-like total set
the Arity of (S,A,X) * ((S,A,X,V) #) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total set
the ResultSort of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X)) Element of bool [: the carrier' of (S,A,X), the carrier of (S,A,X):]
[: the carrier' of (S,A,X), the carrier of (S,A,X):] is Relation-like set
bool [: the carrier' of (S,A,X), the carrier of (S,A,X):] is set
the ResultSort of (S,A,X) * (S,A,X,V) is Relation-like non-empty non empty-yielding the carrier' of (S,A,X) -defined non empty Function-like total set
MSAlgebra(# (S,A,X,V),(S,A,X,V) #) is strict MSAlgebra over (S,A,X)
Den (G,(S,A,X,V)) is Relation-like Args (G,(S,A,X,V)) -defined Result (G,(S,A,X,V)) -valued Function-like V25( Args (G,(S,A,X,V)), Result (G,(S,A,X,V))) Element of bool [:(Args (G,(S,A,X,V))),(Result (G,(S,A,X,V))):]
Args (G,(S,A,X,V)) is non empty Element of proj2 ( the Sorts of (S,A,X,V) #)
the Sorts of (S,A,X,V) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the Sorts of (S,A,X,V) # is Relation-like the carrier of (S,A,X) * -defined non empty Function-like total set
proj2 ( the Sorts of (S,A,X,V) #) is non empty set
the Arity of (S,A,X) * ( the Sorts of (S,A,X,V) #) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total set
( the Arity of (S,A,X) * ( the Sorts of (S,A,X,V) #)) . G is set
Result (G,(S,A,X,V)) is non empty Element of proj2 the Sorts of (S,A,X,V)
proj2 the Sorts of (S,A,X,V) is non empty V141() set
the ResultSort of (S,A,X) * the Sorts of (S,A,X,V) is Relation-like non-empty non empty-yielding the carrier' of (S,A,X) -defined non empty Function-like total set
( the ResultSort of (S,A,X) * the Sorts of (S,A,X,V)) . G is non empty set
[:(Args (G,(S,A,X,V))),(Result (G,(S,A,X,V))):] is Relation-like set
bool [:(Args (G,(S,A,X,V))),(Result (G,(S,A,X,V))):] is set
the Charact of (S,A,X,V) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,X) * ( the Sorts of (S,A,X,V) #), the ResultSort of (S,A,X) * the Sorts of (S,A,X,V)
the Charact of (S,A,X,V) . G is Relation-like Function-like set
(S,A,X,G,V) is Relation-like Function-like set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
the carrier' of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
V is non-empty finite-yielding MSAlgebra over S
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
the carrier' of (S,A,X) is non empty set
(S,A,X,V) is strict non-empty MSAlgebra over (S,A,X)
(S,A,X,V) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the carrier of (S,A,X) is non empty set
(S,A,X,V) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,X) * ((S,A,X,V) #), the ResultSort of (S,A,X) * (S,A,X,V)
the Arity of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) * -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):]
the carrier of (S,A,X) * is non empty functional FinSequence-membered M8( the carrier of (S,A,X))
[: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is Relation-like set
bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is set
(S,A,X,V) # is Relation-like the carrier of (S,A,X) * -defined non empty Function-like total set
the Arity of (S,A,X) * ((S,A,X,V) #) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total set
the ResultSort of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X)) Element of bool [: the carrier' of (S,A,X), the carrier of (S,A,X):]
[: the carrier' of (S,A,X), the carrier of (S,A,X):] is Relation-like set
bool [: the carrier' of (S,A,X), the carrier of (S,A,X):] is set
the ResultSort of (S,A,X) * (S,A,X,V) is Relation-like non-empty non empty-yielding the carrier' of (S,A,X) -defined non empty Function-like total set
MSAlgebra(# (S,A,X,V),(S,A,X,V) #) is strict MSAlgebra over (S,A,X)
G is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier' of (S,A,X)
G . {} is set
Args (G,(S,A,X,V)) is non empty Element of proj2 ( the Sorts of (S,A,X,V) #)
the Sorts of (S,A,X,V) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the Sorts of (S,A,X,V) # is Relation-like the carrier of (S,A,X) * -defined non empty Function-like total set
proj2 ( the Sorts of (S,A,X,V) #) is non empty set
the Arity of (S,A,X) * ( the Sorts of (S,A,X,V) #) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total set
( the Arity of (S,A,X) * ( the Sorts of (S,A,X,V) #)) . G is set
Result (G,(S,A,X,V)) is non empty Element of proj2 the Sorts of (S,A,X,V)
proj2 the Sorts of (S,A,X,V) is non empty V141() set
the ResultSort of (S,A,X) * the Sorts of (S,A,X,V) is Relation-like non-empty non empty-yielding the carrier' of (S,A,X) -defined non empty Function-like total set
( the ResultSort of (S,A,X) * the Sorts of (S,A,X,V)) . G is non empty set
Den (G,(S,A,X,V)) is Relation-like Args (G,(S,A,X,V)) -defined Result (G,(S,A,X,V)) -valued Function-like V25( Args (G,(S,A,X,V)), Result (G,(S,A,X,V))) Element of bool [:(Args (G,(S,A,X,V))),(Result (G,(S,A,X,V))):]
[:(Args (G,(S,A,X,V))),(Result (G,(S,A,X,V))):] is Relation-like set
bool [:(Args (G,(S,A,X,V))),(Result (G,(S,A,X,V))):] is set
the Charact of (S,A,X,V) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,X) * ( the Sorts of (S,A,X,V) #), the ResultSort of (S,A,X) * the Sorts of (S,A,X,V)
the Charact of (S,A,X,V) . G is Relation-like Function-like set
C is Element of the carrier' of S
[C, the carrier of S] is pair set
{C, the carrier of S} is non empty finite countable set
{C} is non empty trivial finite V35(1) countable set
{{C, the carrier of S},{C}} is non empty finite V32() countable set
Args (C,V) is non empty Element of proj2 ( the Sorts of V #)
the Sorts of V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the Sorts of V # is Relation-like the carrier of S * -defined non empty Function-like total set
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
proj2 ( the Sorts of V #) is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Arity of S * ( the Sorts of V #) is Relation-like the carrier' of S -defined non empty Function-like total set
( the Arity of S * ( the Sorts of V #)) . C is set
Result (C,V) is non empty Element of proj2 the Sorts of V
proj2 the Sorts of V is non empty V141() set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of V is Relation-like non-empty non empty-yielding the carrier' of S -defined non empty Function-like total set
( the ResultSort of S * the Sorts of V) . C is non empty set
Den (C,V) is Relation-like Args (C,V) -defined Result (C,V) -valued Function-like V25( Args (C,V), Result (C,V)) Element of bool [:(Args (C,V)),(Result (C,V)):]
[:(Args (C,V)),(Result (C,V)):] is Relation-like set
bool [:(Args (C,V)),(Result (C,V)):] is set
the Charact of V is Relation-like the carrier' of S -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of V #), the ResultSort of S * the Sorts of V
the Charact of V . C is Relation-like Function-like set
(S,A,X,G,V) is Relation-like Function-like set
(G . {}) `1 is set
the Charact of V . ((G . {}) `1) is Relation-like Function-like set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
V is non-empty finite-yielding MSAlgebra over S
X is non empty functional constituted-DTrees Element of bool (S -Terms A)
(S,A,X) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
(S,A,X,V) is strict non-empty MSAlgebra over (S,A,X)
(S,A,X,V) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the carrier of (S,A,X) is non empty set
(S,A,X,V) is Relation-like the carrier' of (S,A,X) -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,X) * ((S,A,X,V) #), the ResultSort of (S,A,X) * (S,A,X,V)
the carrier' of (S,A,X) is set
the Arity of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) * -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):]
the carrier of (S,A,X) * is non empty functional FinSequence-membered M8( the carrier of (S,A,X))
[: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is Relation-like set
bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is set
(S,A,X,V) # is Relation-like the carrier of (S,A,X) * -defined non empty Function-like total set
the Arity of (S,A,X) * ((S,A,X,V) #) is Relation-like the carrier' of (S,A,X) -defined Function-like total set
the ResultSort of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X)) Element of bool [: the carrier' of (S,A,X), the carrier of (S,A,X):]
[: the carrier' of (S,A,X), the carrier of (S,A,X):] is Relation-like set
bool [: the carrier' of (S,A,X), the carrier of (S,A,X):] is set
the ResultSort of (S,A,X) * (S,A,X,V) is Relation-like non-empty the carrier' of (S,A,X) -defined Function-like total set
MSAlgebra(# (S,A,X,V),(S,A,X,V) #) is strict MSAlgebra over (S,A,X)
G is set
the Sorts of (S,A,X,V) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the Sorts of (S,A,X,V) . G is set
C is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,X)
the Sorts of V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the Sorts of (S,A,X,V) . C is non empty set
(S,A,X,C,V) is non empty set
f is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
the_sort_of f is Element of the carrier of S
the Sorts of V . (the_sort_of f) is non empty set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
V is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,V) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
X is non-empty finite-yielding MSAlgebra over S
(S,A,V,X) is strict non-empty MSAlgebra over (S,A,V)
(S,A,V,X) is Relation-like non-empty non empty-yielding the carrier of (S,A,V) -defined non empty Function-like total set
the carrier of (S,A,V) is non empty set
(S,A,V,X) is Relation-like the carrier' of (S,A,V) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,V) * ((S,A,V,X) #), the ResultSort of (S,A,V) * (S,A,V,X)
the carrier' of (S,A,V) is non empty set
the Arity of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) * -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):]
the carrier of (S,A,V) * is non empty functional FinSequence-membered M8( the carrier of (S,A,V))
[: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is Relation-like set
bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is set
(S,A,V,X) # is Relation-like the carrier of (S,A,V) * -defined non empty Function-like total set
the Arity of (S,A,V) * ((S,A,V,X) #) is Relation-like the carrier' of (S,A,V) -defined non empty Function-like total set
the ResultSort of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V)) Element of bool [: the carrier' of (S,A,V), the carrier of (S,A,V):]
[: the carrier' of (S,A,V), the carrier of (S,A,V):] is Relation-like set
bool [: the carrier' of (S,A,V), the carrier of (S,A,V):] is set
the ResultSort of (S,A,V) * (S,A,V,X) is Relation-like non-empty non empty-yielding the carrier' of (S,A,V) -defined non empty Function-like total set
MSAlgebra(# (S,A,V,X),(S,A,V,X) #) is strict MSAlgebra over (S,A,V)
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
V is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,V) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
G is non-empty MSAlgebra over S
(S,A,V,G) is strict non-empty MSAlgebra over (S,A,V)
(S,A,V,G) is Relation-like non-empty non empty-yielding the carrier of (S,A,V) -defined non empty Function-like total set
the carrier of (S,A,V) is non empty set
(S,A,V,G) is Relation-like the carrier' of (S,A,V) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,V) * ((S,A,V,G) #), the ResultSort of (S,A,V) * (S,A,V,G)
the carrier' of (S,A,V) is non empty set
the Arity of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) * -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):]
the carrier of (S,A,V) * is non empty functional FinSequence-membered M8( the carrier of (S,A,V))
[: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is Relation-like set
bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is set
(S,A,V,G) # is Relation-like the carrier of (S,A,V) * -defined non empty Function-like total set
the Arity of (S,A,V) * ((S,A,V,G) #) is Relation-like the carrier' of (S,A,V) -defined non empty Function-like total set
the ResultSort of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V)) Element of bool [: the carrier' of (S,A,V), the carrier of (S,A,V):]
[: the carrier' of (S,A,V), the carrier of (S,A,V):] is Relation-like set
bool [: the carrier' of (S,A,V), the carrier of (S,A,V):] is set
the ResultSort of (S,A,V) * (S,A,V,G) is Relation-like non-empty non empty-yielding the carrier' of (S,A,V) -defined non empty Function-like total set
MSAlgebra(# (S,A,V,G),(S,A,V,G) #) is strict MSAlgebra over (S,A,V)
(S,A,X,G) is strict non-empty MSAlgebra over (S,A,X)
(S,A,X,G) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the carrier of (S,A,X) is non empty set
(S,A,X,G) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,X) * ((S,A,X,G) #), the ResultSort of (S,A,X) * (S,A,X,G)
the carrier' of (S,A,X) is non empty set
the Arity of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) * -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):]
the carrier of (S,A,X) * is non empty functional FinSequence-membered M8( the carrier of (S,A,X))
[: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is Relation-like set
bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is set
(S,A,X,G) # is Relation-like the carrier of (S,A,X) * -defined non empty Function-like total set
the Arity of (S,A,X) * ((S,A,X,G) #) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total set
the ResultSort of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X)) Element of bool [: the carrier' of (S,A,X), the carrier of (S,A,X):]
[: the carrier' of (S,A,X), the carrier of (S,A,X):] is Relation-like set
bool [: the carrier' of (S,A,X), the carrier of (S,A,X):] is set
the ResultSort of (S,A,X) * (S,A,X,G) is Relation-like non-empty non empty-yielding the carrier' of (S,A,X) -defined non empty Function-like total set
MSAlgebra(# (S,A,X,G),(S,A,X,G) #) is strict MSAlgebra over (S,A,X)
the Sorts of (S,A,V,G) is Relation-like non-empty non empty-yielding the carrier of (S,A,V) -defined non empty Function-like total set
the Sorts of (S,A,X,G) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the Charact of (S,A,V,G) is Relation-like the carrier' of (S,A,V) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,V) * ( the Sorts of (S,A,V,G) #), the ResultSort of (S,A,V) * the Sorts of (S,A,V,G)
the Sorts of (S,A,V,G) # is Relation-like the carrier of (S,A,V) * -defined non empty Function-like total set
the Arity of (S,A,V) * ( the Sorts of (S,A,V,G) #) is Relation-like the carrier' of (S,A,V) -defined non empty Function-like total set
the ResultSort of (S,A,V) * the Sorts of (S,A,V,G) is Relation-like non-empty non empty-yielding the carrier' of (S,A,V) -defined non empty Function-like total set
the Charact of (S,A,X,G) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,X) * ( the Sorts of (S,A,X,G) #), the ResultSort of (S,A,X) * the Sorts of (S,A,X,G)
the Sorts of (S,A,X,G) # is Relation-like the carrier of (S,A,X) * -defined non empty Function-like total set
the Arity of (S,A,X) * ( the Sorts of (S,A,X,G) #) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total set
the ResultSort of (S,A,X) * the Sorts of (S,A,X,G) is Relation-like non-empty non empty-yielding the carrier' of (S,A,X) -defined non empty Function-like total set
C is set
proj1 the Sorts of (S,A,V,G) is non empty set
proj1 the Sorts of (S,A,X,G) is non empty set
(proj1 the Sorts of (S,A,V,G)) /\ (proj1 the Sorts of (S,A,X,G)) is set
the Sorts of (S,A,V,G) . C is set
the Sorts of (S,A,X,G) . C is set
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
bool (FinTrees the carrier of K334(S,A)) is set
f is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,V)
(S,A,V,f,G) is non empty set
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
f is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
the_sort_of f is Element of the carrier of S
the Sorts of G . (the_sort_of f) is non empty set
g is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,X)
(S,A,X,g,G) is non empty set
C is set
proj1 the Charact of (S,A,V,G) is non empty set
proj1 the Charact of (S,A,X,G) is non empty set
(proj1 the Charact of (S,A,V,G)) /\ (proj1 the Charact of (S,A,X,G)) is set
the Charact of (S,A,V,G) . C is Relation-like Function-like set
the Charact of (S,A,X,G) . C is Relation-like Function-like set
f is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier' of (S,A,V)
(S,A,V,f,G) is Relation-like Function-like set
the Charact of G is Relation-like the carrier' of S -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of G #), the ResultSort of S * the Sorts of G
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the Sorts of G # is Relation-like the carrier of S * -defined non empty Function-like total set
the Arity of S * ( the Sorts of G #) is Relation-like the carrier' of S -defined non empty Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of G is Relation-like non-empty non empty-yielding the carrier' of S -defined non empty Function-like total set
f . {} is set
(f . {}) `1 is set
the Charact of G . ((f . {}) `1) is Relation-like Function-like set
g is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier' of (S,A,X)
(S,A,X,g,G) is Relation-like Function-like set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
V is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
V \/ X is non empty functional constituted-DTrees Element of bool (S -Terms A)
bool (S -Terms A) is set
(S,A,V) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
(S,A,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
G is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable CompoundTerm of S,A
f is non-empty MSAlgebra over S
(S,A,(V \/ X),f) is strict non-empty MSAlgebra over (S,A,(V \/ X))
(S,A,(V \/ X)) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees (V \/ X) is non empty functional constituted-DTrees set
[: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X) is functional constituted-DTrees Element of bool (Subtrees (V \/ X))
bool (Subtrees (V \/ X)) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees (V \/ X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X) -defined (Subtrees (V \/ X)) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X),(Subtrees (V \/ X)) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),((Subtrees (V \/ X)) *):]
(Subtrees (V \/ X)) * is non empty functional FinSequence-membered M8( Subtrees (V \/ X))
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),((Subtrees (V \/ X)) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),((Subtrees (V \/ X)) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X) -defined Subtrees (V \/ X) -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X) -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X), Subtrees (V \/ X)) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),(Subtrees (V \/ X)):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),(Subtrees (V \/ X)):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),(Subtrees (V \/ X)):] is set
ManySortedSign(# (Subtrees (V \/ X)),([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X)),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees (V \/ X)),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees (V \/ X))) #) is non empty V68() strict V153() ManySortedSign
(S,A,(V \/ X),f) is Relation-like non-empty non empty-yielding the carrier of (S,A,(V \/ X)) -defined non empty Function-like total set
the carrier of (S,A,(V \/ X)) is non empty set
(S,A,(V \/ X),f) is Relation-like the carrier' of (S,A,(V \/ X)) -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,(V \/ X)) * ((S,A,(V \/ X),f) #), the ResultSort of (S,A,(V \/ X)) * (S,A,(V \/ X),f)
the carrier' of (S,A,(V \/ X)) is set
the Arity of (S,A,(V \/ X)) is Relation-like the carrier' of (S,A,(V \/ X)) -defined the carrier of (S,A,(V \/ X)) * -valued Function-like V25( the carrier' of (S,A,(V \/ X)), the carrier of (S,A,(V \/ X)) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,(V \/ X)),( the carrier of (S,A,(V \/ X)) *):]
the carrier of (S,A,(V \/ X)) * is non empty functional FinSequence-membered M8( the carrier of (S,A,(V \/ X)))
[: the carrier' of (S,A,(V \/ X)),( the carrier of (S,A,(V \/ X)) *):] is Relation-like set
bool [: the carrier' of (S,A,(V \/ X)),( the carrier of (S,A,(V \/ X)) *):] is set
(S,A,(V \/ X),f) # is Relation-like the carrier of (S,A,(V \/ X)) * -defined non empty Function-like total set
the Arity of (S,A,(V \/ X)) * ((S,A,(V \/ X),f) #) is Relation-like the carrier' of (S,A,(V \/ X)) -defined Function-like total set
the ResultSort of (S,A,(V \/ X)) is Relation-like the carrier' of (S,A,(V \/ X)) -defined the carrier of (S,A,(V \/ X)) -valued Function-like V25( the carrier' of (S,A,(V \/ X)), the carrier of (S,A,(V \/ X))) Element of bool [: the carrier' of (S,A,(V \/ X)), the carrier of (S,A,(V \/ X)):]
[: the carrier' of (S,A,(V \/ X)), the carrier of (S,A,(V \/ X)):] is Relation-like set
bool [: the carrier' of (S,A,(V \/ X)), the carrier of (S,A,(V \/ X)):] is set
the ResultSort of (S,A,(V \/ X)) * (S,A,(V \/ X),f) is Relation-like non-empty the carrier' of (S,A,(V \/ X)) -defined Function-like total set
MSAlgebra(# (S,A,(V \/ X),f),(S,A,(V \/ X),f) #) is strict MSAlgebra over (S,A,(V \/ X))
(S,A,V,f) is strict non-empty MSAlgebra over (S,A,V)
(S,A,V,f) is Relation-like non-empty non empty-yielding the carrier of (S,A,V) -defined non empty Function-like total set
the carrier of (S,A,V) is non empty set
(S,A,V,f) is Relation-like the carrier' of (S,A,V) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,V) * ((S,A,V,f) #), the ResultSort of (S,A,V) * (S,A,V,f)
the carrier' of (S,A,V) is non empty set
the Arity of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) * -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):]
the carrier of (S,A,V) * is non empty functional FinSequence-membered M8( the carrier of (S,A,V))
[: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is Relation-like set
bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is set
(S,A,V,f) # is Relation-like the carrier of (S,A,V) * -defined non empty Function-like total set
the Arity of (S,A,V) * ((S,A,V,f) #) is Relation-like the carrier' of (S,A,V) -defined non empty Function-like total set
the ResultSort of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V)) Element of bool [: the carrier' of (S,A,V), the carrier of (S,A,V):]
[: the carrier' of (S,A,V), the carrier of (S,A,V):] is Relation-like set
bool [: the carrier' of (S,A,V), the carrier of (S,A,V):] is set
the ResultSort of (S,A,V) * (S,A,V,f) is Relation-like non-empty non empty-yielding the carrier' of (S,A,V) -defined non empty Function-like total set
MSAlgebra(# (S,A,V,f),(S,A,V,f) #) is strict MSAlgebra over (S,A,V)
(S,A,X,f) is strict non-empty MSAlgebra over (S,A,X)
(S,A,X,f) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the carrier of (S,A,X) is non empty set
(S,A,X,f) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,X) * ((S,A,X,f) #), the ResultSort of (S,A,X) * (S,A,X,f)
the carrier' of (S,A,X) is non empty set
the Arity of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) * -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):]
the carrier of (S,A,X) * is non empty functional FinSequence-membered M8( the carrier of (S,A,X))
[: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is Relation-like set
bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is set
(S,A,X,f) # is Relation-like the carrier of (S,A,X) * -defined non empty Function-like total set
the Arity of (S,A,X) * ((S,A,X,f) #) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total set
the ResultSort of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X)) Element of bool [: the carrier' of (S,A,X), the carrier of (S,A,X):]
[: the carrier' of (S,A,X), the carrier of (S,A,X):] is Relation-like set
bool [: the carrier' of (S,A,X), the carrier of (S,A,X):] is set
the ResultSort of (S,A,X) * (S,A,X,f) is Relation-like non-empty non empty-yielding the carrier' of (S,A,X) -defined non empty Function-like total set
MSAlgebra(# (S,A,X,f),(S,A,X,f) #) is strict MSAlgebra over (S,A,X)
(S,A,V,f) +* (S,A,X,f) is strict non-empty MSAlgebra over (S,A,V) +* (S,A,X)
(S,A,V) +* (S,A,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
C is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,C,f) is strict non-empty MSAlgebra over (S,A,C)
(S,A,C) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees C is non empty functional constituted-DTrees set
[: the carrier' of S,{ the carrier of S}:] -Subtrees C is functional constituted-DTrees Element of bool (Subtrees C)
bool (Subtrees C) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees C is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees C -defined (Subtrees C) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees C,(Subtrees C) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees C),((Subtrees C) *):]
(Subtrees C) * is non empty functional FinSequence-membered M8( Subtrees C)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees C),((Subtrees C) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees C),((Subtrees C) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees C) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees C -defined Subtrees C -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees C -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees C, Subtrees C) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees C),(Subtrees C):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees C),(Subtrees C):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees C),(Subtrees C):] is set
ManySortedSign(# (Subtrees C),([: the carrier' of S,{ the carrier of S}:] -Subtrees C),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees C),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees C)) #) is non empty V68() strict V153() ManySortedSign
(S,A,C,f) is Relation-like non-empty non empty-yielding the carrier of (S,A,C) -defined non empty Function-like total set
the carrier of (S,A,C) is non empty set
(S,A,C,f) is Relation-like the carrier' of (S,A,C) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,C) * ((S,A,C,f) #), the ResultSort of (S,A,C) * (S,A,C,f)
the carrier' of (S,A,C) is non empty set
the Arity of (S,A,C) is Relation-like the carrier' of (S,A,C) -defined the carrier of (S,A,C) * -valued Function-like V25( the carrier' of (S,A,C), the carrier of (S,A,C) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,C),( the carrier of (S,A,C) *):]
the carrier of (S,A,C) * is non empty functional FinSequence-membered M8( the carrier of (S,A,C))
[: the carrier' of (S,A,C),( the carrier of (S,A,C) *):] is Relation-like set
bool [: the carrier' of (S,A,C),( the carrier of (S,A,C) *):] is set
(S,A,C,f) # is Relation-like the carrier of (S,A,C) * -defined non empty Function-like total set
the Arity of (S,A,C) * ((S,A,C,f) #) is Relation-like the carrier' of (S,A,C) -defined non empty Function-like total set
the ResultSort of (S,A,C) is Relation-like the carrier' of (S,A,C) -defined the carrier of (S,A,C) -valued Function-like V25( the carrier' of (S,A,C), the carrier of (S,A,C)) Element of bool [: the carrier' of (S,A,C), the carrier of (S,A,C):]
[: the carrier' of (S,A,C), the carrier of (S,A,C):] is Relation-like set
bool [: the carrier' of (S,A,C), the carrier of (S,A,C):] is set
the ResultSort of (S,A,C) * (S,A,C,f) is Relation-like non-empty non empty-yielding the carrier' of (S,A,C) -defined non empty Function-like total set
MSAlgebra(# (S,A,C,f),(S,A,C,f) #) is strict MSAlgebra over (S,A,C)
the Sorts of (S,A,V,f) is Relation-like non-empty non empty-yielding the carrier of (S,A,V) -defined non empty Function-like total set
the Sorts of (S,A,X,f) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the Charact of (S,A,V,f) is Relation-like the carrier' of (S,A,V) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,V) * ( the Sorts of (S,A,V,f) #), the ResultSort of (S,A,V) * the Sorts of (S,A,V,f)
the Sorts of (S,A,V,f) # is Relation-like the carrier of (S,A,V) * -defined non empty Function-like total set
the Arity of (S,A,V) * ( the Sorts of (S,A,V,f) #) is Relation-like the carrier' of (S,A,V) -defined non empty Function-like total set
the ResultSort of (S,A,V) * the Sorts of (S,A,V,f) is Relation-like non-empty non empty-yielding the carrier' of (S,A,V) -defined non empty Function-like total set
the Charact of (S,A,X,f) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,X) * ( the Sorts of (S,A,X,f) #), the ResultSort of (S,A,X) * the Sorts of (S,A,X,f)
the Sorts of (S,A,X,f) # is Relation-like the carrier of (S,A,X) * -defined non empty Function-like total set
the Arity of (S,A,X) * ( the Sorts of (S,A,X,f) #) is Relation-like the carrier' of (S,A,X) -defined non empty Function-like total set
the ResultSort of (S,A,X) * the Sorts of (S,A,X,f) is Relation-like non-empty non empty-yielding the carrier' of (S,A,X) -defined non empty Function-like total set
the Sorts of ((S,A,V,f) +* (S,A,X,f)) is Relation-like non-empty non empty-yielding the carrier of ((S,A,V) +* (S,A,X)) -defined non empty Function-like total set
the carrier of ((S,A,V) +* (S,A,X)) is non empty set
the Sorts of (S,A,V,f) +* the Sorts of (S,A,X,f) is Relation-like the carrier of (S,A,V) \/ the carrier of (S,A,X) -defined non empty Function-like total set
the carrier of (S,A,V) \/ the carrier of (S,A,X) is non empty set
the Charact of ((S,A,V,f) +* (S,A,X,f)) is Relation-like the carrier' of ((S,A,V) +* (S,A,X)) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of ((S,A,V) +* (S,A,X)) * ( the Sorts of ((S,A,V,f) +* (S,A,X,f)) #), the ResultSort of ((S,A,V) +* (S,A,X)) * the Sorts of ((S,A,V,f) +* (S,A,X,f))
the carrier' of ((S,A,V) +* (S,A,X)) is non empty set
the Arity of ((S,A,V) +* (S,A,X)) is Relation-like the carrier' of ((S,A,V) +* (S,A,X)) -defined the carrier of ((S,A,V) +* (S,A,X)) * -valued Function-like V25( the carrier' of ((S,A,V) +* (S,A,X)), the carrier of ((S,A,V) +* (S,A,X)) * ) Function-yielding V54() Element of bool [: the carrier' of ((S,A,V) +* (S,A,X)),( the carrier of ((S,A,V) +* (S,A,X)) *):]
the carrier of ((S,A,V) +* (S,A,X)) * is non empty functional FinSequence-membered M8( the carrier of ((S,A,V) +* (S,A,X)))
[: the carrier' of ((S,A,V) +* (S,A,X)),( the carrier of ((S,A,V) +* (S,A,X)) *):] is Relation-like set
bool [: the carrier' of ((S,A,V) +* (S,A,X)),( the carrier of ((S,A,V) +* (S,A,X)) *):] is set
the Sorts of ((S,A,V,f) +* (S,A,X,f)) # is Relation-like the carrier of ((S,A,V) +* (S,A,X)) * -defined non empty Function-like total set
the Arity of ((S,A,V) +* (S,A,X)) * ( the Sorts of ((S,A,V,f) +* (S,A,X,f)) #) is Relation-like the carrier' of ((S,A,V) +* (S,A,X)) -defined non empty Function-like total set
the ResultSort of ((S,A,V) +* (S,A,X)) is Relation-like the carrier' of ((S,A,V) +* (S,A,X)) -defined the carrier of ((S,A,V) +* (S,A,X)) -valued Function-like V25( the carrier' of ((S,A,V) +* (S,A,X)), the carrier of ((S,A,V) +* (S,A,X))) Element of bool [: the carrier' of ((S,A,V) +* (S,A,X)), the carrier of ((S,A,V) +* (S,A,X)):]
[: the carrier' of ((S,A,V) +* (S,A,X)), the carrier of ((S,A,V) +* (S,A,X)):] is Relation-like set
bool [: the carrier' of ((S,A,V) +* (S,A,X)), the carrier of ((S,A,V) +* (S,A,X)):] is set
the ResultSort of ((S,A,V) +* (S,A,X)) * the Sorts of ((S,A,V,f) +* (S,A,X,f)) is Relation-like non-empty non empty-yielding the carrier' of ((S,A,V) +* (S,A,X)) -defined non empty Function-like total set
the Charact of (S,A,V,f) +* the Charact of (S,A,X,f) is Relation-like the carrier' of (S,A,V) \/ the carrier' of (S,A,X) -defined non empty Function-like total set
the carrier' of (S,A,V) \/ the carrier' of (S,A,X) is non empty set
the Sorts of (S,A,C,f) is Relation-like non-empty non empty-yielding the carrier of (S,A,C) -defined non empty Function-like total set
the Charact of (S,A,C,f) is Relation-like the carrier' of (S,A,C) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,C) * ( the Sorts of (S,A,C,f) #), the ResultSort of (S,A,C) * the Sorts of (S,A,C,f)
the Sorts of (S,A,C,f) # is Relation-like the carrier of (S,A,C) * -defined non empty Function-like total set
the Arity of (S,A,C) * ( the Sorts of (S,A,C,f) #) is Relation-like the carrier' of (S,A,C) -defined non empty Function-like total set
the ResultSort of (S,A,C) * the Sorts of (S,A,C,f) is Relation-like non-empty non empty-yielding the carrier' of (S,A,C) -defined non empty Function-like total set
proj1 the Sorts of ((S,A,V,f) +* (S,A,X,f)) is non empty set
proj1 the Charact of ((S,A,V,f) +* (S,A,X,f)) is non empty set
proj1 the Charact of (S,A,C,f) is non empty set
proj1 the Sorts of (S,A,C,f) is non empty set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is non-empty MSAlgebra over S
X is Relation-like Function-like DecoratedTree-like set
V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total Variables of A
K334(S,V) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,V) is non empty set
FinTrees the carrier of K334(S,V) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,V)
S -Terms V is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,V))
bool (FinTrees the carrier of K334(S,V)) is set
the Sorts of A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the Sorts of A \/ V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
K334(S,( the Sorts of A \/ V)) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,( the Sorts of A \/ V)) is non empty set
FinTrees the carrier of K334(S,( the Sorts of A \/ V)) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,( the Sorts of A \/ V))
S -Terms ( the Sorts of A \/ V) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,( the Sorts of A \/ V)))
bool (FinTrees the carrier of K334(S,( the Sorts of A \/ V))) is set
G is Relation-like the carrier of S -defined non empty Function-like total Function-yielding V54() ManySortedFunction of V, the Sorts of A
C is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
C @ G is Element of the Sorts of A . (the_sort_of C)
the_sort_of C is Element of the carrier of S
the Sorts of A . (the_sort_of C) is non empty set
f is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
f is set
f @ G is Element of the Sorts of A . (the_sort_of f)
the_sort_of f is Element of the carrier of S
the Sorts of A . (the_sort_of f) is non empty set
t is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
g is set
t @ G is Element of the Sorts of A . (the_sort_of t)
the_sort_of t is Element of the carrier of S
the Sorts of A . (the_sort_of t) is non empty set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
V is non empty functional constituted-DTrees SetWithCompoundTerm of S,A
(S,A,V) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees V is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees V is functional constituted-DTrees Element of bool (Subtrees V)
bool (Subtrees V) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined (Subtrees V) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V,(Subtrees V) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):]
(Subtrees V) * is non empty functional FinSequence-membered M8( Subtrees V)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),((Subtrees V) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees V -defined Subtrees V -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees V -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees V, Subtrees V) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees V),(Subtrees V):] is set
ManySortedSign(# (Subtrees V),([: the carrier' of S,{ the carrier of S}:] -Subtrees V),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees V),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees V)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,A,V) is non empty set
X is non-empty finite-yielding MSAlgebra over S
(S,A,V,X) is strict non-empty finite-yielding MSAlgebra over (S,A,V)
(S,A,V,X) is Relation-like non-empty non empty-yielding the carrier of (S,A,V) -defined non empty Function-like total set
(S,A,V,X) is Relation-like the carrier' of (S,A,V) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,V) * ((S,A,V,X) #), the ResultSort of (S,A,V) * (S,A,V,X)
the carrier' of (S,A,V) is non empty set
the Arity of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) * -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):]
the carrier of (S,A,V) * is non empty functional FinSequence-membered M8( the carrier of (S,A,V))
[: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is Relation-like set
bool [: the carrier' of (S,A,V),( the carrier of (S,A,V) *):] is set
(S,A,V,X) # is Relation-like the carrier of (S,A,V) * -defined non empty Function-like total set
the Arity of (S,A,V) * ((S,A,V,X) #) is Relation-like the carrier' of (S,A,V) -defined non empty Function-like total set
the ResultSort of (S,A,V) is Relation-like the carrier' of (S,A,V) -defined the carrier of (S,A,V) -valued Function-like V25( the carrier' of (S,A,V), the carrier of (S,A,V)) Element of bool [: the carrier' of (S,A,V), the carrier of (S,A,V):]
[: the carrier' of (S,A,V), the carrier of (S,A,V):] is Relation-like set
bool [: the carrier' of (S,A,V), the carrier of (S,A,V):] is set
the ResultSort of (S,A,V) * (S,A,V,X) is Relation-like non-empty non empty-yielding the carrier' of (S,A,V) -defined non empty Function-like total set
MSAlgebra(# (S,A,V,X),(S,A,V,X) #) is strict MSAlgebra over (S,A,V)
the Sorts of (S,A,V,X) is Relation-like non-empty non empty-yielding the carrier of (S,A,V) -defined non empty Function-like total set
product the Sorts of (S,A,V,X) is non empty functional with_common_domain product-like set
G is Relation-like the carrier of (S,A,V) -defined non empty Function-like the Sorts of (S,A,V,X) -compatible total Element of product the Sorts of (S,A,V,X)
the Sorts of X is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
C is Element of the carrier of S
A . C is non empty set
the Sorts of X . C is non empty set
f is Element of A . C
[f,C] is pair set
{f,C} is non empty finite countable set
{f} is non empty trivial finite V35(1) countable set
{{f,C},{f}} is non empty finite V32() countable set
root-tree [f,C] is Relation-like trivial Function-like constant finite DecoratedTree-like finite-order finite-branching countable set
G . (root-tree [f,C]) is set
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
bool (FinTrees the carrier of K334(S,A)) is set
g is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,A,V)
f is Relation-like the carrier of K334(S,A) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,A), FinTrees the carrier of K334(S,A),S -Terms A)
the_sort_of f is Element of the carrier of S
(S,A,V,g,X) is non empty set
the Sorts of X . (the_sort_of f) is non empty set
(S,A,V,X) . g is non empty set
G . g is set
t is Element of the Sorts of X . C
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is non-empty finite-yielding MSAlgebra over S
V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total Variables of A
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,V
(S,V,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,V,X) is non empty set
(S,V,X,A) is strict non-empty finite-yielding MSAlgebra over (S,V,X)
(S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
(S,V,X,A) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,V,X) * ((S,V,X,A) #), the ResultSort of (S,V,X) * (S,V,X,A)
the carrier' of (S,V,X) is non empty set
the Arity of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) * -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):]
the carrier of (S,V,X) * is non empty functional FinSequence-membered M8( the carrier of (S,V,X))
[: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is Relation-like set
bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is set
(S,V,X,A) # is Relation-like the carrier of (S,V,X) * -defined non empty Function-like total set
the Arity of (S,V,X) * ((S,V,X,A) #) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total set
the ResultSort of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X)) Element of bool [: the carrier' of (S,V,X), the carrier of (S,V,X):]
[: the carrier' of (S,V,X), the carrier of (S,V,X):] is Relation-like set
bool [: the carrier' of (S,V,X), the carrier of (S,V,X):] is set
the ResultSort of (S,V,X) * (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier' of (S,V,X) -defined non empty Function-like total set
MSAlgebra(# (S,V,X,A),(S,V,X,A) #) is strict MSAlgebra over (S,V,X)
the Sorts of (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
product the Sorts of (S,V,X,A) is non empty functional with_common_domain product-like set
G is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
C is Relation-like the carrier of S -defined non empty Function-like total Function-yielding V54() (S,V,X,A,G)
f is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (G,f) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
g is Element of the carrier of S
V . g is non empty set
C . g is Relation-like Function-like set
f is Element of V . g
[f,g] is pair set
{f,g} is non empty finite countable set
{f} is non empty trivial finite V35(1) countable set
{{f,g},{f}} is non empty finite V32() countable set
root-tree [f,g] is Relation-like trivial Function-like constant finite DecoratedTree-like finite-order finite-branching countable set
(C . g) . f is set
(Following (G,f)) . (root-tree [f,g]) is set
InputVertices (S,V,X) is Element of bool the carrier of (S,V,X)
bool the carrier of (S,V,X) is set
K507( the carrier of (S,V,X), the ResultSort of (S,V,X)) is Element of bool the carrier of (S,V,X)
the carrier of (S,V,X) \ K507( the carrier of (S,V,X), the ResultSort of (S,V,X)) is Element of bool the carrier of (S,V,X)
G . (root-tree [f,g]) is set
A is non empty non void V68() V153() ManySortedSign
the carrier of A is non empty set
V is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
K334(A,V) is non empty V112() V116() V117() V118() L13()
the carrier of K334(A,V) is non empty set
FinTrees the carrier of K334(A,V) is non empty functional constituted-DTrees DTree-set of the carrier of K334(A,V)
A -Terms V is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(A,V))
bool (FinTrees the carrier of K334(A,V)) is set
S is set
X is Relation-like NAT -defined FinTrees the carrier of K334(A,V) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable FinSequence of A -Terms V
S -tree X is Relation-like Function-like DecoratedTree-like set
doms X is Relation-like NAT -defined FinTrees -valued Function-like finite FinSequence-like FinSubsequence-like Tree-yielding FinTree-yielding countable FinSequence of FinTrees
proj1 (S -tree X) is non empty Tree-like set
G is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Tree-yielding FinTree-yielding countable set
tree G is non empty finite Tree-like finite-order finite-branching countable set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is non-empty finite-yielding MSAlgebra over S
V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total Variables of A
K334(S,V) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,V) is non empty set
FinTrees the carrier of K334(S,V) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,V)
S -Terms V is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,V))
bool (FinTrees the carrier of K334(S,V)) is set
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,V
(S,V,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,V,X) is non empty set
(S,V,X,A) is strict non-empty finite-yielding MSAlgebra over (S,V,X)
(S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
(S,V,X,A) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,V,X) * ((S,V,X,A) #), the ResultSort of (S,V,X) * (S,V,X,A)
the carrier' of (S,V,X) is non empty set
the Arity of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) * -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):]
the carrier of (S,V,X) * is non empty functional FinSequence-membered M8( the carrier of (S,V,X))
[: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is Relation-like set
bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is set
(S,V,X,A) # is Relation-like the carrier of (S,V,X) * -defined non empty Function-like total set
the Arity of (S,V,X) * ((S,V,X,A) #) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total set
the ResultSort of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X)) Element of bool [: the carrier' of (S,V,X), the carrier of (S,V,X):]
[: the carrier' of (S,V,X), the carrier of (S,V,X):] is Relation-like set
bool [: the carrier' of (S,V,X), the carrier of (S,V,X):] is set
the ResultSort of (S,V,X) * (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier' of (S,V,X) -defined non empty Function-like total set
MSAlgebra(# (S,V,X,A),(S,V,X,A) #) is strict MSAlgebra over (S,V,X)
the Sorts of (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
product the Sorts of (S,V,X,A) is non empty functional with_common_domain product-like set
G is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
C is Relation-like the carrier of S -defined non empty Function-like total Function-yielding V54() (S,V,X,A,G)
f is Element of the carrier of S
V . f is non empty set
g is Element of V . f
[g,f] is pair set
{g,f} is non empty finite countable set
{g} is non empty trivial finite V35(1) countable set
{{g,f},{g}} is non empty finite V32() countable set
root-tree [g,f] is Relation-like trivial Function-like constant finite DecoratedTree-like finite-order finite-branching countable set
proj1 (root-tree [g,f]) is non empty trivial finite V35(1) Tree-like finite-order finite-branching countable set
height (proj1 (root-tree [g,f])) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
1 + (height (proj1 (root-tree [g,f]))) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (G,(1 + (height (proj1 (root-tree [g,f]))))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
(Following (G,(1 + (height (proj1 (root-tree [g,f])))))) . (root-tree [g,f]) is set
(S,A,V,(root-tree [g,f]),C) is set
InputVertices (S,V,X) is Element of bool the carrier of (S,V,X)
bool the carrier of (S,V,X) is set
K507( the carrier of (S,V,X), the ResultSort of (S,V,X)) is Element of bool the carrier of (S,V,X)
the carrier of (S,V,X) \ K507( the carrier of (S,V,X), the ResultSort of (S,V,X)) is Element of bool the carrier of (S,V,X)
the Sorts of A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the Sorts of A \/ V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
K334(S,( the Sorts of A \/ V)) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,( the Sorts of A \/ V)) is non empty set
FinTrees the carrier of K334(S,( the Sorts of A \/ V)) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,( the Sorts of A \/ V))
S -Terms ( the Sorts of A \/ V) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,( the Sorts of A \/ V)))
bool (FinTrees the carrier of K334(S,( the Sorts of A \/ V))) is set
f is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
G . (root-tree [g,f]) is set
C . f is Relation-like Function-like set
(C . f) . g is set
g -term A is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
(g -term A) @ C is Element of the Sorts of A . (the_sort_of (g -term A))
the_sort_of (g -term A) is Element of the carrier of S
the Sorts of A . (the_sort_of (g -term A)) is non empty set
f @ C is Element of the Sorts of A . (the_sort_of f)
the_sort_of f is Element of the carrier of S
the Sorts of A . (the_sort_of f) is non empty set
f is Element of the carrier' of S
Sym (f,V) is Element of K316(K334(S,V))
K316(K334(S,V)) is non empty Element of bool the carrier of K334(S,V)
bool the carrier of K334(S,V) is set
[f, the carrier of S] is pair set
{f, the carrier of S} is non empty finite countable set
{f} is non empty trivial finite V35(1) countable set
{{f, the carrier of S},{f}} is non empty finite V32() countable set
g is Relation-like NAT -defined FinTrees the carrier of K334(S,V) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable ArgumentSeq of Sym (f,V)
proj2 g is finite countable set
[f, the carrier of S] -tree g is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable set
proj1 ([f, the carrier of S] -tree g) is non empty finite Tree-like finite-order finite-branching countable set
height (proj1 ([f, the carrier of S] -tree g)) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
1 + (height (proj1 ([f, the carrier of S] -tree g))) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (G,(1 + (height (proj1 ([f, the carrier of S] -tree g))))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
(Following (G,(1 + (height (proj1 ([f, the carrier of S] -tree g)))))) . ([f, the carrier of S] -tree g) is set
(S,A,V,([f, the carrier of S] -tree g),C) is set
f is Relation-like Function-like DecoratedTree-like Element of X
proj1 f is non empty Tree-like set
t is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of proj1 f
f | t is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
(proj1 f) | t is non empty Tree-like set
t ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
f . t is Element of the carrier of K334(S,V)
(f | t) . {} is set
t9 is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier' of (S,V,X)
the_result_sort_of t9 is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,V,X)
the ResultSort of (S,V,X) . t9 is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,V,X)
t9 . {} is set
the_arity_of t9 is Relation-like NAT -defined the carrier of (S,V,X) -valued the carrier of (S,V,X) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding countable Element of the carrier of (S,V,X) *
the Arity of (S,V,X) . t9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of (S,V,X) *
(t9 . {}) -tree (the_arity_of t9) is Relation-like Function-like DecoratedTree-like set
proj2 (the_arity_of t9) is finite countable set
doms g is Relation-like NAT -defined FinTrees -valued Function-like finite FinSequence-like FinSubsequence-like Tree-yielding FinTree-yielding countable FinSequence of FinTrees
tree (doms g) is non empty finite Tree-like finite-order finite-branching countable set
v is set
s is Relation-like Function-like DecoratedTree-like Element of Subtrees X
dom g is finite countable Element of bool NAT
c₁₄ is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
vp is set
g . vp is Relation-like Function-like set
dom (doms g) is finite countable Element of bool NAT
(doms g) . vp is set
proj1 c₁₄ is non empty finite Tree-like finite-order finite-branching countable set
proj2 (doms g) is finite countable set
height (tree (doms g)) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
height (proj1 c₁₄) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
1 + (height (proj1 c₁₄)) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
p9 is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
(1 + (height (proj1 c₁₄))) + p9 is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (G,(height (proj1 ([f, the carrier of S] -tree g)))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
Following (G,(1 + (height (proj1 c₁₄)))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
z is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following ((Following (G,(1 + (height (proj1 c₁₄))))),z) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
Following (Following (G,(height (proj1 ([f, the carrier of S] -tree g))))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
the Sorts of A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the Sorts of A \/ V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
K334(S,( the Sorts of A \/ V)) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,( the Sorts of A \/ V)) is non empty set
FinTrees the carrier of K334(S,( the Sorts of A \/ V)) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,( the Sorts of A \/ V))
S -Terms ( the Sorts of A \/ V) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,( the Sorts of A \/ V)))
bool (FinTrees the carrier of K334(S,( the Sorts of A \/ V))) is set
(Sym (f,V)) -tree g is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
Sym (f,( the Sorts of A \/ V)) is Element of K316(K334(S,( the Sorts of A \/ V)))
K316(K334(S,( the Sorts of A \/ V))) is non empty Element of bool the carrier of K334(S,( the Sorts of A \/ V))
bool the carrier of K334(S,( the Sorts of A \/ V)) is set
v is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
proj1 v is non empty finite Tree-like finite-order finite-branching countable set
height (proj1 v) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (G,(height (proj1 v))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
len g is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
s is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len s is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
dom s is finite countable Element of bool NAT
Seg (len g) is finite V35( len g) countable Element of bool NAT
the_arity_of f is Relation-like NAT -defined the carrier of S -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of S *
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Arity of S . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of S *
dom (the_arity_of f) is finite countable Element of bool NAT
c₁₄ is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
g . c₁₄ is Relation-like Function-like set
vp is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
p9 is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
the_sort_of vp is Element of the carrier of S
z is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
the_sort_of z is Element of the carrier of S
(the_arity_of f) . c₁₄ is set
vp is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
p9 is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
g . vp is Relation-like Function-like set
z is Relation-like Function-like DecoratedTree-like Element of Subtrees X
proj1 p9 is non empty finite Tree-like finite-order finite-branching countable set
height (proj1 p9) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
1 + (height (proj1 p9)) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (G,(1 + (height (proj1 p9)))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
i is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
(Following (G,(1 + (height (proj1 p9))))) . i is set
(S,A,V,i,C) is set
s . vp is set
(Following (G,(height (proj1 ([f, the carrier of S] -tree g))))) . p9 is set
(doms g) . vp is set
tt is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
(1 + (height (proj1 p9))) + tt is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
tt is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following ((Following (G,(1 + (height (proj1 p9))))),tt) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
(Following (G,(1 + (height (proj1 p9))))) . p9 is set
p9 @ C is Element of the Sorts of A . (the_sort_of p9)
the_sort_of p9 is Element of the carrier of S
the Sorts of A . (the_sort_of p9) is non empty set
c₁₄ is Relation-like NAT -defined FinTrees the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable ArgumentSeq of Sym (f,( the Sorts of A \/ V))
(Sym (f,( the Sorts of A \/ V))) -tree c₁₄ is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
((Sym (f,( the Sorts of A \/ V))) -tree c₁₄) @ C is Element of the Sorts of A . (the_sort_of ((Sym (f,( the Sorts of A \/ V))) -tree c₁₄))
the_sort_of ((Sym (f,( the Sorts of A \/ V))) -tree c₁₄) is Element of the carrier of S
the Sorts of A . (the_sort_of ((Sym (f,( the Sorts of A \/ V))) -tree c₁₄)) is non empty set
Den (f,A) is Relation-like Args (f,A) -defined Result (f,A) -valued Function-like V25( Args (f,A), Result (f,A)) Element of bool [:(Args (f,A)),(Result (f,A)):]
Args (f,A) is non empty Element of proj2 ( the Sorts of A #)
the Sorts of A # is Relation-like the carrier of S * -defined non empty Function-like total set
proj2 ( the Sorts of A #) is non empty set
the Arity of S * ( the Sorts of A #) is Relation-like the carrier' of S -defined non empty Function-like total set
( the Arity of S * ( the Sorts of A #)) . f is set
Result (f,A) is non empty Element of proj2 the Sorts of A
proj2 the Sorts of A is non empty V141() set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of A is Relation-like non-empty non empty-yielding the carrier' of S -defined non empty Function-like total set
( the ResultSort of S * the Sorts of A) . f is non empty set
[:(Args (f,A)),(Result (f,A)):] is Relation-like set
bool [:(Args (f,A)),(Result (f,A)):] is set
the Charact of A is Relation-like the carrier' of S -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of A #), the ResultSort of S * the Sorts of A
the Charact of A . f is Relation-like Function-like set
(Den (f,A)) . s is set
proj1 (Following (G,(height (proj1 v)))) is non empty set
g * (Following (G,(height (proj1 v)))) is Relation-like NAT -defined Function-like finite countable set
proj1 (g * (Following (G,(height (proj1 v))))) is finite countable set
vp is set
p9 is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
s . p9 is set
g . p9 is Relation-like Function-like set
(Following (G,(height (proj1 v)))) . (g . p9) is set
s . vp is set
(g * (Following (G,(height (proj1 v))))) . vp is set
(the_arity_of t9) * (Following (G,(height (proj1 v)))) is Relation-like NAT -defined Function-like finite countable set
Args (t9,(S,V,X,A)) is non empty Element of proj2 ( the Sorts of (S,V,X,A) #)
the Sorts of (S,V,X,A) # is Relation-like the carrier of (S,V,X) * -defined non empty Function-like total set
proj2 ( the Sorts of (S,V,X,A) #) is non empty set
the Arity of (S,V,X) * ( the Sorts of (S,V,X,A) #) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total set
( the Arity of (S,V,X) * ( the Sorts of (S,V,X,A) #)) . t9 is set
Result (t9,(S,V,X,A)) is non empty Element of proj2 the Sorts of (S,V,X,A)
proj2 the Sorts of (S,V,X,A) is non empty V141() set
the ResultSort of (S,V,X) * the Sorts of (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier' of (S,V,X) -defined non empty Function-like total set
( the ResultSort of (S,V,X) * the Sorts of (S,V,X,A)) . t9 is non empty set
Den (t9,(S,V,X,A)) is Relation-like Args (t9,(S,V,X,A)) -defined Result (t9,(S,V,X,A)) -valued Function-like V25( Args (t9,(S,V,X,A)), Result (t9,(S,V,X,A))) Element of bool [:(Args (t9,(S,V,X,A))),(Result (t9,(S,V,X,A))):]
[:(Args (t9,(S,V,X,A))),(Result (t9,(S,V,X,A))):] is Relation-like set
bool [:(Args (t9,(S,V,X,A))),(Result (t9,(S,V,X,A))):] is set
the Charact of (S,V,X,A) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,V,X) * ( the Sorts of (S,V,X,A) #), the ResultSort of (S,V,X) * the Sorts of (S,V,X,A)
the Charact of (S,V,X,A) . t9 is Relation-like Function-like set
Following (Following (G,(height (proj1 v)))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
(Following (Following (G,(height (proj1 v))))) . v is set
v @ C is Element of the Sorts of A . (the_sort_of v)
the_sort_of v is Element of the carrier of S
the Sorts of A . (the_sort_of v) is non empty set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
the carrier' of S is non empty set
A is non-empty finite-yielding MSAlgebra over S
V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total Variables of A
K334(S,V) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,V) is non empty set
FinTrees the carrier of K334(S,V) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,V)
S -Terms V is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,V))
bool (FinTrees the carrier of K334(S,V)) is set
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,V
Subtrees X is non empty functional constituted-DTrees set
(S,V,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,V,X) is non empty set
(S,V,X,A) is strict non-empty finite-yielding MSAlgebra over (S,V,X)
(S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
(S,V,X,A) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,V,X) * ((S,V,X,A) #), the ResultSort of (S,V,X) * (S,V,X,A)
the carrier' of (S,V,X) is non empty set
the Arity of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) * -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):]
the carrier of (S,V,X) * is non empty functional FinSequence-membered M8( the carrier of (S,V,X))
[: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is Relation-like set
bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is set
(S,V,X,A) # is Relation-like the carrier of (S,V,X) * -defined non empty Function-like total set
the Arity of (S,V,X) * ((S,V,X,A) #) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total set
the ResultSort of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X)) Element of bool [: the carrier' of (S,V,X), the carrier of (S,V,X):]
[: the carrier' of (S,V,X), the carrier of (S,V,X):] is Relation-like set
bool [: the carrier' of (S,V,X), the carrier of (S,V,X):] is set
the ResultSort of (S,V,X) * (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier' of (S,V,X) -defined non empty Function-like total set
MSAlgebra(# (S,V,X,A),(S,V,X,A) #) is strict MSAlgebra over (S,V,X)
the Sorts of (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
product the Sorts of (S,V,X,A) is non empty functional with_common_domain product-like set
G is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
C is Relation-like the carrier of S -defined non empty Function-like total Function-yielding V54() (S,V,X,A,G)
f is Element of the carrier of S
V . f is non empty set
g is Element of V . f
[g,f] is pair set
{g,f} is non empty finite countable set
{g} is non empty trivial finite V35(1) countable set
{{g,f},{g}} is non empty finite V32() countable set
root-tree [g,f] is Relation-like trivial Function-like constant finite DecoratedTree-like finite-order finite-branching countable set
proj1 (root-tree [g,f]) is non empty trivial finite V35(1) Tree-like finite-order finite-branching countable set
height (proj1 (root-tree [g,f])) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (G,(height (proj1 (root-tree [g,f])))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
(Following (G,(height (proj1 (root-tree [g,f]))))) . (root-tree [g,f]) is set
(S,A,V,(root-tree [g,f]),C) is set
InputVertices (S,V,X) is Element of bool the carrier of (S,V,X)
bool the carrier of (S,V,X) is set
K507( the carrier of (S,V,X), the ResultSort of (S,V,X)) is Element of bool the carrier of (S,V,X)
the carrier of (S,V,X) \ K507( the carrier of (S,V,X), the ResultSort of (S,V,X)) is Element of bool the carrier of (S,V,X)
the Sorts of A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the Sorts of A \/ V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
K334(S,( the Sorts of A \/ V)) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,( the Sorts of A \/ V)) is non empty set
FinTrees the carrier of K334(S,( the Sorts of A \/ V)) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,( the Sorts of A \/ V))
S -Terms ( the Sorts of A \/ V) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,( the Sorts of A \/ V)))
bool (FinTrees the carrier of K334(S,( the Sorts of A \/ V))) is set
f is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
G . (root-tree [g,f]) is set
C . f is Relation-like Function-like set
(C . f) . g is set
g -term A is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
(g -term A) @ C is Element of the Sorts of A . (the_sort_of (g -term A))
the_sort_of (g -term A) is Element of the carrier of S
the Sorts of A . (the_sort_of (g -term A)) is non empty set
f @ C is Element of the Sorts of A . (the_sort_of f)
the_sort_of f is Element of the carrier of S
the Sorts of A . (the_sort_of f) is non empty set
f is Element of the carrier' of S
Sym (f,V) is Element of K316(K334(S,V))
K316(K334(S,V)) is non empty Element of bool the carrier of K334(S,V)
bool the carrier of K334(S,V) is set
[f, the carrier of S] is pair set
{f, the carrier of S} is non empty finite countable set
{f} is non empty trivial finite V35(1) countable set
{{f, the carrier of S},{f}} is non empty finite V32() countable set
g is Relation-like NAT -defined FinTrees the carrier of K334(S,V) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable ArgumentSeq of Sym (f,V)
proj2 g is finite countable set
[f, the carrier of S] -tree g is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable set
proj1 ([f, the carrier of S] -tree g) is non empty finite Tree-like finite-order finite-branching countable set
height (proj1 ([f, the carrier of S] -tree g)) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (G,(height (proj1 ([f, the carrier of S] -tree g)))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
(Following (G,(height (proj1 ([f, the carrier of S] -tree g))))) . ([f, the carrier of S] -tree g) is set
(S,A,V,([f, the carrier of S] -tree g),C) is set
f is Relation-like Function-like DecoratedTree-like Element of X
proj1 f is non empty Tree-like set
t is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of proj1 f
f | t is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
(proj1 f) | t is non empty Tree-like set
t ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
f . t is Element of the carrier of K334(S,V)
(f | t) . {} is set
t9 is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier' of (S,V,X)
the_result_sort_of t9 is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,V,X)
the ResultSort of (S,V,X) . t9 is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,V,X)
t9 . {} is set
the_arity_of t9 is Relation-like NAT -defined the carrier of (S,V,X) -valued the carrier of (S,V,X) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding countable Element of the carrier of (S,V,X) *
the Arity of (S,V,X) . t9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of (S,V,X) *
(t9 . {}) -tree (the_arity_of t9) is Relation-like Function-like DecoratedTree-like set
proj2 (the_arity_of t9) is finite countable set
doms g is Relation-like NAT -defined FinTrees -valued Function-like finite FinSequence-like FinSubsequence-like Tree-yielding FinTree-yielding countable FinSequence of FinTrees
tree (doms g) is non empty finite Tree-like finite-order finite-branching countable set
root-tree [f, the carrier of S] is Relation-like trivial Function-like constant finite DecoratedTree-like finite-order finite-branching countable set
len g is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
the_arity_of f is Relation-like NAT -defined the carrier of S -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of S *
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Arity of S . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of S *
len (the_arity_of f) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
v is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
v + 1 is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
c₁₄ is set
vp is Relation-like Function-like DecoratedTree-like Element of Subtrees X
dom g is finite countable Element of bool NAT
p9 is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
z is set
g . z is Relation-like Function-like set
dom (doms g) is finite countable Element of bool NAT
(doms g) . z is set
proj1 p9 is non empty finite Tree-like finite-order finite-branching countable set
proj2 (doms g) is finite countable set
height (tree (doms g)) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
height (proj1 p9) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
s is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
i is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
(height (proj1 p9)) + i is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (G,s) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
Following (G,(height (proj1 p9))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
tt is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following ((Following (G,(height (proj1 p9)))),tt) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
Following (Following (G,s)) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
the Sorts of A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the Sorts of A \/ V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
K334(S,( the Sorts of A \/ V)) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,( the Sorts of A \/ V)) is non empty set
FinTrees the carrier of K334(S,( the Sorts of A \/ V)) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,( the Sorts of A \/ V))
S -Terms ( the Sorts of A \/ V) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,( the Sorts of A \/ V)))
bool (FinTrees the carrier of K334(S,( the Sorts of A \/ V))) is set
(Sym (f,V)) -tree g is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
Sym (f,( the Sorts of A \/ V)) is Element of K316(K334(S,( the Sorts of A \/ V)))
K316(K334(S,( the Sorts of A \/ V))) is non empty Element of bool the carrier of K334(S,( the Sorts of A \/ V))
bool the carrier of K334(S,( the Sorts of A \/ V)) is set
c₁₄ is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
vp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len vp is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
dom vp is finite countable Element of bool NAT
Seg (len g) is finite V35( len g) countable Element of bool NAT
dom (the_arity_of f) is finite countable Element of bool NAT
p9 is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
g . p9 is Relation-like Function-like set
z is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
i is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
the_sort_of z is Element of the carrier of S
tt is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
the_sort_of tt is Element of the carrier of S
(the_arity_of f) . p9 is set
z is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
i is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
g . z is Relation-like Function-like set
tt is Relation-like Function-like DecoratedTree-like Element of Subtrees X
proj1 i is non empty finite Tree-like finite-order finite-branching countable set
height (proj1 i) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (G,(height (proj1 i))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
tt is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
(Following (G,(height (proj1 i)))) . tt is set
(S,A,V,tt,C) is set
vp . z is set
(Following (G,s)) . i is set
(doms g) . z is set
j is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
(height (proj1 i)) + j is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
j is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following ((Following (G,(height (proj1 i)))),j) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
(Following (G,(height (proj1 i)))) . i is set
i @ C is Element of the Sorts of A . (the_sort_of i)
the_sort_of i is Element of the carrier of S
the Sorts of A . (the_sort_of i) is non empty set
p9 is Relation-like NAT -defined FinTrees the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() countable ArgumentSeq of Sym (f,( the Sorts of A \/ V))
(Sym (f,( the Sorts of A \/ V))) -tree p9 is Relation-like the carrier of K334(S,( the Sorts of A \/ V)) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,( the Sorts of A \/ V)), FinTrees the carrier of K334(S,( the Sorts of A \/ V)),S -Terms ( the Sorts of A \/ V))
((Sym (f,( the Sorts of A \/ V))) -tree p9) @ C is Element of the Sorts of A . (the_sort_of ((Sym (f,( the Sorts of A \/ V))) -tree p9))
the_sort_of ((Sym (f,( the Sorts of A \/ V))) -tree p9) is Element of the carrier of S
the Sorts of A . (the_sort_of ((Sym (f,( the Sorts of A \/ V))) -tree p9)) is non empty set
Den (f,A) is Relation-like Args (f,A) -defined Result (f,A) -valued Function-like V25( Args (f,A), Result (f,A)) Element of bool [:(Args (f,A)),(Result (f,A)):]
Args (f,A) is non empty Element of proj2 ( the Sorts of A #)
the Sorts of A # is Relation-like the carrier of S * -defined non empty Function-like total set
proj2 ( the Sorts of A #) is non empty set
the Arity of S * ( the Sorts of A #) is Relation-like the carrier' of S -defined non empty Function-like total set
( the Arity of S * ( the Sorts of A #)) . f is set
Result (f,A) is non empty Element of proj2 the Sorts of A
proj2 the Sorts of A is non empty V141() set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of A is Relation-like non-empty non empty-yielding the carrier' of S -defined non empty Function-like total set
( the ResultSort of S * the Sorts of A) . f is non empty set
[:(Args (f,A)),(Result (f,A)):] is Relation-like set
bool [:(Args (f,A)),(Result (f,A)):] is set
the Charact of A is Relation-like the carrier' of S -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of A #), the ResultSort of S * the Sorts of A
the Charact of A . f is Relation-like Function-like set
(Den (f,A)) . vp is set
proj1 (Following (G,s)) is non empty set
g * (Following (G,s)) is Relation-like NAT -defined Function-like finite countable set
proj1 (g * (Following (G,s))) is finite countable set
z is set
i is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
vp . i is set
g . i is Relation-like Function-like set
(Following (G,s)) . (g . i) is set
vp . z is set
(g * (Following (G,s))) . z is set
(the_arity_of t9) * (Following (G,s)) is Relation-like NAT -defined Function-like finite countable set
Args (t9,(S,V,X,A)) is non empty Element of proj2 ( the Sorts of (S,V,X,A) #)
the Sorts of (S,V,X,A) # is Relation-like the carrier of (S,V,X) * -defined non empty Function-like total set
proj2 ( the Sorts of (S,V,X,A) #) is non empty set
the Arity of (S,V,X) * ( the Sorts of (S,V,X,A) #) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total set
( the Arity of (S,V,X) * ( the Sorts of (S,V,X,A) #)) . t9 is set
Result (t9,(S,V,X,A)) is non empty Element of proj2 the Sorts of (S,V,X,A)
proj2 the Sorts of (S,V,X,A) is non empty V141() set
the ResultSort of (S,V,X) * the Sorts of (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier' of (S,V,X) -defined non empty Function-like total set
( the ResultSort of (S,V,X) * the Sorts of (S,V,X,A)) . t9 is non empty set
Den (t9,(S,V,X,A)) is Relation-like Args (t9,(S,V,X,A)) -defined Result (t9,(S,V,X,A)) -valued Function-like V25( Args (t9,(S,V,X,A)), Result (t9,(S,V,X,A))) Element of bool [:(Args (t9,(S,V,X,A))),(Result (t9,(S,V,X,A))):]
[:(Args (t9,(S,V,X,A))),(Result (t9,(S,V,X,A))):] is Relation-like set
bool [:(Args (t9,(S,V,X,A))),(Result (t9,(S,V,X,A))):] is set
the Charact of (S,V,X,A) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,V,X) * ( the Sorts of (S,V,X,A) #), the ResultSort of (S,V,X) * the Sorts of (S,V,X,A)
the Charact of (S,V,X,A) . t9 is Relation-like Function-like set
(Following (Following (G,s))) . c₁₄ is set
c₁₄ @ C is Element of the Sorts of A . (the_sort_of c₁₄)
the_sort_of c₁₄ is Element of the carrier of S
the Sorts of A . (the_sort_of c₁₄) is non empty set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
the carrier of A is non empty set
the carrier of S is non empty set
the carrier' of A is set
the carrier' of S is set
V is Relation-like Function-like set
X is Relation-like Function-like set
V .: the carrier of S is set
X .: the carrier' of S is set
V " is Relation-like Function-like set
X " is Relation-like Function-like set
proj1 (V ") is set
proj2 V is set
proj1 V is set
V .: (proj1 V) is set
proj1 (X ") is set
proj2 X is set
proj1 X is set
X .: (proj1 X) is set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
the carrier of A is non empty set
the carrier' of A is set
V is Relation-like Function-like set
X is Relation-like Function-like set
proj2 V is set
proj2 X is set
V " is Relation-like Function-like set
X " is Relation-like Function-like set
proj1 (V ") is set
proj1 (X ") is set
S is non empty V68() V153() ManySortedSign
the carrier of S is non empty set
id the carrier of S is Relation-like the carrier of S -defined the carrier of S -valued non empty Function-like one-to-one total Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is Relation-like set
bool [: the carrier of S, the carrier of S:] is set
the carrier' of S is set
id the carrier' of S is Relation-like the carrier' of S -defined the carrier' of S -valued Function-like one-to-one total Element of bool [: the carrier' of S, the carrier' of S:]
[: the carrier' of S, the carrier' of S:] is Relation-like set
bool [: the carrier' of S, the carrier' of S:] is set
(id the carrier of S) " is Relation-like Function-like one-to-one set
(id the carrier' of S) " is Relation-like Function-like one-to-one set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
V is Relation-like Function-like set
X is Relation-like Function-like set
V " is Relation-like Function-like set
X " is Relation-like Function-like set
(V ") " is Relation-like Function-like set
(X ") " is Relation-like Function-like set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
V is non empty V68() V153() ManySortedSign
X is Relation-like Function-like set
G is Relation-like Function-like set
C is Relation-like Function-like set
f is Relation-like Function-like set
X * C is Relation-like Function-like set
G * f is Relation-like Function-like set
X " is Relation-like Function-like set
G " is Relation-like Function-like set
C " is Relation-like Function-like set
f " is Relation-like Function-like set
(X * C) " is Relation-like Function-like set
(G * f) " is Relation-like Function-like set
(C ") * (X ") is Relation-like Function-like set
(f ") * (G ") is Relation-like Function-like set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
InputVertices S is Element of bool the carrier of S
the carrier of S is non empty set
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K507( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
the carrier of S \ K507( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
InputVertices A is Element of bool the carrier of A
the carrier of A is non empty set
bool the carrier of A is set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
the carrier' of A is set
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
K507( the carrier of A, the ResultSort of A) is Element of bool the carrier of A
the carrier of A \ K507( the carrier of A, the ResultSort of A) is Element of bool the carrier of A
InnerVertices S is Element of bool the carrier of S
InnerVertices A is Element of bool the carrier of A
V is Relation-like Function-like set
X is Relation-like Function-like set
V .: (InputVertices S) is set
V .: (InnerVertices S) is set
proj2 X is set
proj1 the ResultSort of A is set
proj2 the ResultSort of S is set
V .: (proj2 the ResultSort of S) is set
the ResultSort of S * V is Relation-like the carrier' of S -defined Function-like set
proj2 ( the ResultSort of S * V) is set
X * the ResultSort of A is Relation-like the carrier of A -valued Function-like set
proj2 (X * the ResultSort of A) is set
proj2 the ResultSort of A is set
V .: the carrier of S is set
(V .: the carrier of S) \ (V .: (proj2 the ResultSort of S)) is Element of bool (V .: the carrier of S)
bool (V .: the carrier of S) is set
V is non empty V68() V153() ManySortedSign
the carrier of V is non empty set
id the carrier of V is Relation-like the carrier of V -defined the carrier of V -valued non empty Function-like one-to-one total Element of bool [: the carrier of V, the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like set
bool [: the carrier of V, the carrier of V:] is set
the carrier' of V is set
id the carrier' of V is Relation-like the carrier' of V -defined the carrier' of V -valued Function-like one-to-one total Element of bool [: the carrier' of V, the carrier' of V:]
[: the carrier' of V, the carrier' of V:] is Relation-like set
bool [: the carrier' of V, the carrier' of V:] is set
V is non empty V68() V153() ManySortedSign
X is non empty V68() V153() ManySortedSign
G is Relation-like Function-like one-to-one set
C is Relation-like Function-like one-to-one set
G " is Relation-like Function-like one-to-one set
C " is Relation-like Function-like one-to-one set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
V is non empty V68() V153() ManySortedSign
X is Relation-like Function-like one-to-one set
G is Relation-like Function-like one-to-one set
C is Relation-like Function-like one-to-one set
f is Relation-like Function-like one-to-one set
X * C is Relation-like Function-like one-to-one set
G * f is Relation-like Function-like one-to-one set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
the carrier of S is non empty set
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
proj1 V is set
proj1 X is set
the carrier' of S is set
proj2 V is set
proj2 X is set
the carrier' of A is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * V is Relation-like the carrier' of S -defined Function-like set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
X * the ResultSort of A is Relation-like the carrier of A -valued Function-like set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Arity of A is Relation-like the carrier' of A -defined the carrier of A * -valued Function-like V25( the carrier' of A, the carrier of A * ) Function-yielding V54() Element of bool [: the carrier' of A,( the carrier of A *):]
the carrier of A * is non empty functional FinSequence-membered M8( the carrier of A)
[: the carrier' of A,( the carrier of A *):] is Relation-like set
bool [: the carrier' of A,( the carrier of A *):] is set
G is Element of the carrier of S
V . G is set
G is Element of the carrier of S
V . G is set
S is non empty non void V68() V153() ManySortedSign
A is non empty non void V68() V153() ManySortedSign
the carrier' of S is non empty set
the carrier' of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
proj1 V is set
the carrier of S is non empty set
proj1 X is set
proj2 V is set
the carrier of A is non empty set
proj2 X is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * V is Relation-like the carrier' of S -defined Function-like set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
X * the ResultSort of A is Relation-like the carrier of A -valued Function-like set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Arity of A is Relation-like the carrier' of A -defined the carrier of A * -valued Function-like V25( the carrier' of A, the carrier of A * ) Function-yielding V54() Element of bool [: the carrier' of A,( the carrier of A *):]
the carrier of A * is non empty functional FinSequence-membered M8( the carrier of A)
[: the carrier' of A,( the carrier of A *):] is Relation-like set
bool [: the carrier' of A,( the carrier of A *):] is set
G is Element of the carrier' of S
X . G is set
G is Element of the carrier' of S
X . G is set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
InnerVertices S is Element of bool the carrier of S
the carrier of S is non empty set
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K507( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
InnerVertices A is Element of bool the carrier of A
the carrier of A is non empty set
bool the carrier of A is set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
the carrier' of A is set
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
K507( the carrier of A, the ResultSort of A) is Element of bool the carrier of A
V is Relation-like Function-like set
X is Relation-like Function-like set
V .: (InnerVertices S) is set
the ResultSort of S * V is Relation-like the carrier' of S -defined Function-like set
X * the ResultSort of A is Relation-like the carrier of A -valued Function-like set
proj2 (X * the ResultSort of A) is set
S is non empty non void V68() Circuit-like V153() ManySortedSign
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
InnerVertices S is Element of bool the carrier of S
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K507( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is Element of the carrier of S
V . G is set
action_at G is Element of the carrier' of S
X . (action_at G) is set
C is Element of the carrier of A
action_at C is Element of the carrier' of A
the carrier' of A is non empty set
proj1 X is set
proj1 V is set
proj1 the ResultSort of S is set
V .: (InnerVertices S) is set
InnerVertices A is Element of bool the carrier of A
bool the carrier of A is set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
K507( the carrier of A, the ResultSort of A) is Element of bool the carrier of A
f is Element of the carrier' of A
the_result_sort_of f is Element of the carrier of A
the ResultSort of A . f is Element of the carrier of A
X * the ResultSort of A is Relation-like the carrier of A -valued Function-like set
(X * the ResultSort of A) . (action_at G) is set
the ResultSort of S * V is Relation-like the carrier' of S -defined Function-like set
( the ResultSort of S * V) . (action_at G) is set
the_result_sort_of (action_at G) is Element of the carrier of S
the ResultSort of S . (action_at G) is Element of the carrier of S
V . (the_result_sort_of (action_at G)) is set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
S is non empty V68() V153() ManySortedSign
the carrier of S is non empty set
id the carrier of S is Relation-like the carrier of S -defined the carrier of S -valued non empty Function-like one-to-one total Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is Relation-like set
bool [: the carrier of S, the carrier of S:] is set
the carrier' of S is set
id the carrier' of S is Relation-like the carrier' of S -defined the carrier' of S -valued Function-like one-to-one total Element of bool [: the carrier' of S, the carrier' of S:]
[: the carrier' of S, the carrier' of S:] is Relation-like set
bool [: the carrier' of S, the carrier' of S:] is set
A is non-empty MSAlgebra over S
the Sorts of A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
(id the carrier of S) * the Sorts of A is Relation-like non-empty the carrier of S -defined Function-like set
the Charact of A is Relation-like the carrier' of S -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of A #), the ResultSort of S * the Sorts of A
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of A # is Relation-like the carrier of S * -defined non empty Function-like total set
the Arity of S * ( the Sorts of A #) is Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of A is Relation-like non-empty the carrier' of S -defined Function-like total set
(id the carrier' of S) * the Charact of A is Relation-like the carrier' of S -defined Function-like Function-yielding V54() set
proj1 the Sorts of A is non empty set
proj1 the Charact of A is set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
V is non empty V68() V153() ManySortedSign
X is Relation-like Function-like set
G is Relation-like Function-like set
C is Relation-like Function-like set
f is Relation-like Function-like set
X * C is Relation-like Function-like set
G * f is Relation-like Function-like set
g is non-empty MSAlgebra over S
f is non-empty MSAlgebra over A
t is non-empty MSAlgebra over V
the Sorts of g is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the carrier of S is non empty set
the Sorts of f is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
the carrier of A is non empty set
X * the Sorts of f is Relation-like non-empty Function-like set
the Charact of g is Relation-like the carrier' of S -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of g #), the ResultSort of S * the Sorts of g
the carrier' of S is set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of g # is Relation-like the carrier of S * -defined non empty Function-like total set
the Arity of S * ( the Sorts of g #) is Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of g is Relation-like non-empty the carrier' of S -defined Function-like total set
the Charact of f is Relation-like the carrier' of A -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of A * ( the Sorts of f #), the ResultSort of A * the Sorts of f
the carrier' of A is set
the Arity of A is Relation-like the carrier' of A -defined the carrier of A * -valued Function-like V25( the carrier' of A, the carrier of A * ) Function-yielding V54() Element of bool [: the carrier' of A,( the carrier of A *):]
the carrier of A * is non empty functional FinSequence-membered M8( the carrier of A)
[: the carrier' of A,( the carrier of A *):] is Relation-like set
bool [: the carrier' of A,( the carrier of A *):] is set
the Sorts of f # is Relation-like the carrier of A * -defined non empty Function-like total set
the Arity of A * ( the Sorts of f #) is Relation-like the carrier' of A -defined Function-like total set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
the ResultSort of A * the Sorts of f is Relation-like non-empty the carrier' of A -defined Function-like total set
G * the Charact of f is Relation-like Function-like Function-yielding V54() set
the Sorts of t is Relation-like non-empty non empty-yielding the carrier of V -defined non empty Function-like total set
the carrier of V is non empty set
C * the Sorts of t is Relation-like non-empty Function-like set
the Charact of t is Relation-like the carrier' of V -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of V * ( the Sorts of t #), the ResultSort of V * the Sorts of t
the carrier' of V is set
the Arity of V is Relation-like the carrier' of V -defined the carrier of V * -valued Function-like V25( the carrier' of V, the carrier of V * ) Function-yielding V54() Element of bool [: the carrier' of V,( the carrier of V *):]
the carrier of V * is non empty functional FinSequence-membered M8( the carrier of V)
[: the carrier' of V,( the carrier of V *):] is Relation-like set
bool [: the carrier' of V,( the carrier of V *):] is set
the Sorts of t # is Relation-like the carrier of V * -defined non empty Function-like total set
the Arity of V * ( the Sorts of t #) is Relation-like the carrier' of V -defined Function-like total set
the ResultSort of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
[: the carrier' of V, the carrier of V:] is Relation-like set
bool [: the carrier' of V, the carrier of V:] is set
the ResultSort of V * the Sorts of t is Relation-like non-empty the carrier' of V -defined Function-like total set
f * the Charact of t is Relation-like Function-like Function-yielding V54() set
(X * C) * the Sorts of t is Relation-like non-empty Function-like set
(G * f) * the Charact of t is Relation-like Function-like Function-yielding V54() set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty MSAlgebra over S
C is non-empty MSAlgebra over A
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the carrier of S is non empty set
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
the carrier of A is non empty set
V * the Sorts of C is Relation-like non-empty Function-like set
the Charact of G is Relation-like the carrier' of S -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of G #), the ResultSort of S * the Sorts of G
the carrier' of S is set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of G # is Relation-like the carrier of S * -defined non empty Function-like total set
the Arity of S * ( the Sorts of G #) is Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of G is Relation-like non-empty the carrier' of S -defined Function-like total set
the Charact of C is Relation-like the carrier' of A -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of A * ( the Sorts of C #), the ResultSort of A * the Sorts of C
the carrier' of A is set
the Arity of A is Relation-like the carrier' of A -defined the carrier of A * -valued Function-like V25( the carrier' of A, the carrier of A * ) Function-yielding V54() Element of bool [: the carrier' of A,( the carrier of A *):]
the carrier of A * is non empty functional FinSequence-membered M8( the carrier of A)
[: the carrier' of A,( the carrier of A *):] is Relation-like set
bool [: the carrier' of A,( the carrier of A *):] is set
the Sorts of C # is Relation-like the carrier of A * -defined non empty Function-like total set
the Arity of A * ( the Sorts of C #) is Relation-like the carrier' of A -defined Function-like total set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
the ResultSort of A * the Sorts of C is Relation-like non-empty the carrier' of A -defined Function-like total set
X * the Charact of C is Relation-like Function-like Function-yielding V54() set
V " is Relation-like Function-like set
X " is Relation-like Function-like set
(V ") * the Sorts of G is Relation-like non-empty Function-like set
(X ") * the Charact of G is Relation-like Function-like Function-yielding V54() set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty MSAlgebra over S
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the carrier of S is non empty set
the Charact of G is Relation-like the carrier' of S -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of G #), the ResultSort of S * the Sorts of G
the carrier' of S is set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of G # is Relation-like the carrier of S * -defined non empty Function-like total set
the Arity of S * ( the Sorts of G #) is Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of G is Relation-like non-empty the carrier' of S -defined Function-like total set
C is non-empty MSAlgebra over A
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
the carrier of A is non empty set
V * the Sorts of C is Relation-like non-empty Function-like set
the Charact of C is Relation-like the carrier' of A -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of A * ( the Sorts of C #), the ResultSort of A * the Sorts of C
the carrier' of A is set
the Arity of A is Relation-like the carrier' of A -defined the carrier of A * -valued Function-like V25( the carrier' of A, the carrier of A * ) Function-yielding V54() Element of bool [: the carrier' of A,( the carrier of A *):]
the carrier of A * is non empty functional FinSequence-membered M8( the carrier of A)
[: the carrier' of A,( the carrier of A *):] is Relation-like set
bool [: the carrier' of A,( the carrier of A *):] is set
the Sorts of C # is Relation-like the carrier of A * -defined non empty Function-like total set
the Arity of A * ( the Sorts of C #) is Relation-like the carrier' of A -defined Function-like total set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
the ResultSort of A * the Sorts of C is Relation-like non-empty the carrier' of A -defined Function-like total set
X * the Charact of C is Relation-like Function-like Function-yielding V54() set
V " is Relation-like Function-like set
X " is Relation-like Function-like set
(V ") * the Sorts of G is Relation-like non-empty Function-like set
(X ") * the Charact of G is Relation-like Function-like Function-yielding V54() set
proj1 (V ") is set
proj2 V is set
(V ") * V is Relation-like Function-like set
id the carrier of A is Relation-like the carrier of A -defined the carrier of A -valued non empty Function-like one-to-one total Element of bool [: the carrier of A, the carrier of A:]
[: the carrier of A, the carrier of A:] is Relation-like set
bool [: the carrier of A, the carrier of A:] is set
proj1 the Sorts of C is non empty set
id (proj1 the Sorts of C) is Relation-like proj1 the Sorts of C -defined proj1 the Sorts of C -valued non empty Function-like one-to-one total Element of bool [:(proj1 the Sorts of C),(proj1 the Sorts of C):]
[:(proj1 the Sorts of C),(proj1 the Sorts of C):] is Relation-like set
bool [:(proj1 the Sorts of C),(proj1 the Sorts of C):] is set
((V ") * V) * the Sorts of C is Relation-like non-empty Function-like set
proj1 (X ") is set
proj2 X is set
(X ") * X is Relation-like Function-like set
id the carrier' of A is Relation-like the carrier' of A -defined the carrier' of A -valued Function-like one-to-one total Element of bool [: the carrier' of A, the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is Relation-like set
bool [: the carrier' of A, the carrier' of A:] is set
proj1 the Charact of C is set
id (proj1 the Charact of C) is Relation-like proj1 the Charact of C -defined proj1 the Charact of C -valued Function-like one-to-one total Element of bool [:(proj1 the Charact of C),(proj1 the Charact of C):]
[:(proj1 the Charact of C),(proj1 the Charact of C):] is Relation-like set
bool [:(proj1 the Charact of C),(proj1 the Charact of C):] is set
((X ") * X) * the Charact of C is Relation-like Function-like Function-yielding V54() set
S is non empty V68() V153() ManySortedSign
the carrier of S is non empty set
id the carrier of S is Relation-like the carrier of S -defined the carrier of S -valued non empty Function-like one-to-one total Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is Relation-like set
bool [: the carrier of S, the carrier of S:] is set
the carrier' of S is set
id the carrier' of S is Relation-like the carrier' of S -defined the carrier' of S -valued Function-like one-to-one total Element of bool [: the carrier' of S, the carrier' of S:]
[: the carrier' of S, the carrier' of S:] is Relation-like set
bool [: the carrier' of S, the carrier' of S:] is set
A is non-empty MSAlgebra over S
(id the carrier of S) " is Relation-like Function-like one-to-one set
(id the carrier' of S) " is Relation-like Function-like one-to-one set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
V is Relation-like Function-like set
X is Relation-like Function-like set
V " is Relation-like Function-like set
X " is Relation-like Function-like set
G is non-empty MSAlgebra over S
C is non-empty MSAlgebra over A
(V ") " is Relation-like Function-like set
(X ") " is Relation-like Function-like set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
V is non empty V68() V153() ManySortedSign
X is Relation-like Function-like set
G is Relation-like Function-like set
C is Relation-like Function-like set
f is Relation-like Function-like set
X * C is Relation-like Function-like set
G * f is Relation-like Function-like set
g is non-empty MSAlgebra over S
f is non-empty MSAlgebra over A
t is non-empty MSAlgebra over V
X " is Relation-like Function-like set
G " is Relation-like Function-like set
C " is Relation-like Function-like set
f " is Relation-like Function-like set
(X * C) " is Relation-like Function-like set
(G * f) " is Relation-like Function-like set
(C ") * (X ") is Relation-like Function-like set
(f ") * (G ") is Relation-like Function-like set
S is non empty V68() V153() ManySortedSign
A is non empty V68() V153() ManySortedSign
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
the carrier' of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
the carrier' of A is non empty set
V is Relation-like Function-like set
proj1 V is set
proj2 V is set
X is Relation-like Function-like set
proj1 X is set
proj2 X is set
G is non-empty finite-yielding MSAlgebra over S
C is non-empty finite-yielding MSAlgebra over A
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * V is Relation-like the carrier' of S -defined Function-like set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
X * the ResultSort of A is Relation-like the carrier of A -valued Function-like set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Arity of A is Relation-like the carrier' of A -defined the carrier of A * -valued Function-like V25( the carrier' of A, the carrier of A * ) Function-yielding V54() Element of bool [: the carrier' of A,( the carrier of A *):]
the carrier of A * is non empty functional FinSequence-membered M8( the carrier of A)
[: the carrier' of A,( the carrier of A *):] is Relation-like set
bool [: the carrier' of A,( the carrier of A *):] is set
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
V * the Sorts of C is Relation-like non-empty Function-like set
the Charact of G is Relation-like the carrier' of S -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of G #), the ResultSort of S * the Sorts of G
the Sorts of G # is Relation-like the carrier of S * -defined non empty Function-like total set
the Arity of S * ( the Sorts of G #) is Relation-like the carrier' of S -defined non empty Function-like total set
the ResultSort of S * the Sorts of G is Relation-like non-empty non empty-yielding the carrier' of S -defined non empty Function-like total set
the Charact of C is Relation-like the carrier' of A -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of A * ( the Sorts of C #), the ResultSort of A * the Sorts of C
the Sorts of C # is Relation-like the carrier of A * -defined non empty Function-like total set
the Arity of A * ( the Sorts of C #) is Relation-like the carrier' of A -defined non empty Function-like total set
the ResultSort of A * the Sorts of C is Relation-like non-empty non empty-yielding the carrier' of A -defined non empty Function-like total set
X * the Charact of C is Relation-like Function-like Function-yielding V54() set
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier' of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier' of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
C is non-empty finite-yielding MSAlgebra over A
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
the carrier of S is non empty set
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
the carrier of A is non empty set
V * the Sorts of C is Relation-like non-empty Function-like set
the Charact of G is Relation-like the carrier' of S -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of G #), the ResultSort of S * the Sorts of G
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of G # is Relation-like the carrier of S * -defined non empty Function-like total set
the Arity of S * ( the Sorts of G #) is Relation-like the carrier' of S -defined non empty Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of G is Relation-like non-empty non empty-yielding the carrier' of S -defined non empty Function-like total set
the Charact of C is Relation-like the carrier' of A -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of A * ( the Sorts of C #), the ResultSort of A * the Sorts of C
the Arity of A is Relation-like the carrier' of A -defined the carrier of A * -valued Function-like V25( the carrier' of A, the carrier of A * ) Function-yielding V54() Element of bool [: the carrier' of A,( the carrier of A *):]
the carrier of A * is non empty functional FinSequence-membered M8( the carrier of A)
[: the carrier' of A,( the carrier of A *):] is Relation-like set
bool [: the carrier' of A,( the carrier of A *):] is set
the Sorts of C # is Relation-like the carrier of A * -defined non empty Function-like total set
the Arity of A * ( the Sorts of C #) is Relation-like the carrier' of A -defined non empty Function-like total set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
the ResultSort of A * the Sorts of C is Relation-like non-empty non empty-yielding the carrier' of A -defined non empty Function-like total set
X * the Charact of C is Relation-like Function-like Function-yielding V54() set
f is Element of the carrier' of S
X . f is set
Args (f,G) is non empty Element of proj2 ( the Sorts of G #)
proj2 ( the Sorts of G #) is non empty set
( the Arity of S * ( the Sorts of G #)) . f is set
Result (f,G) is non empty Element of proj2 the Sorts of G
proj2 the Sorts of G is non empty V141() set
( the ResultSort of S * the Sorts of G) . f is non empty set
Den (f,G) is Relation-like Args (f,G) -defined Result (f,G) -valued Function-like V25( Args (f,G), Result (f,G)) Element of bool [:(Args (f,G)),(Result (f,G)):]
[:(Args (f,G)),(Result (f,G)):] is Relation-like set
bool [:(Args (f,G)),(Result (f,G)):] is set
the Charact of G . f is Relation-like Function-like set
g is Element of the carrier' of A
Args (g,C) is non empty Element of proj2 ( the Sorts of C #)
proj2 ( the Sorts of C #) is non empty set
( the Arity of A * ( the Sorts of C #)) . g is set
Result (g,C) is non empty Element of proj2 the Sorts of C
proj2 the Sorts of C is non empty V141() set
( the ResultSort of A * the Sorts of C) . g is non empty set
Den (g,C) is Relation-like Args (g,C) -defined Result (g,C) -valued Function-like V25( Args (g,C), Result (g,C)) Element of bool [:(Args (g,C)),(Result (g,C)):]
[:(Args (g,C)),(Result (g,C)):] is Relation-like set
bool [:(Args (g,C)),(Result (g,C)):] is set
the Charact of C . g is Relation-like Function-like set
proj1 X is set
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier' of S is non empty set
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier' of A is non empty set
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over A
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
V * the Sorts of C is Relation-like non-empty Function-like set
the Charact of G is Relation-like the carrier' of S -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of G #), the ResultSort of S * the Sorts of G
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of G # is Relation-like the carrier of S * -defined non empty Function-like total set
the Arity of S * ( the Sorts of G #) is Relation-like the carrier' of S -defined non empty Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of G is Relation-like non-empty non empty-yielding the carrier' of S -defined non empty Function-like total set
the Charact of C is Relation-like the carrier' of A -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of A * ( the Sorts of C #), the ResultSort of A * the Sorts of C
the Arity of A is Relation-like the carrier' of A -defined the carrier of A * -valued Function-like V25( the carrier' of A, the carrier of A * ) Function-yielding V54() Element of bool [: the carrier' of A,( the carrier of A *):]
the carrier of A * is non empty functional FinSequence-membered M8( the carrier of A)
[: the carrier' of A,( the carrier of A *):] is Relation-like set
bool [: the carrier' of A,( the carrier of A *):] is set
the Sorts of C # is Relation-like the carrier of A * -defined non empty Function-like total set
the Arity of A * ( the Sorts of C #) is Relation-like the carrier' of A -defined non empty Function-like total set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
the ResultSort of A * the Sorts of C is Relation-like non-empty non empty-yielding the carrier' of A -defined non empty Function-like total set
X * the Charact of C is Relation-like Function-like Function-yielding V54() set
f is Element of the carrier' of S
X . f is set
g is Element of the carrier' of A
f is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
f depends_on_in f is Element of Args (f,G)
Args (f,G) is non empty Element of proj2 ( the Sorts of G #)
proj2 ( the Sorts of G #) is non empty set
( the Arity of S * ( the Sorts of G #)) . f is set
t is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * t is Relation-like Function-like set
g depends_on_in t is Element of Args (g,C)
Args (g,C) is non empty Element of proj2 ( the Sorts of C #)
proj2 ( the Sorts of C #) is non empty set
( the Arity of A * ( the Sorts of C #)) . g is set
the_arity_of g is Relation-like NAT -defined the carrier of A -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of A *
the Arity of A . g is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of A *
(the_arity_of g) * t is Relation-like NAT -defined Function-like finite countable set
the_arity_of f is Relation-like NAT -defined the carrier of S -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of S *
the Arity of S . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable Element of the carrier of S *
(the_arity_of f) * V is Relation-like NAT -defined Function-like finite countable set
((the_arity_of f) * V) * t is Relation-like NAT -defined Function-like finite countable set
(the_arity_of f) * f is Relation-like NAT -defined Function-like finite countable set
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over A
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
V * the Sorts of C is Relation-like non-empty Function-like set
the Charact of G is Relation-like the carrier' of S -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of G #), the ResultSort of S * the Sorts of G
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Sorts of G # is Relation-like the carrier of S * -defined non empty Function-like total set
the Arity of S * ( the Sorts of G #) is Relation-like the carrier' of S -defined non empty Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
the ResultSort of S * the Sorts of G is Relation-like non-empty non empty-yielding the carrier' of S -defined non empty Function-like total set
the Charact of C is Relation-like the carrier' of A -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of A * ( the Sorts of C #), the ResultSort of A * the Sorts of C
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 V25( the carrier' of A, the carrier of A * ) Function-yielding V54() Element of bool [: the carrier' of A,( the carrier of A *):]
the carrier of A * is non empty functional FinSequence-membered M8( the carrier of A)
[: the carrier' of A,( the carrier of A *):] is Relation-like set
bool [: the carrier' of A,( the carrier of A *):] is set
the Sorts of C # is Relation-like the carrier of A * -defined non empty Function-like total set
the Arity of A * ( the Sorts of C #) is Relation-like the carrier' of A -defined non empty Function-like total set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
the ResultSort of A * the Sorts of C is Relation-like non-empty non empty-yielding the carrier' of A -defined non empty Function-like total set
X * the Charact of C is Relation-like Function-like Function-yielding V54() set
f is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * f is Relation-like Function-like set
proj1 the Sorts of C is non empty set
proj1 the Sorts of G is non empty set
proj1 f is non empty set
proj2 V is set
proj1 V is set
proj1 (V * f) is set
t is set
V . t is set
(V * f) . t is set
f . (V . t) is set
the Sorts of C . (V . t) is set
the Sorts of G . t is set
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
InputVertices A is Element of bool the carrier of A
bool the carrier of A is set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
the carrier' of A is non empty set
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
K507( the carrier of A, the ResultSort of A) is Element of bool the carrier of A
the carrier of A \ K507( the carrier of A, the ResultSort of A) is Element of bool the carrier of A
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over A
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over S
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
f is Relation-like the carrier of S -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * f is Relation-like Function-like set
Following f is Relation-like the carrier of S -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * (Following f) is Relation-like Function-like set
g is Relation-like the carrier of A -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
Following g is Relation-like the carrier of A -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
proj1 V is set
f is Relation-like the carrier of A -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
t is Element of the carrier of A
f . t is set
V . t is set
(Following f) . (V . t) is set
Following (f,1) is Relation-like the carrier of S -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
f . (V . t) is set
g . t is set
InnerVertices A is Element of bool the carrier of A
V .: (InnerVertices A) is set
InnerVertices S is Element of bool the carrier of S
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K507( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
t9 is Element of the carrier of S
action_at t9 is Element of the carrier' of S
action_at t is Element of the carrier' of A
X . (action_at t) is set
Args ((action_at t9),C) is non empty Element of proj2 ( the Sorts of C #)
the Sorts of C # is Relation-like the carrier of S * -defined non empty Function-like total set
the carrier of S * is non empty functional FinSequence-membered M8( the carrier of S)
proj2 ( the Sorts of C #) is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V25( the carrier' of S, the carrier of S * ) Function-yielding V54() Element of bool [: the carrier' of S,( the carrier of S *):]
[: the carrier' of S,( the carrier of S *):] is Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is set
the Arity of S * ( the Sorts of C #) is Relation-like the carrier' of S -defined non empty Function-like total set
( the Arity of S * ( the Sorts of C #)) . (action_at t9) is set
Result ((action_at t9),C) is non empty Element of proj2 the Sorts of C
proj2 the Sorts of C is non empty V141() set
the ResultSort of S * the Sorts of C is Relation-like non-empty non empty-yielding the carrier' of S -defined non empty Function-like total set
( the ResultSort of S * the Sorts of C) . (action_at t9) is non empty set
Den ((action_at t9),C) is Relation-like Args ((action_at t9),C) -defined Result ((action_at t9),C) -valued Function-like V25( Args ((action_at t9),C), Result ((action_at t9),C)) Element of bool [:(Args ((action_at t9),C)),(Result ((action_at t9),C)):]
[:(Args ((action_at t9),C)),(Result ((action_at t9),C)):] is Relation-like set
bool [:(Args ((action_at t9),C)),(Result ((action_at t9),C)):] is set
the Charact of C is Relation-like the carrier' of S -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of S * ( the Sorts of C #), the ResultSort of S * the Sorts of C
the Charact of C . (action_at t9) is Relation-like Function-like set
(action_at t9) depends_on_in f is Element of Args ((action_at t9),C)
(Den ((action_at t9),C)) . ((action_at t9) depends_on_in f) is Element of Result ((action_at t9),C)
Den ((action_at t),G) is Relation-like Args ((action_at t),G) -defined Result ((action_at t),G) -valued Function-like V25( Args ((action_at t),G), Result ((action_at t),G)) Element of bool [:(Args ((action_at t),G)),(Result ((action_at t),G)):]
Args ((action_at t),G) is non empty Element of proj2 ( the Sorts of G #)
the Sorts of G # is Relation-like the carrier of A * -defined non empty Function-like total set
the carrier of A * is non empty functional FinSequence-membered M8( the carrier of A)
proj2 ( the Sorts of G #) is non empty set
the Arity of A is Relation-like the carrier' of A -defined the carrier of A * -valued Function-like V25( the carrier' of A, the carrier of A * ) Function-yielding V54() Element of bool [: the carrier' of A,( the carrier of A *):]
[: the carrier' of A,( the carrier of A *):] is Relation-like set
bool [: the carrier' of A,( the carrier of A *):] is set
the Arity of A * ( the Sorts of G #) is Relation-like the carrier' of A -defined non empty Function-like total set
( the Arity of A * ( the Sorts of G #)) . (action_at t) is set
Result ((action_at t),G) is non empty Element of proj2 the Sorts of G
proj2 the Sorts of G is non empty V141() set
the ResultSort of A * the Sorts of G is Relation-like non-empty non empty-yielding the carrier' of A -defined non empty Function-like total set
( the ResultSort of A * the Sorts of G) . (action_at t) is non empty set
[:(Args ((action_at t),G)),(Result ((action_at t),G)):] is Relation-like set
bool [:(Args ((action_at t),G)),(Result ((action_at t),G)):] is set
the Charact of G is Relation-like the carrier' of A -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of A * ( the Sorts of G #), the ResultSort of A * the Sorts of G
the Charact of G . (action_at t) is Relation-like Function-like set
(Den ((action_at t),G)) . ((action_at t9) depends_on_in f) is set
(action_at t) depends_on_in g is Element of Args ((action_at t),G)
(Den ((action_at t),G)) . ((action_at t) depends_on_in g) is Element of Result ((action_at t),G)
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over A
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
InputVertices S is Element of bool the carrier of S
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K507( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
the carrier of S \ K507( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
V .: (InputVertices S) is set
InputVertices A is Element of bool the carrier of A
bool the carrier of A is set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
the carrier' of A is non empty set
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
K507( the carrier of A, the ResultSort of A) is Element of bool the carrier of A
the carrier of A \ K507( the carrier of A, the ResultSort of A) is Element of bool the carrier of A
f is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * f is Relation-like Function-like set
Following f is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * (Following f) is Relation-like Function-like set
g is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
Following g is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
proj1 V is set
f is Element of the carrier of S
V . f is set
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over A
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
f is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * f is Relation-like Function-like set
g is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
Following (g,0) is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
Following (f,0) is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * (Following (f,0)) is Relation-like Function-like set
f is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (g,f) is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
Following (f,f) is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * (Following (f,f)) is Relation-like Function-like set
Following (Following (g,f)) is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
Following (Following (f,f)) is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * (Following (Following (f,f))) is Relation-like Function-like set
f + 1 is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (g,(f + 1)) is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
Following (f,(f + 1)) is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * (Following (f,(f + 1))) is Relation-like Function-like set
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over A
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
f is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * f is Relation-like Function-like set
g is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
Following f is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
Following g is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over A
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
f is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * f is Relation-like Function-like set
g is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
f is Element of the carrier of S
V . f is set
proj1 V is set
g . f is set
t9 is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
Following (f,t9) is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
(Following (f,t9)) . (V . f) is set
f . (V . f) is set
Following (g,t9) is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
V * (Following (f,t9)) is Relation-like Function-like set
(Following (g,t9)) . f is set
f . (V . f) is set
t9 is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
Following (g,t9) is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
(Following (g,t9)) . f is set
g . f is set
Following (f,t9) is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * (Following (f,t9)) is Relation-like Function-like set
t is Element of the carrier of A
(Following (f,t9)) . t is set
f . t is set
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over A
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
V " is Relation-like Function-like set
X " is Relation-like Function-like set
f is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * f is Relation-like Function-like set
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
V is Relation-like Function-like set
V " is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over A
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
X " is Relation-like Function-like set
f is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
(V ") * f is Relation-like Function-like set
g is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * g is Relation-like Function-like set
proj1 V is set
proj1 f is non empty set
V * ((V ") * f) is Relation-like Function-like set
V * (V ") is Relation-like Function-like set
(V * (V ")) * f is Relation-like Function-like set
id (proj1 V) is Relation-like proj1 V -defined proj1 V -valued Function-like one-to-one total Element of bool [:(proj1 V),(proj1 V):]
[:(proj1 V),(proj1 V):] is Relation-like set
bool [:(proj1 V),(proj1 V):] is set
(id (proj1 V)) * f is Relation-like proj1 V -defined Function-like set
proj1 (V ") is set
proj1 g is non empty set
(V ") * (V * g) is Relation-like Function-like set
(V ") * V is Relation-like Function-like set
((V ") * V) * g is Relation-like Function-like set
(V ") " is Relation-like Function-like set
(V ") * ((V ") ") is Relation-like Function-like set
((V ") * ((V ") ")) * g is Relation-like Function-like set
id (proj1 (V ")) is Relation-like proj1 (V ") -defined proj1 (V ") -valued Function-like one-to-one total Element of bool [:(proj1 (V ")),(proj1 (V ")):]
[:(proj1 (V ")),(proj1 (V ")):] is Relation-like set
bool [:(proj1 (V ")),(proj1 (V ")):] is set
(id (proj1 (V "))) * g is Relation-like proj1 (V ") -defined Function-like set
S is non empty non void V68() Circuit-like V153() ManySortedSign
InputVertices S is Element of bool the carrier of S
the carrier of S is non empty set
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K507( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
the carrier of S \ K507( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
InnerVertices S is Element of bool the carrier of S
A is non empty non void V68() Circuit-like V153() ManySortedSign
InputVertices A is Element of bool the carrier of A
the carrier of A is non empty set
bool the carrier of A is set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
the carrier' of A is non empty set
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
K507( the carrier of A, the ResultSort of A) is Element of bool the carrier of A
the carrier of A \ K507( the carrier of A, the ResultSort of A) is Element of bool the carrier of A
InnerVertices A is Element of bool the carrier of A
V is Relation-like Function-like set
V .: (InputVertices S) is set
V .: (InnerVertices S) is set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
C is non-empty finite-yielding MSAlgebra over A
S is non empty non void V68() Circuit-like V153() ManySortedSign
A is non empty non void V68() Circuit-like V153() ManySortedSign
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
C is non-empty finite-yielding MSAlgebra over A
InputVertices S is Element of bool the carrier of S
the carrier of S is non empty set
bool the carrier of S is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V25( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
the carrier' of S is non empty set
[: the carrier' of S, the carrier of S:] is Relation-like set
bool [: the carrier' of S, the carrier of S:] is set
K507( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
the carrier of S \ K507( the carrier of S, the ResultSort of S) is Element of bool the carrier of S
V .: (InputVertices S) is set
InputVertices A is Element of bool the carrier of A
the carrier of A is non empty set
bool the carrier of A is set
the ResultSort of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like V25( the carrier' of A, the carrier of A) Element of bool [: the carrier' of A, the carrier of A:]
the carrier' of A is non empty set
[: the carrier' of A, the carrier of A:] is Relation-like set
bool [: the carrier' of A, the carrier of A:] is set
K507( the carrier of A, the ResultSort of A) is Element of bool the carrier of A
the carrier of A \ K507( the carrier of A, the ResultSort of A) is Element of bool the carrier of A
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over A
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
f is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
g is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * g is Relation-like Function-like set
Following f is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
Following g is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * (Following g) is Relation-like Function-like set
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over A
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
f is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
g is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * g is Relation-like Function-like set
f is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (f,f) is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
Following (g,f) is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * (Following (g,f)) is Relation-like Function-like set
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over S
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over A
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
V " is Relation-like Function-like set
X " is Relation-like Function-like set
f is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
g is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * g is Relation-like Function-like set
(V ") * f is Relation-like Function-like set
Following f is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
Following g is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
Following g is Relation-like the carrier of A -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
Following f is Relation-like the carrier of S -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
S is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of S is non empty set
A is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of A is non empty set
V is Relation-like Function-like set
X is Relation-like Function-like set
G is non-empty finite-yielding MSAlgebra over A
the Sorts of G is Relation-like non-empty non empty-yielding the carrier of A -defined non empty Function-like total set
product the Sorts of G is non empty functional with_common_domain product-like set
C is non-empty finite-yielding MSAlgebra over S
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
V " is Relation-like Function-like set
X " is Relation-like Function-like set
f is Relation-like the carrier of A -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
g is Relation-like the carrier of S -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
V * g is Relation-like Function-like set
f is Element of the carrier of A
V . f is set
proj1 V is set
proj1 (V ") is set
t is Element of the carrier of S
(V ") . t is set
f . f is set
t9 is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
Following (g,t9) is Relation-like the carrier of S -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
(Following (g,t9)) . (V . f) is set
g . (V . f) is set
Following (f,t9) is Relation-like the carrier of A -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
V * (Following (g,t9)) is Relation-like Function-like set
(Following (f,t9)) . f is set
g . (V . f) is set
t9 is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() set
Following (f,t9) is Relation-like the carrier of A -defined non empty Function-like the Sorts of G -compatible total Element of product the Sorts of G
(Following (f,t9)) . f is set
f . f is set
(V ") * f is Relation-like Function-like set
Following (g,t9) is Relation-like the carrier of S -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
(V ") * (Following (f,t9)) is Relation-like Function-like set
(Following (g,t9)) . t is set
g . t is set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms V is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,V))
K334(S,V) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,V) is non empty set
FinTrees the carrier of K334(S,V) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,V)
bool (FinTrees the carrier of K334(S,V)) is set
bool (S -Terms V) is set
G is non empty non void V68() Circuit-like V153() ManySortedSign
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
G is non empty non void V68() Circuit-like V153() ManySortedSign
V is non-empty MSAlgebra over S
X is non empty functional constituted-DTrees Element of bool (S -Terms A)
C is non-empty finite-yielding MSAlgebra over G
(S,A,X) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
(S,A,X,V) is strict non-empty MSAlgebra over (S,A,X)
(S,A,X,V) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the carrier of (S,A,X) is non empty set
(S,A,X,V) is Relation-like the carrier' of (S,A,X) -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,X) * ((S,A,X,V) #), the ResultSort of (S,A,X) * (S,A,X,V)
the carrier' of (S,A,X) is set
the Arity of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) * -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):]
the carrier of (S,A,X) * is non empty functional FinSequence-membered M8( the carrier of (S,A,X))
[: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is Relation-like set
bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is set
(S,A,X,V) # is Relation-like the carrier of (S,A,X) * -defined non empty Function-like total set
the Arity of (S,A,X) * ((S,A,X,V) #) is Relation-like the carrier' of (S,A,X) -defined Function-like total set
the ResultSort of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X)) Element of bool [: the carrier' of (S,A,X), the carrier of (S,A,X):]
[: the carrier' of (S,A,X), the carrier of (S,A,X):] is Relation-like set
bool [: the carrier' of (S,A,X), the carrier of (S,A,X):] is set
the ResultSort of (S,A,X) * (S,A,X,V) is Relation-like non-empty the carrier' of (S,A,X) -defined Function-like total set
MSAlgebra(# (S,A,X,V),(S,A,X,V) #) is strict MSAlgebra over (S,A,X)
f is Relation-like Function-like set
g is Relation-like Function-like set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total set
S -Terms A is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,A))
K334(S,A) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,A) is non empty set
FinTrees the carrier of K334(S,A) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,A)
bool (FinTrees the carrier of K334(S,A)) is set
bool (S -Terms A) is set
G is non empty non void V68() Circuit-like V153() ManySortedSign
V is non-empty MSAlgebra over S
X is non empty functional constituted-DTrees Element of bool (S -Terms A)
C is non-empty finite-yielding MSAlgebra over G
(S,A,X) is non empty V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
f is Relation-like Function-like one-to-one (S,A,V,X,G,C)
(S,A,X,V) is strict non-empty MSAlgebra over (S,A,X)
(S,A,X,V) is Relation-like non-empty non empty-yielding the carrier of (S,A,X) -defined non empty Function-like total set
the carrier of (S,A,X) is non empty set
(S,A,X,V) is Relation-like the carrier' of (S,A,X) -defined Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,A,X) * ((S,A,X,V) #), the ResultSort of (S,A,X) * (S,A,X,V)
the carrier' of (S,A,X) is set
the Arity of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) * -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):]
the carrier of (S,A,X) * is non empty functional FinSequence-membered M8( the carrier of (S,A,X))
[: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is Relation-like set
bool [: the carrier' of (S,A,X),( the carrier of (S,A,X) *):] is set
(S,A,X,V) # is Relation-like the carrier of (S,A,X) * -defined non empty Function-like total set
the Arity of (S,A,X) * ((S,A,X,V) #) is Relation-like the carrier' of (S,A,X) -defined Function-like total set
the ResultSort of (S,A,X) is Relation-like the carrier' of (S,A,X) -defined the carrier of (S,A,X) -valued Function-like V25( the carrier' of (S,A,X), the carrier of (S,A,X)) Element of bool [: the carrier' of (S,A,X), the carrier of (S,A,X):]
[: the carrier' of (S,A,X), the carrier of (S,A,X):] is Relation-like set
bool [: the carrier' of (S,A,X), the carrier of (S,A,X):] is set
the ResultSort of (S,A,X) * (S,A,X,V) is Relation-like non-empty the carrier' of (S,A,X) -defined Function-like total set
MSAlgebra(# (S,A,X,V),(S,A,X,V) #) is strict MSAlgebra over (S,A,X)
g is Relation-like Function-like set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is non-empty finite-yielding MSAlgebra over S
V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total Variables of A
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,V
G is non empty non void V68() Circuit-like V153() ManySortedSign
C is non-empty finite-yielding MSAlgebra over G
(S,V,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
Subtrees X is non empty functional constituted-DTrees set
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
(S,V,X,A) is strict non-empty finite-yielding MSAlgebra over (S,V,X)
(S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
the carrier of (S,V,X) is non empty set
(S,V,X,A) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,V,X) * ((S,V,X,A) #), the ResultSort of (S,V,X) * (S,V,X,A)
the carrier' of (S,V,X) is non empty set
the Arity of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) * -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):]
the carrier of (S,V,X) * is non empty functional FinSequence-membered M8( the carrier of (S,V,X))
[: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is Relation-like set
bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is set
(S,V,X,A) # is Relation-like the carrier of (S,V,X) * -defined non empty Function-like total set
the Arity of (S,V,X) * ((S,V,X,A) #) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total set
the ResultSort of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X)) Element of bool [: the carrier' of (S,V,X), the carrier of (S,V,X):]
[: the carrier' of (S,V,X), the carrier of (S,V,X):] is Relation-like set
bool [: the carrier' of (S,V,X), the carrier of (S,V,X):] is set
the ResultSort of (S,V,X) * (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier' of (S,V,X) -defined non empty Function-like total set
MSAlgebra(# (S,V,X,A),(S,V,X,A) #) is strict MSAlgebra over (S,V,X)
f is Relation-like Function-like set
g is Relation-like Function-like set
f " is Relation-like Function-like set
g " is Relation-like Function-like set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is non-empty finite-yielding MSAlgebra over S
V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total Variables of A
K334(S,V) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,V) is non empty set
FinTrees the carrier of K334(S,V) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,V)
S -Terms V is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,V))
bool (FinTrees the carrier of K334(S,V)) is set
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,V
Subtrees X is non empty functional constituted-DTrees set
(S,V,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,V,X) is non empty set
(S,V,X,A) is strict non-empty finite-yielding MSAlgebra over (S,V,X)
(S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
(S,V,X,A) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,V,X) * ((S,V,X,A) #), the ResultSort of (S,V,X) * (S,V,X,A)
the carrier' of (S,V,X) is non empty set
the Arity of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) * -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):]
the carrier of (S,V,X) * is non empty functional FinSequence-membered M8( the carrier of (S,V,X))
[: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is Relation-like set
bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is set
(S,V,X,A) # is Relation-like the carrier of (S,V,X) * -defined non empty Function-like total set
the Arity of (S,V,X) * ((S,V,X,A) #) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total set
the ResultSort of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X)) Element of bool [: the carrier' of (S,V,X), the carrier of (S,V,X):]
[: the carrier' of (S,V,X), the carrier of (S,V,X):] is Relation-like set
bool [: the carrier' of (S,V,X), the carrier of (S,V,X):] is set
the ResultSort of (S,V,X) * (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier' of (S,V,X) -defined non empty Function-like total set
MSAlgebra(# (S,V,X,A),(S,V,X,A) #) is strict MSAlgebra over (S,V,X)
the Sorts of (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
product the Sorts of (S,V,X,A) is non empty functional with_common_domain product-like set
G is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of G is non empty set
C is non-empty finite-yielding MSAlgebra over G
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of G -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
f is Relation-like Function-like one-to-one (S,V,A,X,G,C)
g is Relation-like Function-like set
f is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
proj1 f is non empty finite Tree-like finite-order finite-branching countable set
height (proj1 f) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
1 + (height (proj1 f)) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
f . f is set
t is Relation-like the carrier of G -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
Following (t,(1 + (height (proj1 f)))) is Relation-like the carrier of G -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
f * t is Relation-like Function-like set
(Following (t,(1 + (height (proj1 f))))) . (f . f) is set
t9 is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
Following (t9,(1 + (height (proj1 f)))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
v is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,V,X)
f * (Following (t,(1 + (height (proj1 f))))) is Relation-like Function-like set
s is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
c₁₄ is Relation-like the carrier of S -defined non empty Function-like total Function-yielding V54() (S,V,X,A,s)
(S,A,V,f,c₁₄) is set
proj1 f is set
Following (s,(1 + (height (proj1 f)))) is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
(Following (s,(1 + (height (proj1 f))))) . v is set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is non-empty finite-yielding MSAlgebra over S
V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total Variables of A
K334(S,V) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,V) is non empty set
FinTrees the carrier of K334(S,V) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,V)
S -Terms V is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,V))
bool (FinTrees the carrier of K334(S,V)) is set
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,V
Subtrees X is non empty functional constituted-DTrees set
(S,V,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,V,X) is non empty set
(S,V,X,A) is strict non-empty finite-yielding MSAlgebra over (S,V,X)
(S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
(S,V,X,A) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,V,X) * ((S,V,X,A) #), the ResultSort of (S,V,X) * (S,V,X,A)
the carrier' of (S,V,X) is non empty set
the Arity of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) * -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):]
the carrier of (S,V,X) * is non empty functional FinSequence-membered M8( the carrier of (S,V,X))
[: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is Relation-like set
bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is set
(S,V,X,A) # is Relation-like the carrier of (S,V,X) * -defined non empty Function-like total set
the Arity of (S,V,X) * ((S,V,X,A) #) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total set
the ResultSort of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X)) Element of bool [: the carrier' of (S,V,X), the carrier of (S,V,X):]
[: the carrier' of (S,V,X), the carrier of (S,V,X):] is Relation-like set
bool [: the carrier' of (S,V,X), the carrier of (S,V,X):] is set
the ResultSort of (S,V,X) * (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier' of (S,V,X) -defined non empty Function-like total set
MSAlgebra(# (S,V,X,A),(S,V,X,A) #) is strict MSAlgebra over (S,V,X)
the Sorts of (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
product the Sorts of (S,V,X,A) is non empty functional with_common_domain product-like set
G is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of G is non empty set
C is non-empty finite-yielding MSAlgebra over G
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of G -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
f is Relation-like Function-like set
g is Relation-like Function-like set
t is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
proj1 t is non empty finite Tree-like finite-order finite-branching countable set
height (proj1 t) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
1 + (height (proj1 t)) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
f is Relation-like Function-like one-to-one (S,V,A,X,G,C)
t9 is Relation-like Function-like finite DecoratedTree-like finite-order finite-branching countable Element of the carrier of (S,V,X)
f . t9 is set
v is Element of the carrier of G
s is Relation-like the carrier of G -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
Following (s,(1 + (height (proj1 t)))) is Relation-like the carrier of G -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
(Following (s,(1 + (height (proj1 t))))) . v is set
f * s is Relation-like Function-like set
c₁₄ is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
vp is Relation-like the carrier of S -defined non empty Function-like total Function-yielding V54() (S,V,X,A,c₁₄)
(S,A,V,t,vp) is set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is non-empty finite-yielding MSAlgebra over S
V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total Variables of A
K334(S,V) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,V) is non empty set
FinTrees the carrier of K334(S,V) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,V)
S -Terms V is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,V))
bool (FinTrees the carrier of K334(S,V)) is set
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,V
Subtrees X is non empty functional constituted-DTrees set
(S,V,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,V,X) is non empty set
(S,V,X,A) is strict non-empty finite-yielding MSAlgebra over (S,V,X)
(S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
(S,V,X,A) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,V,X) * ((S,V,X,A) #), the ResultSort of (S,V,X) * (S,V,X,A)
the carrier' of (S,V,X) is non empty set
the Arity of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) * -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):]
the carrier of (S,V,X) * is non empty functional FinSequence-membered M8( the carrier of (S,V,X))
[: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is Relation-like set
bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is set
(S,V,X,A) # is Relation-like the carrier of (S,V,X) * -defined non empty Function-like total set
the Arity of (S,V,X) * ((S,V,X,A) #) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total set
the ResultSort of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X)) Element of bool [: the carrier' of (S,V,X), the carrier of (S,V,X):]
[: the carrier' of (S,V,X), the carrier of (S,V,X):] is Relation-like set
bool [: the carrier' of (S,V,X), the carrier of (S,V,X):] is set
the ResultSort of (S,V,X) * (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier' of (S,V,X) -defined non empty Function-like total set
MSAlgebra(# (S,V,X,A),(S,V,X,A) #) is strict MSAlgebra over (S,V,X)
the Sorts of (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
product the Sorts of (S,V,X,A) is non empty functional with_common_domain product-like set
G is non empty non void V68() Circuit-like V153() ManySortedSign
the carrier of G is non empty set
C is non-empty finite-yielding MSAlgebra over G
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of G -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
t is Relation-like the carrier of (S,V,X) -defined non empty Function-like the Sorts of (S,V,X,A) -compatible total Element of product the Sorts of (S,V,X,A)
f is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
g is Relation-like the carrier of G -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
proj1 f is non empty finite Tree-like finite-order finite-branching countable set
height (proj1 f) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
1 + (height (proj1 f)) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
Following (g,(1 + (height (proj1 f)))) is Relation-like the carrier of G -defined non empty Function-like the Sorts of C -compatible total Element of product the Sorts of C
f is Relation-like Function-like one-to-one (S,V,A,X,G,C)
f . f is set
f * g is Relation-like Function-like set
(Following (g,(1 + (height (proj1 f))))) . (f . f) is set
t9 is Relation-like the carrier of S -defined non empty Function-like total Function-yielding V54() (S,V,X,A,t)
(S,A,V,f,t9) is set
S is non empty non void V68() V153() ManySortedSign
the carrier of S is non empty set
A is non-empty finite-yielding MSAlgebra over S
V is Relation-like non-empty non empty-yielding the carrier of S -defined non empty Function-like total Variables of A
G is non empty non void V68() Circuit-like V153() ManySortedSign
K334(S,V) is non empty V112() V116() V117() V118() L13()
the carrier of K334(S,V) is non empty set
FinTrees the carrier of K334(S,V) is non empty functional constituted-DTrees DTree-set of the carrier of K334(S,V)
S -Terms V is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of K334(S,V))
bool (FinTrees the carrier of K334(S,V)) is set
X is non empty functional constituted-DTrees SetWithCompoundTerm of S,V
C is non-empty finite-yielding MSAlgebra over G
f is Relation-like the carrier of K334(S,V) -valued Function-like finite DecoratedTree-like finite-order finite-branching countable M26( the carrier of K334(S,V), FinTrees the carrier of K334(S,V),S -Terms V)
Subtrees X is non empty functional constituted-DTrees set
the carrier of G is non empty set
the Sorts of C is Relation-like non-empty non empty-yielding the carrier of G -defined non empty Function-like total set
product the Sorts of C is non empty functional with_common_domain product-like set
proj1 f is non empty finite Tree-like finite-order finite-branching countable set
height (proj1 f) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
1 + (height (proj1 f)) is V6() V7() V8() V12() finite V33() countable V154() ext-real V158() Element of NAT
(S,V,X) is non empty non void V68() strict Circuit-like unsplit V153() ManySortedSign
the carrier' of S is non empty set
{ the carrier of S} is non empty trivial finite V35(1) countable set
[: the carrier' of S,{ the carrier of S}:] is Relation-like set
[: the carrier' of S,{ the carrier of S}:] -Subtrees X is functional constituted-DTrees Element of bool (Subtrees X)
bool (Subtrees X) is set
[: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined (Subtrees X) * -valued Function-like V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X,(Subtrees X) * ) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):]
(Subtrees X) * is non empty functional FinSequence-membered M8( Subtrees X)
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),((Subtrees X) *):] is set
incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X) is Relation-like [: the carrier' of S,{ the carrier of S}:] -Subtrees X -defined Subtrees X -valued [: the carrier' of S,{ the carrier of S}:] -Subtrees X -valued Function-like one-to-one V25([: the carrier' of S,{ the carrier of S}:] -Subtrees X, Subtrees X) Function-yielding V54() Element of bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):]
[:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] -Subtrees X),(Subtrees X):] is set
ManySortedSign(# (Subtrees X),([: the carrier' of S,{ the carrier of S}:] -Subtrees X),([: the carrier' of S,{ the carrier of S}:] -ImmediateSubtrees X),(incl ([: the carrier' of S,{ the carrier of S}:] -Subtrees X)) #) is non empty V68() strict V153() ManySortedSign
the carrier of (S,V,X) is non empty set
(S,V,X,A) is strict non-empty finite-yielding MSAlgebra over (S,V,X)
(S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
(S,V,X,A) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total Function-yielding V54() ManySortedFunction of the Arity of (S,V,X) * ((S,V,X,A) #), the ResultSort of (S,V,X) * (S,V,X,A)
the carrier' of (S,V,X) is non empty set
the Arity of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) * -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X) * ) Function-yielding V54() Element of bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):]
the carrier of (S,V,X) * is non empty functional FinSequence-membered M8( the carrier of (S,V,X))
[: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is Relation-like set
bool [: the carrier' of (S,V,X),( the carrier of (S,V,X) *):] is set
(S,V,X,A) # is Relation-like the carrier of (S,V,X) * -defined non empty Function-like total set
the Arity of (S,V,X) * ((S,V,X,A) #) is Relation-like the carrier' of (S,V,X) -defined non empty Function-like total set
the ResultSort of (S,V,X) is Relation-like the carrier' of (S,V,X) -defined the carrier of (S,V,X) -valued Function-like V25( the carrier' of (S,V,X), the carrier of (S,V,X)) Element of bool [: the carrier' of (S,V,X), the carrier of (S,V,X):]
[: the carrier' of (S,V,X), the carrier of (S,V,X):] is Relation-like set
bool [: the carrier' of (S,V,X), the carrier of (S,V,X):] is set
the ResultSort of (S,V,X) * (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier' of (S,V,X) -defined non empty Function-like total set
MSAlgebra(# (S,V,X,A),(S,V,X,A) #) is strict MSAlgebra over (S,V,X)
the Sorts of (S,V,X,A) is Relation-like non-empty non empty-yielding the carrier of (S,V,X) -defined non empty Function-like total set
product the Sorts of (S,V,X,A) is non empty functional with_common_domain product-like set