:: OSAFREE semantic presentation

K32() is non empty V4() V5() V6() Element of bool K28()
K28() is set
bool K28() is non empty set
K27() is non empty V4() V5() V6() set
bool K27() is non empty set
bool K32() is non empty set
{} is empty V4() V5() V6() V8() V9() V10() Relation-like non-empty empty-yielding K32() -defined Function-like one-to-one constant functional V32() V33() V34() FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding set
the empty V4() V5() V6() V8() V9() V10() Relation-like non-empty empty-yielding K32() -defined Function-like one-to-one constant functional V32() V33() V34() FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding set is empty V4() V5() V6() V8() V9() V10() Relation-like non-empty empty-yielding K32() -defined Function-like one-to-one constant functional V32() V33() V34() FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding set
1 is non empty set
{{},1} is non empty set
Trees is non empty constituted-Trees set
bool Trees is non empty set
FinTrees is non empty constituted-Trees constituted-FinTrees Element of bool Trees
PeanoNat is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier of PeanoNat is non empty set
FinTrees the carrier of PeanoNat is non empty functional constituted-DTrees DTree-set of the carrier of PeanoNat
TS PeanoNat is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of PeanoNat)
bool (FinTrees the carrier of PeanoNat) is non empty set
[:(TS PeanoNat),K32():] is non empty Relation-like set
bool [:(TS PeanoNat),K32():] is non empty set
[:K32(),(TS PeanoNat):] is non empty Relation-like set
bool [:K32(),(TS PeanoNat):] is non empty set
2 is non empty set
3 is non empty set
K33() is empty V4() V5() V6() V8() V9() V10() Relation-like non-empty empty-yielding K32() -defined Function-like one-to-one constant functional V32() V33() V34() FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Element of K32()
K289(K33()) is non empty V104() set
<*> K32() is empty proper V4() V5() V6() V8() V9() V10() Relation-like non-empty empty-yielding K32() -defined K32() -valued Function-like one-to-one constant functional V32() V33() V34() FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding FinSequence of K32()
[:K32(),K32():] is non empty Relation-like set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is order-sorted MSAlgebra over S
the Sorts of X is non empty Relation-like the carrier of S -defined Function-like total set
y is non empty Relation-like the carrier of S -defined Function-like total ManySortedSubset of the Sorts of X
t is non empty Relation-like the carrier of S -defined Function-like total OSSubset of X
OSCl t is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
GenOSAlg t is strict order-sorted MSSubAlgebra of X
the Sorts of (GenOSAlg t) is non empty Relation-like the carrier of S -defined Function-like total set
P is non empty Relation-like the carrier of S -defined Function-like total OSSubset of X
GenOSAlg P is strict order-sorted MSSubAlgebra of X
the Sorts of (GenOSAlg P) is non empty Relation-like the carrier of S -defined Function-like total set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is strict non-empty order-sorted MSAlgebra over S
the Sorts of X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is non empty Relation-like the carrier of S -defined Function-like total ManySortedSubset of the Sorts of X
OSCl x is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
t is non empty Relation-like the carrier of S -defined Function-like total OSSubset of X
GenOSAlg t is strict order-sorted MSSubAlgebra of X
the Sorts of (GenOSAlg t) is non empty Relation-like the carrier of S -defined Function-like total set
y is MSSubAlgebra of X
the Sorts of y is non empty Relation-like the carrier of S -defined Function-like total set
y is non empty Relation-like the carrier of S -defined Function-like total OSSubset of X
GenOSAlg y is strict order-sorted MSSubAlgebra of X
the Sorts of (GenOSAlg y) is non empty Relation-like the carrier of S -defined Function-like total set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is order-sorted monotone MSAlgebra over S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
X is non empty Relation-like the carrier of S -defined Function-like total set
coprod X is non empty Relation-like the carrier of S -defined Function-like total set
Union (coprod X) is set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
y is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
t is Element of [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))
tx is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
[t,tx] is V26() set
{t,tx} is non empty set
{t} is non empty set
{{t,tx},{t}} is non empty set
len tx is V4() V5() V6() V10() Element of K32()
dom tx is Element of bool K32()
P is Element of the carrier' of S
[P, the carrier of S] is V26() set
{P, the carrier of S} is non empty set
{P} is non empty set
{{P, the carrier of S},{P}} is non empty set
the_arity_of P is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
len (the_arity_of P) is V4() V5() V6() V10() Element of K32()
O1 is set
tx . O1 is set
R is Element of the carrier' of S
[R, the carrier of S] is V26() set
{R, the carrier of S} is non empty set
{R} is non empty set
{{R, the carrier of S},{R}} is non empty set
the_result_sort_of R is Element of the carrier of S
(the_arity_of P) /. O1 is Element of the carrier of S
y is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
t is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
tx is set
P is set
[tx,P] is V26() set
{tx,P} is non empty set
{tx} is non empty set
{{tx,P},{tx}} is non empty set
O1 is Element of [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))
R is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
[O1,R] is V26() set
{O1,R} is non empty set
{O1} is non empty set
{{O1,R},{O1}} is non empty set
len R is V4() V5() V6() V10() Element of K32()
dom R is Element of bool K32()
i is Element of the carrier' of S
[i, the carrier of S] is V26() set
{i, the carrier of S} is non empty set
{i} is non empty set
{{i, the carrier of S},{i}} is non empty set
the_arity_of i is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
len (the_arity_of i) is V4() V5() V6() V10() Element of K32()
s is set
R . s is set
a is Element of the carrier' of S
[a, the carrier of S] is V26() set
{a, the carrier of S} is non empty set
{a} is non empty set
{{a, the carrier of S},{a}} is non empty set
the_result_sort_of a is Element of the carrier of S
(the_arity_of i) /. s is Element of the carrier of S
O1 is Element of [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))
R is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
[O1,R] is V26() set
{O1,R} is non empty set
{O1} is non empty set
{{O1,R},{O1}} is non empty set
len R is V4() V5() V6() V10() Element of K32()
dom R is Element of bool K32()
i is Element of the carrier' of S
[i, the carrier of S] is V26() set
{i, the carrier of S} is non empty set
{i} is non empty set
{{i, the carrier of S},{i}} is non empty set
the_arity_of i is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
len (the_arity_of i) is V4() V5() V6() V10() Element of K32()
s is set
R . s is set
a is Element of the carrier' of S
[a, the carrier of S] is V26() set
{a, the carrier of S} is non empty set
{a} is non empty set
{{a, the carrier of S},{a}} is non empty set
the_result_sort_of a is Element of the carrier of S
(the_arity_of i) /. s is Element of the carrier of S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
X is non empty Relation-like the carrier of S -defined Function-like total set
coprod X is non empty Relation-like the carrier of S -defined Function-like total set
Union (coprod X) is set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
x is Element of the carrier' of S
[x, the carrier of S] is V26() set
{x, the carrier of S} is non empty set
{x} is non empty set
{{x, the carrier of S},{x}} is non empty set
the_arity_of x is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
len (the_arity_of x) is V4() V5() V6() V10() Element of K32()
y is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
[[x, the carrier of S],y] is V26() set
{[x, the carrier of S],y} is non empty set
{[x, the carrier of S]} is non empty Relation-like Function-like set
{{[x, the carrier of S],y},{[x, the carrier of S]}} is non empty set
len y is V4() V5() V6() V10() Element of K32()
dom y is Element of bool K32()
tx is Element of [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))
P is Element of the carrier' of S
[P, the carrier of S] is V26() set
{P, the carrier of S} is non empty set
{P} is non empty set
{{P, the carrier of S},{P}} is non empty set
the_arity_of P is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of P) is V4() V5() V6() V10() Element of K32()
O1 is set
y . O1 is set
R is Element of the carrier' of S
[R, the carrier of S] is V26() set
{R, the carrier of S} is non empty set
{R} is non empty set
{{R, the carrier of S},{R}} is non empty set
the_result_sort_of R is Element of the carrier of S
(the_arity_of P) /. O1 is Element of the carrier of S
P is set
y . P is set
O1 is Element of the carrier' of S
[O1, the carrier of S] is V26() set
{O1, the carrier of S} is non empty set
{O1} is non empty set
{{O1, the carrier of S},{O1}} is non empty set
the_result_sort_of O1 is Element of the carrier of S
(the_arity_of x) /. P is Element of the carrier of S
P is Element of the carrier' of S
[P, the carrier of S] is V26() set
{P, the carrier of S} is non empty set
{P} is non empty set
{{P, the carrier of S},{P}} is non empty set
tx is Element of [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))
the_arity_of P is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of P) is V4() V5() V6() V10() Element of K32()
O1 is set
y . O1 is set
R is Element of the carrier' of S
[R, the carrier of S] is V26() set
{R, the carrier of S} is non empty set
{R} is non empty set
{{R, the carrier of S},{R}} is non empty set
the_result_sort_of R is Element of the carrier of S
(the_arity_of P) /. O1 is Element of the carrier of S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
X is non empty Relation-like the carrier of S -defined Function-like total set
coprod X is non empty Relation-like the carrier of S -defined Function-like total set
Union (coprod X) is set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like the carrier of S -defined Function-like total set
(S,X) is DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like the carrier of S -defined Function-like total set
Union (coprod X) is set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict DTConstrStr
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
NonTerminals (S,X) is set
Terminals (S,X) is set
the carrier of (S,X) is non empty set
(Terminals (S,X)) \/ (NonTerminals (S,X)) is set
t is set
{ b₁ where b₁ is Element of the carrier of (S,X) : ex b₂ being Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
tx is Element of the carrier of (S,X)
P is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
P is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
[tx,P] is V26() set
{tx,P} is non empty set
{tx} is non empty set
{{tx,P},{tx}} is non empty set
the Rules of (S,X) is Relation-like the carrier of (S,X) -defined the carrier of (S,X) * -valued Element of bool [: the carrier of (S,X),( the carrier of (S,X) *):]
the carrier of (S,X) * is non empty functional FinSequence-membered M10( the carrier of (S,X))
[: the carrier of (S,X),( the carrier of (S,X) *):] is non empty Relation-like set
bool [: the carrier of (S,X),( the carrier of (S,X) *):] is non empty set
R is Element of [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))
O1 is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
[R,O1] is V26() set
{R,O1} is non empty set
{R} is non empty set
{{R,O1},{R}} is non empty set
t is set
tx is Element of the carrier' of S
P is Element of { the carrier of S}
[tx,P] is V26() set
{tx,P} is non empty set
{tx} is non empty set
{{tx,P},{tx}} is non empty set
the_arity_of tx is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
len (the_arity_of tx) is V4() V5() V6() V10() Element of K32()
Seg (len (the_arity_of tx)) is V34() V41( len (the_arity_of tx)) Element of bool K32()
R is set
(the_arity_of tx) /. R is Element of the carrier of S
dom (the_arity_of tx) is Element of bool K32()
(the_arity_of tx) . R is set
proj2 (the_arity_of tx) is set
X . ((the_arity_of tx) . R) is set
i is set
[i,((the_arity_of tx) . R)] is V26() set
{i,((the_arity_of tx) . R)} is non empty set
{i} is non empty set
{{i,((the_arity_of tx) . R)},{i}} is non empty set
s is V26() set
coprod (((the_arity_of tx) /. R),X) is set
coprod (((the_arity_of tx) . R),X) is set
R is Relation-like Function-like set
proj1 R is set
i is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
proj2 i is set
s is set
dom i is Element of bool K32()
a is set
i . a is set
(the_arity_of tx) /. a is Element of the carrier of S
b is Element of the carrier of S
coprod (b,X) is set
dom (coprod X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
(coprod X) . b is non empty set
proj2 (coprod X) is non empty V205() set
union (proj2 (coprod X)) is set
s is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))
b is set
a is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
dom a is Element of bool K32()
(the_arity_of tx) /. b is Element of the carrier of S
a . b is set
ta is Element of the carrier of S
coprod (ta,X) is set
dom (coprod X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
(coprod X) . ta is non empty set
proj2 (coprod X) is non empty V205() set
union (proj2 (coprod X)) is set
tb is Element of the carrier' of S
[tb, the carrier of S] is V26() set
{tb, the carrier of S} is non empty set
{tb} is non empty set
{{tb, the carrier of S},{tb}} is non empty set
the_result_sort_of tb is Element of the carrier of S
[tx, the carrier of S] is V26() set
{tx, the carrier of S} is non empty set
{{tx, the carrier of S},{tx}} is non empty set
len a is V4() V5() V6() V10() Element of K32()
b is Element of the carrier of (S,X)
[b,a] is V26() set
{b,a} is non empty set
{b} is non empty set
{{b,a},{b}} is non empty set
{ b₁ where b₁ is Element of the carrier of (S,X) : ex b₂ being Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
t is set
t is set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
Terminals (S,X) is set
NonTerminals (S,X) is set
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
t is Element of the carrier of (S,X)
tx is Element of the carrier' of S
P is Element of { the carrier of S}
[tx,P] is V26() set
{tx,P} is non empty set
{tx} is non empty set
{{tx,P},{tx}} is non empty set
the_arity_of tx is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
len (the_arity_of tx) is V4() V5() V6() V10() Element of K32()
Seg (len (the_arity_of tx)) is V34() V41( len (the_arity_of tx)) Element of bool K32()
R is set
(the_arity_of tx) /. R is Element of the carrier of S
dom (the_arity_of tx) is Element of bool K32()
(the_arity_of tx) . R is set
proj2 (the_arity_of tx) is set
X . ((the_arity_of tx) . R) is set
i is set
[i,((the_arity_of tx) . R)] is V26() set
{i,((the_arity_of tx) . R)} is non empty set
{i} is non empty set
{{i,((the_arity_of tx) . R)},{i}} is non empty set
s is V26() set
coprod (((the_arity_of tx) /. R),X) is set
coprod (((the_arity_of tx) . R),X) is set
R is Relation-like Function-like set
proj1 R is set
i is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
proj2 i is set
s is set
dom i is Element of bool K32()
a is set
i . a is set
(the_arity_of tx) /. a is Element of the carrier of S
b is Element of the carrier of S
coprod (b,X) is set
dom (coprod X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
(coprod X) . b is non empty set
proj2 (coprod X) is non empty V205() set
union (proj2 (coprod X)) is set
s is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))
a is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
dom a is Element of bool K32()
b is Relation-like Function-like set
proj1 b is set
ta is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
proj2 ta is set
tb is set
dom ta is Element of bool K32()
t1 is set
ta . t1 is set
a . t1 is set
proj2 a is set
(the_arity_of tx) /. t1 is Element of the carrier of S
t1 is Element of the carrier of S
coprod (t1,X) is set
dom (coprod X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
(coprod X) . t1 is non empty set
proj2 (coprod X) is non empty V205() set
union (proj2 (coprod X)) is set
t2 is Element of the carrier of (S,X)
root-tree (a . t1) is Relation-like Function-like DecoratedTree-like set
tb is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like FinSequence of TS (S,X)
roots tb is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
t1 is set
(roots tb) . t1 is set
a . t1 is set
t2 is V4() V5() V6() V10() set
tb . t2 is Relation-like Function-like set
(roots tb) . t2 is set
tb . t1 is Relation-like Function-like set
root-tree (a . t1) is Relation-like Function-like DecoratedTree-like set
t1 is Relation-like Function-like DecoratedTree-like set
t1 . {} is set
t1 is set
(the_arity_of tx) /. t1 is Element of the carrier of S
a . t1 is set
t2 is Element of the carrier of S
coprod (t2,X) is set
dom (coprod X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
(coprod X) . t2 is non empty set
proj2 (coprod X) is non empty V205() set
union (proj2 (coprod X)) is set
t1 is Element of the carrier' of S
[t1, the carrier of S] is V26() set
{t1, the carrier of S} is non empty set
{t1} is non empty set
{{t1, the carrier of S},{t1}} is non empty set
the_result_sort_of t1 is Element of the carrier of S
len a is V4() V5() V6() V10() Element of K32()
[t,a] is V26() set
{t,a} is non empty set
{t} is non empty set
{{t,a},{t}} is non empty set
dom (roots tb) is Element of bool K32()
dom tb is Element of bool K32()
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
the carrier of (S,X) is non empty set
bool the carrier of (S,X) is non empty set
x is set
proj2 (coprod X) is non empty V205() set
union (proj2 (coprod X)) is set
t is set
dom (coprod X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
tx is set
(coprod X) . tx is set
P is Element of the carrier of S
(coprod X) . P is non empty set
coprod (P,X) is set
X . P is non empty set
O1 is set
[O1,P] is V26() set
{O1,P} is non empty set
{O1} is non empty set
{{O1,P},{O1}} is non empty set
tx is set
t is Element of the carrier of S
X . t is non empty set
[tx,t] is V26() set
{tx,t} is non empty set
{tx} is non empty set
{{tx,t},{tx}} is non empty set
coprod (t,X) is set
(coprod X) . t is non empty set
dom (coprod X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
x is Element of the carrier' of S
[x, the carrier of S] is V26() set
{x, the carrier of S} is non empty set
{x} is non empty set
{{x, the carrier of S},{x}} is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is Element of the carrier of S
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= x & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= x ) ) } is set
bool (TS (S,X)) is non empty set
t is set
tx is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
P is Element of the carrier of S
O1 is set
X . P is non empty set
[O1,P] is V26() set
{O1,P} is non empty set
{O1} is non empty set
{{O1,P},{O1}} is non empty set
root-tree [O1,P] is Relation-like Function-like DecoratedTree-like set
R is Element of the carrier' of S
[R, the carrier of S] is V26() set
{R, the carrier of S} is non empty set
{R} is non empty set
{{R, the carrier of S},{R}} is non empty set
tx . {} is set
the_result_sort_of R is Element of the carrier of S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is Element of the carrier of S
(S,X,x) is functional constituted-DTrees Element of bool (TS (S,X))
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= x & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= x ) ) } is set
dom (coprod X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
(coprod X) . x is non empty set
proj2 (coprod X) is non empty V205() set
coprod (x,X) is set
X . x is non empty set
t is set
[t,x] is V26() set
{t,x} is non empty set
{t} is non empty set
{{t,x},{t}} is non empty set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
union (proj2 (coprod X)) is set
P is Element of the carrier of (S,X)
root-tree P is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
bool (TS (S,X)) is non empty set
x is Relation-like Function-like set
proj1 x is set
y is non empty Relation-like the carrier of S -defined Function-like total set
t is Element of the carrier of S
tx is Element of the carrier of S
y . t is set
y . tx is set
P is set
(S,X,t) is non empty functional constituted-DTrees Element of bool (TS (S,X))
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= t & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= t ) ) } is set
O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
O1 . {} is set
R is Element of the carrier of S
i is set
X . R is non empty set
[i,R] is V26() set
{i,R} is non empty set
{i} is non empty set
{{i,R},{i}} is non empty set
root-tree [i,R] is Relation-like Function-like DecoratedTree-like set
R is Element of the carrier of S
i is set
X . R is non empty set
[i,R] is V26() set
{i,R} is non empty set
{i} is non empty set
{{i,R},{i}} is non empty set
root-tree [i,R] is Relation-like Function-like DecoratedTree-like set
i is Element of the carrier' of S
[i, the carrier of S] is V26() set
{i, the carrier of S} is non empty set
{i} is non empty set
{{i, the carrier of S},{i}} is non empty set
the_result_sort_of i is Element of the carrier of S
i is Element of the carrier' of S
[i, the carrier of S] is V26() set
{i, the carrier of S} is non empty set
{i} is non empty set
{{i, the carrier of S},{i}} is non empty set
the_result_sort_of i is Element of the carrier of S
R is Element of the carrier of S
R is Element of the carrier of S
i is set
X . R is non empty set
[i,R] is V26() set
{i,R} is non empty set
{i} is non empty set
{{i,R},{i}} is non empty set
root-tree [i,R] is Relation-like Function-like DecoratedTree-like set
s is Element of the carrier' of S
[s, the carrier of S] is V26() set
{s, the carrier of S} is non empty set
{s} is non empty set
{{s, the carrier of S},{s}} is non empty set
the_result_sort_of s is Element of the carrier of S
(S,X,tx) is non empty functional constituted-DTrees Element of bool (TS (S,X))
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= tx & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= tx ) ) } is set
R is Element of the carrier of S
i is set
X . R is non empty set
[i,R] is V26() set
{i,R} is non empty set
{i} is non empty set
{{i,R},{i}} is non empty set
root-tree [i,R] is Relation-like Function-like DecoratedTree-like set
s is Element of the carrier' of S
[s, the carrier of S] is V26() set
{s, the carrier of S} is non empty set
{s} is non empty set
{{s, the carrier of S},{s}} is non empty set
the_result_sort_of s is Element of the carrier of S
t is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
tx is Element of the carrier of S
t . tx is set
(S,X,tx) is non empty functional constituted-DTrees Element of bool (TS (S,X))
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= tx & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= tx ) ) } is set
x is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
y is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
t is set
x . t is set
y . t is set
tx is Element of the carrier of S
x . tx is set
(S,X,tx) is non empty functional constituted-DTrees Element of bool (TS (S,X))
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= tx & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= tx ) ) } is set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
x is set
(S,X) . x is set
y is Element of the carrier of S
(S,X) . y is set
(S,X,y) is non empty functional constituted-DTrees Element of bool (TS (S,X))
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= y & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= y ) ) } is set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty Relation-like the carrier' of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is Element of the carrier' of S
( the Arity of S * ((S,X) #)) . x is set
y is set
the_arity_of x is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the Arity of S . x is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
(the_arity_of x) * (S,X) is Relation-like non-empty K32() -defined dom (the_arity_of x) -defined Function-like total V34() FinSequence-like FinSubsequence-like set
dom (the_arity_of x) is Element of bool K32()
product ((the_arity_of x) * (S,X)) is set
dom ((the_arity_of x) * (S,X)) is Element of bool K32()
P is Relation-like Function-like set
proj1 P is set
len (the_arity_of x) is V4() V5() V6() V10() Element of K32()
Seg (len (the_arity_of x)) is V34() V41( len (the_arity_of x)) Element of bool K32()
O1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
proj2 O1 is set
R is set
dom O1 is Element of bool K32()
i is set
O1 . i is set
((the_arity_of x) * (S,X)) . i is set
s is V4() V5() V6() V10() set
((the_arity_of x) * (S,X)) . s is set
(the_arity_of x) . s is set
(S,X) . ((the_arity_of x) . s) is set
(the_arity_of x) /. s is Element of the carrier of S
(S,X) . ((the_arity_of x) /. s) is non empty set
(S,X,((the_arity_of x) /. s)) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= (the_arity_of x) /. s & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= (the_arity_of x) /. s ) ) } is set
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
b is Element of the carrier of S
ta is set
X . b is non empty set
[ta,b] is V26() set
{ta,b} is non empty set
{ta} is non empty set
{{ta,b},{ta}} is non empty set
root-tree [ta,b] is Relation-like Function-like DecoratedTree-like set
tb is Element of the carrier' of S
[tb, the carrier of S] is V26() set
{tb, the carrier of S} is non empty set
{tb} is non empty set
{{tb, the carrier of S},{tb}} is non empty set
a . {} is set
the_result_sort_of tb is Element of the carrier of S
R is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty Relation-like the carrier' of S -defined Function-like total set
x is Element of the carrier' of S
( the Arity of S * ((S,X) #)) . x is set
the_arity_of x is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom (the_arity_of x) is Element of bool K32()
y is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
dom y is Element of bool K32()
the Arity of S . x is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
(the_arity_of x) * (S,X) is Relation-like non-empty K32() -defined dom (the_arity_of x) -defined Function-like total V34() FinSequence-like FinSubsequence-like set
product ((the_arity_of x) * (S,X)) is set
dom ((the_arity_of x) * (S,X)) is Element of bool K32()
P is V4() V5() V6() V10() set
y . P is Relation-like Function-like set
(the_arity_of x) /. P is Element of the carrier of S
(S,X,((the_arity_of x) /. P)) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= (the_arity_of x) /. P & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= (the_arity_of x) /. P ) ) } is set
((the_arity_of x) * (S,X)) . P is set
(the_arity_of x) . P is set
(S,X) . ((the_arity_of x) . P) is set
(S,X) . ((the_arity_of x) /. P) is non empty set
(the_arity_of x) * (S,X) is Relation-like non-empty K32() -defined dom (the_arity_of x) -defined Function-like total V34() FinSequence-like FinSubsequence-like set
dom ((the_arity_of x) * (S,X)) is Element of bool K32()
P is set
y . P is Relation-like Function-like set
((the_arity_of x) * (S,X)) . P is set
O1 is V4() V5() V6() V10() set
(the_arity_of x) /. O1 is Element of the carrier of S
(S,X,((the_arity_of x) /. O1)) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= (the_arity_of x) /. O1 & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= (the_arity_of x) /. O1 ) ) } is set
(S,X) . ((the_arity_of x) /. O1) is non empty set
(the_arity_of x) . O1 is set
(S,X) . ((the_arity_of x) . O1) is set
the Arity of S . x is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
product ((the_arity_of x) * (S,X)) is set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty Relation-like the carrier' of S -defined Function-like total set
x is Element of the carrier' of S
(S,X,x) is Element of the carrier of (S,X)
[x, the carrier of S] is V26() set
{x, the carrier of S} is non empty set
{x} is non empty set
{{x, the carrier of S},{x}} is non empty set
( the Arity of S * ((S,X) #)) . x is set
y is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots y is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
the_arity_of x is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom y is Element of bool K32()
dom (roots y) is Element of bool K32()
[[x, the carrier of S],(roots y)] is V26() set
{[x, the carrier of S],(roots y)} is non empty set
{[x, the carrier of S]} is non empty Relation-like Function-like set
{{[x, the carrier of S],(roots y)},{[x, the carrier of S]}} is non empty set
R is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
dom R is Element of bool K32()
i is V4() V5() V6() V10() set
y . i is Relation-like Function-like set
(the_arity_of x) /. i is Element of the carrier of S
(S,X,((the_arity_of x) /. i)) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= (the_arity_of x) /. i & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= (the_arity_of x) /. i ) ) } is set
proj2 R is set
proj2 y is set
R . i is set
a is Relation-like Function-like DecoratedTree-like set
a . {} is set
ta is Element of the carrier' of S
tb is Element of { the carrier of S}
[ta,tb] is V26() set
{ta,tb} is non empty set
{ta} is non empty set
{{ta,tb},{ta}} is non empty set
the_result_sort_of ta is Element of the carrier of S
b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
b . {} is set
t1 is Element of the carrier' of S
[t1, the carrier of S] is V26() set
{t1, the carrier of S} is non empty set
{t1} is non empty set
{{t1, the carrier of S},{t1}} is non empty set
the_result_sort_of t1 is Element of the carrier of S
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
ta is Element of Terminals (S,X)
root-tree ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
tb is Element of the carrier of S
coprod (tb,X) is set
X . tb is non empty set
t1 is set
[t1,tb] is V26() set
{t1,tb} is non empty set
{t1} is non empty set
{{t1,tb},{t1}} is non empty set
len (the_arity_of x) is V4() V5() V6() V10() Element of K32()
Seg (len (the_arity_of x)) is V34() V41( len (the_arity_of x)) Element of bool K32()
dom (the_arity_of x) is Element of bool K32()
len R is V4() V5() V6() V10() Element of K32()
Seg (len R) is V34() V41( len R) Element of bool K32()
len (roots y) is V4() V5() V6() V10() Element of K32()
Seg (len (roots y)) is V34() V41( len (roots y)) Element of bool K32()
R is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))
i is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
dom i is Element of bool K32()
s is set
i . s is set
(the_arity_of x) /. s is Element of the carrier of S
a is V4() V5() V6() V10() set
(the_arity_of x) /. a is Element of the carrier of S
y . a is Relation-like Function-like set
(S,X,((the_arity_of x) /. a)) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= (the_arity_of x) /. a & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= (the_arity_of x) /. a ) ) } is set
ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
ta . {} is set
i . a is set
tb is Element of the carrier of S
t1 is set
X . tb is non empty set
[t1,tb] is V26() set
{t1,tb} is non empty set
{t1} is non empty set
{{t1,tb},{t1}} is non empty set
root-tree [t1,tb] is Relation-like Function-like DecoratedTree-like set
coprod (tb,X) is set
dom (coprod X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
(coprod X) . tb is non empty set
proj2 (coprod X) is non empty V205() set
t2 is Relation-like Function-like DecoratedTree-like set
t2 . {} is set
union (proj2 (coprod X)) is set
tb is Element of the carrier' of S
[tb, the carrier of S] is V26() set
{tb, the carrier of S} is non empty set
{tb} is non empty set
{{tb, the carrier of S},{tb}} is non empty set
the_result_sort_of tb is Element of the carrier of S
t1 is Element of the carrier of S
t2 is set
X . t1 is non empty set
[t2,t1] is V26() set
{t2,t1} is non empty set
{t2} is non empty set
{{t2,t1},{t2}} is non empty set
root-tree [t2,t1] is Relation-like Function-like DecoratedTree-like set
t1 is Element of the carrier' of S
[t1, the carrier of S] is V26() set
{t1, the carrier of S} is non empty set
{t1} is non empty set
{{t1, the carrier of S},{t1}} is non empty set
the_result_sort_of t1 is Element of the carrier of S
t2 is Relation-like Function-like DecoratedTree-like set
t2 . {} is set
tb is Element of the carrier' of S
[tb, the carrier of S] is V26() set
{tb, the carrier of S} is non empty set
{tb} is non empty set
{{tb, the carrier of S},{tb}} is non empty set
the_result_sort_of tb is Element of the carrier of S
t1 is Relation-like Function-like DecoratedTree-like set
t1 . {} is set
tb is Element of the carrier of S
t1 is set
X . tb is non empty set
[t1,tb] is V26() set
{t1,tb} is non empty set
{t1} is non empty set
{{t1,tb},{t1}} is non empty set
root-tree [t1,tb] is Relation-like Function-like DecoratedTree-like set
t2 is Element of the carrier' of S
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
the_result_sort_of t2 is Element of the carrier of S
tb is Element of the carrier of S
t1 is set
X . tb is non empty set
[t1,tb] is V26() set
{t1,tb} is non empty set
{t1} is non empty set
{{t1,tb},{t1}} is non empty set
root-tree [t1,tb] is Relation-like Function-like DecoratedTree-like set
coprod (tb,X) is set
t2 is Relation-like Function-like DecoratedTree-like set
t2 . {} is set
dom (the_arity_of x) is Element of bool K32()
len i is V4() V5() V6() V10() Element of K32()
len (the_arity_of x) is V4() V5() V6() V10() Element of K32()
[[x, the carrier of S],i] is V26() set
{[x, the carrier of S],i} is non empty set
{[x, the carrier of S]} is non empty Relation-like Function-like set
{{[x, the carrier of S],i},{[x, the carrier of S]}} is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
proj2 (S,X) is non empty V205() set
union (proj2 (S,X)) is set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
dom (S,X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
y is set
t is set
tx is set
(S,X) . tx is set
P is Element of the carrier of S
(S,X,P) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= P & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= P ) ) } is set
O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
R is Element of the carrier of S
i is set
X . R is non empty set
[i,R] is V26() set
{i,R} is non empty set
{i} is non empty set
{{i,R},{i}} is non empty set
root-tree [i,R] is Relation-like Function-like DecoratedTree-like set
s is Element of the carrier' of S
[s, the carrier of S] is V26() set
{s, the carrier of S} is non empty set
{s} is non empty set
{{s, the carrier of S},{s}} is non empty set
O1 . {} is set
the_result_sort_of s is Element of the carrier of S
y is set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
(Terminals (S,X)) \/ (NonTerminals (S,X)) is non empty Element of bool the carrier of (S,X)
t is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
proj2 t is set
proj1 t is non empty V34() V104() set
t . {} is set
tx is Element of Terminals (S,X)
proj2 (coprod X) is non empty V205() set
union (proj2 (coprod X)) is set
P is set
dom (coprod X) is non empty Element of bool the carrier of S
O1 is set
(coprod X) . O1 is set
R is Element of the carrier of S
coprod (R,X) is set
X . R is non empty set
root-tree tx is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,R) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= R & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= R ) ) } is set
i is set
[i,R] is V26() set
{i,R} is non empty set
{i} is non empty set
{{i,R},{i}} is non empty set
(S,X) . R is non empty set
tx is Element of NonTerminals (S,X)
P is Element of the carrier' of S
O1 is Element of { the carrier of S}
[P,O1] is V26() set
{P,O1} is non empty set
{P} is non empty set
{{P,O1},{P}} is non empty set
the_result_sort_of P is Element of the carrier of S
(S,X,(the_result_sort_of P)) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= the_result_sort_of P & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= the_result_sort_of P ) ) } is set
(S,X) . (the_result_sort_of P) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty Relation-like the carrier' of S -defined Function-like total set
x is Element of the carrier' of S
( the Arity of S * ((S,X) #)) . x is set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
( the ResultSort of S * (S,X)) . x is non empty set
[:(( the Arity of S * ((S,X) #)) . x),(( the ResultSort of S * (S,X)) . x):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . x),(( the ResultSort of S * (S,X)) . x):] is non empty set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X,x) is Element of the carrier of (S,X)
[x, the carrier of S] is V26() set
{x, the carrier of S} is non empty set
{x} is non empty set
{{x, the carrier of S},{x}} is non empty set
the_result_sort_of x is Element of the carrier of S
i is set
s is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots s is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
(S,X,x) -tree s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
dom ( the ResultSort of S * (S,X)) is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
the ResultSort of S . x is Element of the carrier of S
(S,X) . ( the ResultSort of S . x) is non empty set
(S,X) . (the_result_sort_of x) is non empty set
(S,X,(the_result_sort_of x)) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= the_result_sort_of x & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= the_result_sort_of x ) ) } is set
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
a . {} is set
ta is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
(S,X,x) -tree ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
i is Relation-like Function-like set
proj1 i is set
proj2 i is set
[:(( the Arity of S * ((S,X) #)) . x),(proj2 i):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . x),(proj2 i):] is non empty set
s is Relation-like ( the Arity of S * ((S,X) #)) . x -defined proj2 i -valued Function-like V29(( the Arity of S * ((S,X) #)) . x, proj2 i) Element of bool [:(( the Arity of S * ((S,X) #)) . x),(proj2 i):]
a is Relation-like ( the Arity of S * ((S,X) #)) . x -defined ( the ResultSort of S * (S,X)) . x -valued Function-like V29(( the Arity of S * ((S,X) #)) . x,( the ResultSort of S * (S,X)) . x) Element of bool [:(( the Arity of S * ((S,X) #)) . x),(( the ResultSort of S * (S,X)) . x):]
b is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots b is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
a . b is set
(S,X,x) -tree b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
P is Relation-like ( the Arity of S * ((S,X) #)) . x -defined ( the ResultSort of S * (S,X)) . x -valued Function-like V29(( the Arity of S * ((S,X) #)) . x,( the ResultSort of S * (S,X)) . x) Element of bool [:(( the Arity of S * ((S,X) #)) . x),(( the ResultSort of S * (S,X)) . x):]
O1 is Relation-like ( the Arity of S * ((S,X) #)) . x -defined ( the ResultSort of S * (S,X)) . x -valued Function-like V29(( the Arity of S * ((S,X) #)) . x,( the ResultSort of S * (S,X)) . x) Element of bool [:(( the Arity of S * ((S,X) #)) . x),(( the ResultSort of S * (S,X)) . x):]
R is set
P . R is set
O1 . R is set
i is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots i is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
P . i is set
(S,X,x) -tree i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
dom O1 is Element of bool (( the Arity of S * ((S,X) #)) . x)
bool (( the Arity of S * ((S,X) #)) . x) is non empty set
dom P is Element of bool (( the Arity of S * ((S,X) #)) . x)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
y is set
t is Element of the carrier' of S
(S,X,t) is Relation-like ( the Arity of S * ((S,X) #)) . t -defined ( the ResultSort of S * (S,X)) . t -valued Function-like V29(( the Arity of S * ((S,X) #)) . t,( the ResultSort of S * (S,X)) . t) Element of bool [:(( the Arity of S * ((S,X) #)) . t),(( the ResultSort of S * (S,X)) . t):]
( the Arity of S * ((S,X) #)) . t is set
( the ResultSort of S * (S,X)) . t is non empty set
[:(( the Arity of S * ((S,X) #)) . t),(( the ResultSort of S * (S,X)) . t):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . t),(( the ResultSort of S * (S,X)) . t):] is non empty set
tx is Element of the carrier' of S
(S,X,tx) is Relation-like ( the Arity of S * ((S,X) #)) . tx -defined ( the ResultSort of S * (S,X)) . tx -valued Function-like V29(( the Arity of S * ((S,X) #)) . tx,( the ResultSort of S * (S,X)) . tx) Element of bool [:(( the Arity of S * ((S,X) #)) . tx),(( the ResultSort of S * (S,X)) . tx):]
( the Arity of S * ((S,X) #)) . tx is set
( the ResultSort of S * (S,X)) . tx is non empty set
[:(( the Arity of S * ((S,X) #)) . tx),(( the ResultSort of S * (S,X)) . tx):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . tx),(( the ResultSort of S * (S,X)) . tx):] is non empty set
y is Relation-like Function-like set
proj1 y is set
t is non empty Relation-like the carrier' of S -defined Function-like total set
dom t is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
tx is set
t . tx is set
P is Element of the carrier' of S
t . P is set
(S,X,P) is Relation-like ( the Arity of S * ((S,X) #)) . P -defined ( the ResultSort of S * (S,X)) . P -valued Function-like V29(( the Arity of S * ((S,X) #)) . P,( the ResultSort of S * (S,X)) . P) Element of bool [:(( the Arity of S * ((S,X) #)) . P),(( the ResultSort of S * (S,X)) . P):]
( the Arity of S * ((S,X) #)) . P is set
( the ResultSort of S * (S,X)) . P is non empty set
[:(( the Arity of S * ((S,X) #)) . P),(( the ResultSort of S * (S,X)) . P):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . P),(( the ResultSort of S * (S,X)) . P):] is non empty set
tx is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() set
P is set
tx . P is Relation-like Function-like set
( the Arity of S * ((S,X) #)) . P is set
( the ResultSort of S * (S,X)) . P is set
[:(( the Arity of S * ((S,X) #)) . P),(( the ResultSort of S * (S,X)) . P):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . P),(( the ResultSort of S * (S,X)) . P):] is non empty set
O1 is Element of the carrier' of S
tx . O1 is Relation-like Function-like set
(S,X,O1) is Relation-like ( the Arity of S * ((S,X) #)) . O1 -defined ( the ResultSort of S * (S,X)) . O1 -valued Function-like V29(( the Arity of S * ((S,X) #)) . O1,( the ResultSort of S * (S,X)) . O1) Element of bool [:(( the Arity of S * ((S,X) #)) . O1),(( the ResultSort of S * (S,X)) . O1):]
( the Arity of S * ((S,X) #)) . O1 is set
( the ResultSort of S * (S,X)) . O1 is non empty set
[:(( the Arity of S * ((S,X) #)) . O1),(( the ResultSort of S * (S,X)) . O1):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . O1),(( the ResultSort of S * (S,X)) . O1):] is non empty set
P is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
O1 is Element of the carrier' of S
( the Arity of S * ((S,X) #)) . O1 is set
( the ResultSort of S * (S,X)) . O1 is non empty set
P . O1 is Relation-like ( the Arity of S * ((S,X) #)) . O1 -defined ( the ResultSort of S * (S,X)) . O1 -valued Function-like V29(( the Arity of S * ((S,X) #)) . O1,( the ResultSort of S * (S,X)) . O1) Element of bool [:(( the Arity of S * ((S,X) #)) . O1),(( the ResultSort of S * (S,X)) . O1):]
[:(( the Arity of S * ((S,X) #)) . O1),(( the ResultSort of S * (S,X)) . O1):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . O1),(( the ResultSort of S * (S,X)) . O1):] is non empty set
(S,X,O1) is Relation-like ( the Arity of S * ((S,X) #)) . O1 -defined ( the ResultSort of S * (S,X)) . O1 -valued Function-like V29(( the Arity of S * ((S,X) #)) . O1,( the ResultSort of S * (S,X)) . O1) Element of bool [:(( the Arity of S * ((S,X) #)) . O1),(( the ResultSort of S * (S,X)) . O1):]
x is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
y is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
t is set
x . t is Relation-like Function-like set
y . t is Relation-like Function-like set
tx is Element of the carrier' of S
( the Arity of S * ((S,X) #)) . tx is set
( the ResultSort of S * (S,X)) . tx is non empty set
x . tx is Relation-like ( the Arity of S * ((S,X) #)) . tx -defined ( the ResultSort of S * (S,X)) . tx -valued Function-like V29(( the Arity of S * ((S,X) #)) . tx,( the ResultSort of S * (S,X)) . tx) Element of bool [:(( the Arity of S * ((S,X) #)) . tx),(( the ResultSort of S * (S,X)) . tx):]
[:(( the Arity of S * ((S,X) #)) . tx),(( the ResultSort of S * (S,X)) . tx):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . tx),(( the ResultSort of S * (S,X)) . tx):] is non empty set
(S,X,tx) is Relation-like ( the Arity of S * ((S,X) #)) . tx -defined ( the ResultSort of S * (S,X)) . tx -valued Function-like V29(( the Arity of S * ((S,X) #)) . tx,( the ResultSort of S * (S,X)) . tx) Element of bool [:(( the Arity of S * ((S,X) #)) . tx),(( the ResultSort of S * (S,X)) . tx):]
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is Element of the carrier' of S
(S,X,x) is Element of the carrier of (S,X)
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
[x, the carrier of S] is V26() set
{x, the carrier of S} is non empty set
{x} is non empty set
{{x, the carrier of S},{x}} is non empty set
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is Element of the carrier of S
the Sorts of (S,X) . x is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= x & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= x ) ) } is set
(S,X,x) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is Element of the carrier of S
X . x is non empty set
y is Element of the carrier of S
the Sorts of (S,X) . y is non empty set
t is set
[t,x] is V26() set
{t,x} is non empty set
{t} is non empty set
{{t,x},{t}} is non empty set
root-tree [t,x] is Relation-like Function-like DecoratedTree-like set
(root-tree [t,x]) . {} is set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
O1 is Element of Terminals (S,X)
root-tree O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
a is set
[a, the carrier of S] is V26() set
{a, the carrier of S} is non empty set
{a} is non empty set
{{a, the carrier of S},{a}} is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= y & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= y ) ) } is set
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
a . {} is set
b is Element of the carrier of S
ta is set
X . b is non empty set
[ta,b] is V26() set
{ta,b} is non empty set
{ta} is non empty set
{{ta,b},{ta}} is non empty set
root-tree [ta,b] is Relation-like Function-like DecoratedTree-like set
tb is Element of the carrier' of S
[tb, the carrier of S] is V26() set
{tb, the carrier of S} is non empty set
{tb} is non empty set
{{tb, the carrier of S},{tb}} is non empty set
the_result_sort_of tb is Element of the carrier of S
b is Element of the carrier of S
ta is set
X . b is non empty set
[ta,b] is V26() set
{ta,b} is non empty set
{ta} is non empty set
{{ta,b},{ta}} is non empty set
root-tree [ta,b] is Relation-like Function-like DecoratedTree-like set
s is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
R is Element of the carrier of S
s . R is set
i is Element of the carrier of S
s . i is set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= x & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= x ) ) } is set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
x . {} is set
y is Element of the carrier' of S
[y, the carrier of S] is V26() set
{y, the carrier of S} is non empty set
{y} is non empty set
{{y, the carrier of S},{y}} is non empty set
(S,X,y) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
Args (y,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (y,(S,X)) is Relation-like Args (y,(S,X)) -defined Result (y,(S,X)) -valued Function-like V29( Args (y,(S,X)), Result (y,(S,X))) Element of bool [:(Args (y,(S,X))),(Result (y,(S,X))):]
Result (y,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (y,(S,X))),(Result (y,(S,X))):] is non empty Relation-like set
bool [:(Args (y,(S,X))),(Result (y,(S,X))):] is non empty set
the_result_sort_of y is Element of the carrier of S
P is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
(S,X,y) -tree P is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
roots P is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
O1 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding SubtreeSeq of (S,X,y)
( the Arity of S * ((S,X) #)) . y is set
(Den (y,(S,X))) . O1 is set
the Arity of S * ( the Sorts of (S,X) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the Charact of (S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ( the Sorts of (S,X) #), the ResultSort of S * the Sorts of (S,X)
the Charact of (S,X) . y is Relation-like ( the Arity of S * ( the Sorts of (S,X) #)) . y -defined ( the ResultSort of S * the Sorts of (S,X)) . y -valued Function-like V29(( the Arity of S * ( the Sorts of (S,X) #)) . y,( the ResultSort of S * the Sorts of (S,X)) . y) Element of bool [:(( the Arity of S * ( the Sorts of (S,X) #)) . y),(( the ResultSort of S * the Sorts of (S,X)) . y):]
( the Arity of S * ( the Sorts of (S,X) #)) . y is set
( the ResultSort of S * the Sorts of (S,X)) . y is non empty set
[:(( the Arity of S * ( the Sorts of (S,X) #)) . y),(( the ResultSort of S * the Sorts of (S,X)) . y):] is Relation-like set
bool [:(( the Arity of S * ( the Sorts of (S,X) #)) . y),(( the ResultSort of S * the Sorts of (S,X)) . y):] is non empty set
( the Charact of (S,X) . y) . O1 is set
(S,X,y) is Relation-like ( the Arity of S * ((S,X) #)) . y -defined ( the ResultSort of S * (S,X)) . y -valued Function-like V29(( the Arity of S * ((S,X) #)) . y,( the ResultSort of S * (S,X)) . y) Element of bool [:(( the Arity of S * ((S,X) #)) . y),(( the ResultSort of S * (S,X)) . y):]
( the ResultSort of S * (S,X)) . y is non empty set
[:(( the Arity of S * ((S,X) #)) . y),(( the ResultSort of S * (S,X)) . y):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . y),(( the ResultSort of S * (S,X)) . y):] is non empty set
(S,X,y) . O1 is set
R is Element of the carrier of S
i is set
[i,R] is V26() set
{i,R} is non empty set
{i} is non empty set
{{i,R},{i}} is non empty set
root-tree [i,R] is Relation-like Function-like DecoratedTree-like set
i is Element of the carrier of S
the Sorts of (S,X) . i is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= i & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= i ) ) } is set
s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
s . {} is set
a is Element of the carrier of S
b is set
X . a is non empty set
[b,a] is V26() set
{b,a} is non empty set
{b} is non empty set
{{b,a},{b}} is non empty set
root-tree [b,a] is Relation-like Function-like DecoratedTree-like set
ta is Element of the carrier' of S
[ta, the carrier of S] is V26() set
{ta, the carrier of S} is non empty set
{ta} is non empty set
{{ta, the carrier of S},{ta}} is non empty set
the_result_sort_of ta is Element of the carrier of S
b is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
s is Element of the carrier of S
b . s is set
a is Element of the carrier of S
b . a is set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= the_result_sort_of y & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= the_result_sort_of y ) ) } is set
b . (the_result_sort_of y) is set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is Element of the carrier of (S,X)
y is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots y is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
x -tree y is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
{ b₁ where b₁ is Element of the carrier of (S,X) : ex b₂ being Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
P is Element of NonTerminals (S,X)
R is set
i is set
[R,i] is V26() set
{R,i} is non empty set
{R} is non empty set
{{R,i},{R}} is non empty set
O1 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding SubtreeSeq of P
P -tree O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
s is Element of the carrier' of S
[s, the carrier of S] is V26() set
{s, the carrier of S} is non empty set
{s} is non empty set
{{s, the carrier of S},{s}} is non empty set
Args (s,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (s,(S,X)) is Relation-like Args (s,(S,X)) -defined Result (s,(S,X)) -valued Function-like V29( Args (s,(S,X)), Result (s,(S,X))) Element of bool [:(Args (s,(S,X))),(Result (s,(S,X))):]
Result (s,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (s,(S,X))),(Result (s,(S,X))):] is non empty Relation-like set
bool [:(Args (s,(S,X))),(Result (s,(S,X))):] is non empty set
(Den (s,(S,X))) . y is set
the_result_sort_of s is Element of the carrier of S
P -tree y is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(P -tree y) . {} is set
(S,X,s) is Element of NonTerminals (S,X)
a is Element of the carrier of S
the Sorts of (S,X) . a is non empty set
b is Element of the carrier of S
the Sorts of (S,X) . b is non empty set
ta is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding SubtreeSeq of (S,X,s)
(S,X,s) -tree ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
roots ta is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
(Den (s,(S,X))) . ta is set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is Element of the carrier' of S
Args (x,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
(S,X,x) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
[x, the carrier of S] is V26() set
{x, the carrier of S} is non empty set
{x} is non empty set
{{x, the carrier of S},{x}} is non empty set
y is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
roots y is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
the Arity of S * ( the Sorts of (S,X) #) is non empty Relation-like the carrier' of S -defined Function-like total set
( the Arity of S * ( the Sorts of (S,X) #)) . x is set
( the Arity of S * ((S,X) #)) . x is set
tx is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots tx is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
tx is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
t is Element of the carrier of (S,X)
tx is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots tx is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
proj2 tx is set
t -tree tx is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
P is Element of the carrier' of S
[P, the carrier of S] is V26() set
{P, the carrier of S} is non empty set
{P} is non empty set
{{P, the carrier of S},{P}} is non empty set
Args (P,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (P,(S,X)) is Relation-like Args (P,(S,X)) -defined Result (P,(S,X)) -valued Function-like V29( Args (P,(S,X)), Result (P,(S,X))) Element of bool [:(Args (P,(S,X))),(Result (P,(S,X))):]
Result (P,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (P,(S,X))),(Result (P,(S,X))):] is non empty Relation-like set
bool [:(Args (P,(S,X))),(Result (P,(S,X))):] is non empty set
(Den (P,(S,X))) . tx is set
the_result_sort_of P is Element of the carrier of S
O1 is Element of the carrier of S
the Sorts of (S,X) . O1 is non empty set
R is Element of the carrier of S
the Sorts of (S,X) . R is non empty set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
t is Element of the carrier of (S,X)
root-tree t is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
P is set
tx is Element of the carrier of S
X . tx is non empty set
[P,tx] is V26() set
{P,tx} is non empty set
{P} is non empty set
{{P,tx},{P}} is non empty set
O1 is Element of the carrier of S
the Sorts of (S,X) . O1 is non empty set
R is Element of the carrier of S
the Sorts of (S,X) . R is non empty set
y is Element of the carrier of S
the Sorts of (S,X) . y is non empty set
t is Element of the carrier of S
the Sorts of (S,X) . t is non empty set
S is non empty non void V60() ManySortedSign
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union the Sorts of (S,X) is non empty set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is set
proj2 (S,X) is non empty V205() set
union (proj2 (S,X)) is set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is Element of the carrier of S
the Sorts of (S,X) . x is non empty set
y is set
dom the Sorts of (S,X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
proj2 the Sorts of (S,X) is non empty V205() set
union (proj2 the Sorts of (S,X)) is set
Union the Sorts of (S,X) is non empty set
P is Element of Union the Sorts of (S,X)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is Element of the carrier of S
X . x is non empty set
y is set
[y,x] is V26() set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
root-tree [y,x] is Relation-like Function-like DecoratedTree-like set
tx is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,tx) is Element of the carrier of S
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
t is Element of the carrier of S
P is Element of the carrier of S
the Sorts of (S,X) . P is non empty set
the Sorts of (S,X) . t is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is Element of the carrier' of S
Args (x,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Result (x,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
Den (x,(S,X)) is Relation-like Args (x,(S,X)) -defined Result (x,(S,X)) -valued Function-like V29( Args (x,(S,X)), Result (x,(S,X))) Element of bool [:(Args (x,(S,X))),(Result (x,(S,X))):]
[:(Args (x,(S,X))),(Result (x,(S,X))):] is non empty Relation-like set
bool [:(Args (x,(S,X))),(Result (x,(S,X))):] is non empty set
the_result_sort_of x is Element of the carrier of S
y is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (x,(S,X))
(Den (x,(S,X))) . y is Element of Result (x,(S,X))
P is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,P) is Element of the carrier of S
(S,X,x) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
[x, the carrier of S] is V26() set
{x, the carrier of S} is non empty set
{x} is non empty set
{{x, the carrier of S},{x}} is non empty set
roots y is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
t is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
(S,X,x) -tree t is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
O1 is Element of the carrier' of S
[O1, the carrier of S] is V26() set
{O1, the carrier of S} is non empty set
{O1} is non empty set
{{O1, the carrier of S},{O1}} is non empty set
Args (O1,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Den (O1,(S,X)) is Relation-like Args (O1,(S,X)) -defined Result (O1,(S,X)) -valued Function-like V29( Args (O1,(S,X)), Result (O1,(S,X))) Element of bool [:(Args (O1,(S,X))),(Result (O1,(S,X))):]
Result (O1,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (O1,(S,X))),(Result (O1,(S,X))):] is non empty Relation-like set
bool [:(Args (O1,(S,X))),(Result (O1,(S,X))):] is non empty set
(Den (O1,(S,X))) . t is set
the_result_sort_of O1 is Element of the carrier of S
the Sorts of (S,X) . (the_result_sort_of x) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
x is Element of the carrier' of S
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
Args (x,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
x is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
dom x is Element of bool K32()
proj2 x is set
t is set
tx is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,tx) is Element of the carrier of S
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
t is Relation-like TS (S,X) -defined the carrier of S -valued Function-like V29( TS (S,X), the carrier of S) Element of bool [:(TS (S,X)), the carrier of S:]
t * x is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom (t * x) is Element of bool K32()
tx is V4() V5() V6() V10() set
x . tx is Relation-like Function-like set
(t * x) . tx is set
P is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,P) is Element of the carrier of S
t . P is Element of the carrier of S
O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,O1) is Element of the carrier of S
t is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom t is Element of bool K32()
tx is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom tx is Element of bool K32()
P is V4() V5() V6() V10() set
t . P is set
tx . P is set
x . P is Relation-like Function-like set
O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,O1) is Element of the carrier of S
R is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,R) is Element of the carrier of S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
x is Element of the carrier' of S
the_arity_of x is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
Args (x,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
y is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
(S,X,y) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom (S,X,y) is Element of bool K32()
dom y is Element of bool K32()
len (S,X,y) is V4() V5() V6() V10() Element of K32()
len (the_arity_of x) is V4() V5() V6() V10() Element of K32()
dom (the_arity_of x) is Element of bool K32()
i is V4() V5() V6() V10() set
y . i is Relation-like Function-like set
(the_arity_of x) /. i is Element of the carrier of S
the Sorts of (S,X) . ((the_arity_of x) /. i) is non empty set
(S,X,y) . i is set
s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,s) is Element of the carrier of S
(the_arity_of x) . i is set
a is Element of the carrier of S
R is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
R . (S,X,s) is set
R . a is set
the Sorts of (S,X) . (S,X,s) is non empty set
len y is V4() V5() V6() V10() Element of K32()
i is set
(S,X,y) . i is set
(the_arity_of x) . i is set
s is V4() V5() V6() V10() set
y . s is Relation-like Function-like set
(the_arity_of x) /. s is Element of the carrier of S
the Sorts of (S,X) . ((the_arity_of x) /. s) is non empty set
(S,X,y) . s is set
a is Element of the carrier of S
b is Element of the carrier of S
(the_arity_of x) . s is set
ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,ta) is Element of the carrier of S
the non empty non void V60() reflexive transitive antisymmetric discrete order-sorted discernable op-discrete monotone regular locally_directed OverloadedRSSign is non empty non void V60() reflexive transitive antisymmetric discrete order-sorted discernable op-discrete monotone regular locally_directed OverloadedRSSign
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable monotone regular locally_directed OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is monotone regular Element of the carrier' of S
y is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
(S,X,y) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
LBound (x,(S,X,y)) is monotone regular Element of the carrier' of S
(S,X,(LBound (x,(S,X,y)))) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
[(LBound (x,(S,X,y))), the carrier of S] is V26() set
{(LBound (x,(S,X,y))), the carrier of S} is non empty set
{(LBound (x,(S,X,y)))} is non empty set
{{(LBound (x,(S,X,y))), the carrier of S},{(LBound (x,(S,X,y)))}} is non empty set
roots y is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
(S,X,(LBound (x,(S,X,y)))) -tree y is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
x is Element of the carrier of (S,X)
P is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
P is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
[x,P] is V26() set
{x,P} is non empty set
{x} is non empty set
{{x,P},{x}} is non empty set
the Rules of (S,X) is Relation-like the carrier of (S,X) -defined the carrier of (S,X) * -valued Element of bool [: the carrier of (S,X),( the carrier of (S,X) *):]
the carrier of (S,X) * is non empty functional FinSequence-membered M10( the carrier of (S,X))
[: the carrier of (S,X),( the carrier of (S,X) *):] is non empty Relation-like set
bool [: the carrier of (S,X),( the carrier of (S,X) *):] is non empty set
tx is Element of [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))
O1 is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
[tx,O1] is V26() set
{tx,O1} is non empty set
{tx} is non empty set
{{tx,O1},{tx}} is non empty set
R is Element of the carrier' of S
i is Element of { the carrier of S}
[R,i] is V26() set
{R,i} is non empty set
{R} is non empty set
{{R,i},{R}} is non empty set
[R, the carrier of S] is V26() set
{R, the carrier of S} is non empty set
{{R, the carrier of S},{R}} is non empty set
y is Element of the carrier' of S
[y, the carrier of S] is V26() set
{y, the carrier of S} is non empty set
{y} is non empty set
{{y, the carrier of S},{y}} is non empty set
t is Element of the carrier' of S
[t, the carrier of S] is V26() set
{t, the carrier of S} is non empty set
{t} is non empty set
{{t, the carrier of S},{t}} is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
x is Element of the carrier of (S,X)
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
root-tree x is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( b₁ in the Sorts of (S,X) . a₁ & b₂ in the Sorts of (S,X) . a₁ & ( for b₃ being non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X) holds [b₁,b₂] in b₃ . a₁ ) ) } is set
tx is non empty Relation-like the carrier of S -defined Function-like total set
P is set
tx . P is set
the Sorts of (S,X) . P is set
[:( the Sorts of (S,X) . P),( the Sorts of (S,X) . P):] is Relation-like set
bool [:( the Sorts of (S,X) . P),( the Sorts of (S,X) . P):] is non empty set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( b₁ in the Sorts of (S,X) . P & b₂ in the Sorts of (S,X) . P & ( for b₃ being non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X) holds [b₁,b₂] in b₃ . P ) ) } is set
R is set
i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[i,s] is V26() set
{i,s} is non empty functional set
{i} is non empty functional set
{{i,s},{i}} is non empty set
i is set
O1 is Element of the carrier of S
the Sorts of (S,X) . O1 is non empty set
s is set
a is set
[i,s] is V26() set
{i,s} is non empty set
{i} is non empty set
{{i,s},{i}} is non empty set
R is Relation-like the Sorts of (S,X) . P -defined the Sorts of (S,X) . P -valued Element of bool [:( the Sorts of (S,X) . P),( the Sorts of (S,X) . P):]
[s,a] is V26() set
{s,a} is non empty set
{s} is non empty set
{{s,a},{s}} is non empty set
[i,a] is V26() set
{i,a} is non empty set
{{i,a},{i}} is non empty set
ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
tb is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[ta,tb] is V26() set
{ta,tb} is non empty functional set
{ta} is non empty functional set
{{ta,tb},{ta}} is non empty set
b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[b,ta] is V26() set
{b,ta} is non empty functional set
{b} is non empty functional set
{{b,ta},{b}} is non empty set
t1 is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
t1 . O1 is Relation-like the Sorts of (S,X) . O1 -defined the Sorts of (S,X) . O1 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . O1),( the Sorts of (S,X) . O1):]
[:( the Sorts of (S,X) . O1),( the Sorts of (S,X) . O1):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . O1),( the Sorts of (S,X) . O1):] is non empty set
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[t2,t1] is V26() set
{t2,t1} is non empty functional set
{t2} is non empty functional set
{{t2,t1},{t2}} is non empty set
field (t1 . O1) is set
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[t2,t1] is V26() set
{t2,t1} is non empty functional set
{t2} is non empty functional set
{{t2,t1},{t2}} is non empty set
[b,tb] is V26() set
{b,tb} is non empty functional set
{{b,tb},{b}} is non empty set
i is set
s is set
[i,s] is V26() set
{i,s} is non empty set
{i} is non empty set
{{i,s},{i}} is non empty set
[s,i] is V26() set
{s,i} is non empty set
{s} is non empty set
{{s,i},{s}} is non empty set
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[a,b] is V26() set
{a,b} is non empty functional set
{a} is non empty functional set
{{a,b},{a}} is non empty set
ta is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
ta . O1 is Relation-like the Sorts of (S,X) . O1 -defined the Sorts of (S,X) . O1 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . O1),( the Sorts of (S,X) . O1):]
[:( the Sorts of (S,X) . O1),( the Sorts of (S,X) . O1):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . O1),( the Sorts of (S,X) . O1):] is non empty set
field (ta . O1) is set
tb is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[tb,t1] is V26() set
{tb,t1} is non empty functional set
{tb} is non empty functional set
{{tb,t1},{tb}} is non empty set
[b,a] is V26() set
{b,a} is non empty functional set
{b} is non empty functional set
{{b,a},{b}} is non empty set
i is set
[i,i] is V26() set
{i,i} is non empty set
{i} is non empty set
{{i,i},{i}} is non empty set
a is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
a . O1 is Relation-like the Sorts of (S,X) . O1 -defined the Sorts of (S,X) . O1 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . O1),( the Sorts of (S,X) . O1):]
[:( the Sorts of (S,X) . O1),( the Sorts of (S,X) . O1):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . O1),( the Sorts of (S,X) . O1):] is non empty set
field (a . O1) is set
s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[s,s] is V26() set
{s,s} is non empty functional set
{s} is non empty functional set
{{s,s},{s}} is non empty set
field R is set
dom R is Element of bool ( the Sorts of (S,X) . P)
bool ( the Sorts of (S,X) . P) is non empty set
P is set
tx . P is set
the Sorts of (S,X) . P is set
[:( the Sorts of (S,X) . P),( the Sorts of (S,X) . P):] is Relation-like set
bool [:( the Sorts of (S,X) . P),( the Sorts of (S,X) . P):] is non empty set
P is non empty Relation-like the carrier of S -defined Function-like total V33() ManySortedRelation of the Sorts of (S,X), the Sorts of (S,X)
O1 is non empty Relation-like the carrier of S -defined Function-like total V33() ManySortedRelation of the Sorts of (S,X), the Sorts of (S,X)
R is set
the Sorts of (S,X) . R is set
[:( the Sorts of (S,X) . R),( the Sorts of (S,X) . R):] is Relation-like set
bool [:( the Sorts of (S,X) . R),( the Sorts of (S,X) . R):] is non empty set
O1 . R is set
i is Relation-like the Sorts of (S,X) . R -defined the Sorts of (S,X) . R -valued Element of bool [:( the Sorts of (S,X) . R),( the Sorts of (S,X) . R):]
R is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like ManySortedRelation of the Sorts of (S,X), the Sorts of (S,X)
i is Element of the carrier of S
s is Element of the carrier of S
the Sorts of (S,X) . i is non empty set
R . i is Relation-like the Sorts of (S,X) . i -defined the Sorts of (S,X) . i -valued Element of bool [:( the Sorts of (S,X) . i),( the Sorts of (S,X) . i):]
[:( the Sorts of (S,X) . i),( the Sorts of (S,X) . i):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . i),( the Sorts of (S,X) . i):] is non empty set
R . s is Relation-like the Sorts of (S,X) . s -defined the Sorts of (S,X) . s -valued Element of bool [:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):]
the Sorts of (S,X) . s is non empty set
[:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):] is non empty set
R . i is Relation-like the Sorts of (S,X) . i -defined the Sorts of (S,X) . i -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . i),( the Sorts of (S,X) . i):]
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( b₁ in the Sorts of (S,X) . i & b₂ in the Sorts of (S,X) . i & S₁[b₁,b₂,i] ) } is set
R . s is Relation-like the Sorts of (S,X) . s -defined the Sorts of (S,X) . s -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):]
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( b₁ in the Sorts of (S,X) . s & b₂ in the Sorts of (S,X) . s & S₁[b₁,b₂,s] ) } is set
a is set
b is set
[a,b] is V26() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
tb is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[ta,tb] is V26() set
{ta,tb} is non empty functional set
{ta} is non empty functional set
{{ta,tb},{ta}} is non empty set
t1 is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
t1 . i is Relation-like the Sorts of (S,X) . i -defined the Sorts of (S,X) . i -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . i),( the Sorts of (S,X) . i):]
t1 . s is Relation-like the Sorts of (S,X) . s -defined the Sorts of (S,X) . s -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):]
ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
tb is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[ta,tb] is V26() set
{ta,tb} is non empty functional set
{ta} is non empty functional set
{{ta,tb},{ta}} is non empty set
t1 is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
t1 . s is Relation-like the Sorts of (S,X) . s -defined the Sorts of (S,X) . s -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):]
t1 . i is Relation-like the Sorts of (S,X) . i -defined the Sorts of (S,X) . i -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . i),( the Sorts of (S,X) . i):]
i is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like OrderSortedRelation of (S,X)
s is Element of the carrier' of S
a is Element of the carrier' of S
Args (s,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Args (a,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the_arity_of a is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
Result (s,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
Den (s,(S,X)) is Relation-like Args (s,(S,X)) -defined Result (s,(S,X)) -valued Function-like V29( Args (s,(S,X)), Result (s,(S,X))) Element of bool [:(Args (s,(S,X))),(Result (s,(S,X))):]
[:(Args (s,(S,X))),(Result (s,(S,X))):] is non empty Relation-like set
bool [:(Args (s,(S,X))),(Result (s,(S,X))):] is non empty set
Result (a,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (a,(S,X)) is Relation-like Args (a,(S,X)) -defined Result (a,(S,X)) -valued Function-like V29( Args (a,(S,X)), Result (a,(S,X))) Element of bool [:(Args (a,(S,X))),(Result (a,(S,X))):]
[:(Args (a,(S,X))),(Result (a,(S,X))):] is non empty Relation-like set
bool [:(Args (a,(S,X))),(Result (a,(S,X))):] is non empty set
the_result_sort_of a is Element of the carrier of S
i . (the_result_sort_of a) is Relation-like the Sorts of (S,X) . (the_result_sort_of a) -defined the Sorts of (S,X) . (the_result_sort_of a) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (the_result_sort_of a)),( the Sorts of (S,X) . (the_result_sort_of a)):]
the Sorts of (S,X) . (the_result_sort_of a) is non empty set
[:( the Sorts of (S,X) . (the_result_sort_of a)),( the Sorts of (S,X) . (the_result_sort_of a)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (the_result_sort_of a)),( the Sorts of (S,X) . (the_result_sort_of a)):] is non empty set
tb is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (s,(S,X))
proj1 tb is set
(Den (s,(S,X))) . tb is Element of Result (s,(S,X))
t1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (a,(S,X))
(Den (a,(S,X))) . t1 is Element of Result (a,(S,X))
[((Den (s,(S,X))) . tb),((Den (a,(S,X))) . t1)] is V26() set
{((Den (s,(S,X))) . tb),((Den (a,(S,X))) . t1)} is non empty set
{((Den (s,(S,X))) . tb)} is non empty set
{{((Den (s,(S,X))) . tb),((Den (a,(S,X))) . t1)},{((Den (s,(S,X))) . tb)}} is non empty set
dom tb is Element of bool K32()
t2 is V4() V5() V6() V10() set
tb . t2 is set
t1 . t2 is set
[(tb . t2),(t1 . t2)] is V26() set
{(tb . t2),(t1 . t2)} is non empty set
{(tb . t2)} is non empty set
{{(tb . t2),(t1 . t2)},{(tb . t2)}} is non empty set
(the_arity_of a) /. t2 is Element of the carrier of S
i . ((the_arity_of a) /. t2) is Relation-like the Sorts of (S,X) . ((the_arity_of a) /. t2) -defined the Sorts of (S,X) . ((the_arity_of a) /. t2) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . ((the_arity_of a) /. t2)),( the Sorts of (S,X) . ((the_arity_of a) /. t2)):]
the Sorts of (S,X) . ((the_arity_of a) /. t2) is non empty set
[:( the Sorts of (S,X) . ((the_arity_of a) /. t2)),( the Sorts of (S,X) . ((the_arity_of a) /. t2)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . ((the_arity_of a) /. t2)),( the Sorts of (S,X) . ((the_arity_of a) /. t2)):] is non empty set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( b₁ in the Sorts of (S,X) . ((the_arity_of a) /. t2) & b₂ in the Sorts of (S,X) . ((the_arity_of a) /. t2) & S₁[b₁,b₂,(the_arity_of a) /. t2] ) } is set
t2 is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
t2 . ((the_arity_of a) /. t2) is Relation-like the Sorts of (S,X) . ((the_arity_of a) /. t2) -defined the Sorts of (S,X) . ((the_arity_of a) /. t2) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . ((the_arity_of a) /. t2)),( the Sorts of (S,X) . ((the_arity_of a) /. t2)):]
s3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
o1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[s3,o1] is V26() set
{s3,o1} is non empty functional set
{s3} is non empty functional set
{{s3,o1},{s3}} is non empty set
t2 . (the_result_sort_of a) is Relation-like the Sorts of (S,X) . (the_result_sort_of a) -defined the Sorts of (S,X) . (the_result_sort_of a) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (the_result_sort_of a)),( the Sorts of (S,X) . (the_result_sort_of a)):]
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( b₁ in the Sorts of (S,X) . (the_result_sort_of a) & b₂ in the Sorts of (S,X) . (the_result_sort_of a) & S₁[b₁,b₂, the_result_sort_of a] ) } is set
s is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
a is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
b is set
s . b is set
a . b is set
ta is Element of the carrier of S
s . ta is Relation-like the Sorts of (S,X) . ta -defined the Sorts of (S,X) . ta -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . ta),( the Sorts of (S,X) . ta):]
the Sorts of (S,X) . ta is non empty set
[:( the Sorts of (S,X) . ta),( the Sorts of (S,X) . ta):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . ta),( the Sorts of (S,X) . ta):] is non empty set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( b₁ in the Sorts of (S,X) . ta & b₂ in the Sorts of (S,X) . ta & S₁[b₁,b₂,ta] ) } is set
tb is set
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[t1,t2] is V26() set
{t1,t2} is non empty functional set
{t1} is non empty functional set
{{t1,t2},{t1}} is non empty set
y is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
t is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
QuotOSAlg ((S,X),(S,X)) is strict non-empty order-sorted monotone MSAlgebra over S
OSClass (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
OSQuotCharact (S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((OSClass (S,X)) #), the ResultSort of S * (OSClass (S,X))
(OSClass (S,X)) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((OSClass (S,X)) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * (OSClass (S,X)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (OSClass (S,X)),(OSQuotCharact (S,X)) #) is strict MSAlgebra over S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
x is Element of the carrier of (S,X)
root-tree x is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
{ [(root-tree x),b₁] where b₁ is Element of the carrier of S : ex b₂ being Element of the carrier of S ex b₃ being set st
( b₃ in X . b₂ & x = [b₃,b₂] & b₂ <= b₁ ) } is set
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
t is set
tx is Element of the carrier of S
[(root-tree x),tx] is V26() set
{(root-tree x),tx} is non empty set
{(root-tree x)} is non empty functional set
{{(root-tree x),tx},{(root-tree x)}} is non empty set
O1 is set
P is Element of the carrier of S
X . P is non empty set
[O1,P] is V26() set
{O1,P} is non empty set
{O1} is non empty set
{{O1,P},{O1}} is non empty set
O1 is set
P is Element of the carrier of S
X . P is non empty set
[O1,P] is V26() set
{O1,P} is non empty set
{O1} is non empty set
{{O1,P},{O1}} is non empty set
root-tree [O1,P] is Relation-like Function-like DecoratedTree-like set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
x is Element of the carrier of (S,X)
y is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of bool [:(TS (S,X)), the carrier of S:]
dom y is Element of bool K32()
{ [((Den (b₁,(S,X))) . b₂),b₃] where b₁ is Element of the carrier' of S, b₂ is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (b₁,(S,X)), b₃ is Element of the carrier of S : ( ex b₄ being Element of the carrier' of S st
( x = [b₄, the carrier of S] & b₄ ~= b₁ & len (the_arity_of b₄) = len (the_arity_of b₁) & the_result_sort_of b₄ <= b₃ & the_result_sort_of b₁ <= b₃ ) & ex b₄ being Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S * st
( dom b₄ = dom y & ( for b₅ being V4() V5() V6() V10() set holds
( not b₅ in dom y or [(b₂ . b₅),(b₄ /. b₅)] in y . b₅ ) ) ) ) } is set
tx is set
P is Element of the carrier' of S
Args (P,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Result (P,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
Den (P,(S,X)) is Relation-like Args (P,(S,X)) -defined Result (P,(S,X)) -valued Function-like V29( Args (P,(S,X)), Result (P,(S,X))) Element of bool [:(Args (P,(S,X))),(Result (P,(S,X))):]
[:(Args (P,(S,X))),(Result (P,(S,X))):] is non empty Relation-like set
bool [:(Args (P,(S,X))),(Result (P,(S,X))):] is non empty set
O1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (P,(S,X))
(Den (P,(S,X))) . O1 is Element of Result (P,(S,X))
R is Element of the carrier of S
[((Den (P,(S,X))) . O1),R] is V26() set
{((Den (P,(S,X))) . O1),R} is non empty set
{((Den (P,(S,X))) . O1)} is non empty set
{{((Den (P,(S,X))) . O1),R},{((Den (P,(S,X))) . O1)}} is non empty set
the_arity_of P is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of P) is V4() V5() V6() V10() Element of K32()
the_result_sort_of P is Element of the carrier of S
(S,X,P) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
[P, the carrier of S] is V26() set
{P, the carrier of S} is non empty set
{P} is non empty set
{{P, the carrier of S},{P}} is non empty set
roots O1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
(S,X,P) -tree O1 is Relation-like Function-like DecoratedTree-like set
i is Element of the carrier' of S
[i, the carrier of S] is V26() set
{i, the carrier of S} is non empty set
{i} is non empty set
{{i, the carrier of S},{i}} is non empty set
Args (i,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Den (i,(S,X)) is Relation-like Args (i,(S,X)) -defined Result (i,(S,X)) -valued Function-like V29( Args (i,(S,X)), Result (i,(S,X))) Element of bool [:(Args (i,(S,X))),(Result (i,(S,X))):]
Result (i,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (i,(S,X))),(Result (i,(S,X))):] is non empty Relation-like set
bool [:(Args (i,(S,X))),(Result (i,(S,X))):] is non empty set
(Den (i,(S,X))) . O1 is set
the_result_sort_of i is Element of the carrier of S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
t is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
tx is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
(S,X) is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
x is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . x is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
R is Element of the carrier of (S,X)
i is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots i is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
proj2 i is set
R -tree i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) . (R -tree i) is set
s is Element of the carrier' of S
[s, the carrier of S] is V26() set
{s, the carrier of S} is non empty set
{s} is non empty set
{{s, the carrier of S},{s}} is non empty set
Args (s,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (s,(S,X)) is Relation-like Args (s,(S,X)) -defined Result (s,(S,X)) -valued Function-like V29( Args (s,(S,X)), Result (s,(S,X))) Element of bool [:(Args (s,(S,X))),(Result (s,(S,X))):]
Result (s,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (s,(S,X))),(Result (s,(S,X))):] is non empty Relation-like set
bool [:(Args (s,(S,X))),(Result (s,(S,X))):] is non empty set
(Den (s,(S,X))) . i is set
the_result_sort_of s is Element of the carrier of S
(S,X) * i is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like Element of (bool [:(TS (S,X)), the carrier of S:]) *
(bool [:(TS (S,X)), the carrier of S:]) * is non empty functional FinSequence-membered M10( bool [:(TS (S,X)), the carrier of S:])
a is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of bool [:(TS (S,X)), the carrier of S:]
(S,X,R,a) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
dom a is Element of bool K32()
{ [((Den (b₁,(S,X))) . b₂),b₃] where b₁ is Element of the carrier' of S, b₂ is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (b₁,(S,X)), b₃ is Element of the carrier of S : ( ex b₄ being Element of the carrier' of S st
( R = [b₄, the carrier of S] & b₄ ~= b₁ & len (the_arity_of b₄) = len (the_arity_of b₁) & the_result_sort_of b₄ <= b₃ & the_result_sort_of b₁ <= b₃ ) & ex b₄ being Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S * st
( dom b₄ = dom a & ( for b₅ being V4() V5() V6() V10() set holds
( not b₅ in dom a or [(b₂ . b₅),(b₄ /. b₅)] in a . b₅ ) ) ) ) } is set
the_arity_of s is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom (S,X) is functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
len a is V4() V5() V6() V10() Element of K32()
len i is V4() V5() V6() V10() Element of K32()
dom i is Element of bool K32()
dom (the_arity_of s) is Element of bool K32()
b is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (s,(S,X))
tb is V4() V5() V6() V10() set
b . tb is set
(the_arity_of s) /. tb is Element of the carrier of S
[(b . tb),((the_arity_of s) /. tb)] is V26() set
{(b . tb),((the_arity_of s) /. tb)} is non empty set
{(b . tb)} is non empty set
{{(b . tb),((the_arity_of s) /. tb)},{(b . tb)}} is non empty set
a . tb is set
proj2 b is set
the Sorts of (S,X) . ((the_arity_of s) /. tb) is non empty set
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[t1,((the_arity_of s) /. tb)] is V26() set
{t1,((the_arity_of s) /. tb)} is non empty set
{t1} is non empty functional set
{{t1,((the_arity_of s) /. tb)},{t1}} is non empty set
(S,X) . t1 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
tb is Element of the carrier of S
the Sorts of (S,X) . tb is non empty set
[(R -tree i),tb] is V26() set
{(R -tree i),tb} is non empty set
{(R -tree i)} is non empty functional set
{{(R -tree i),tb},{(R -tree i)}} is non empty set
len (the_arity_of s) is V4() V5() V6() V10() Element of K32()
t1 is Element of the carrier' of S
Args (t1,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Result (t1,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (t1,(S,X)) is Relation-like Args (t1,(S,X)) -defined Result (t1,(S,X)) -valued Function-like V29( Args (t1,(S,X)), Result (t1,(S,X))) Element of bool [:(Args (t1,(S,X))),(Result (t1,(S,X))):]
[:(Args (t1,(S,X))),(Result (t1,(S,X))):] is non empty Relation-like set
bool [:(Args (t1,(S,X))),(Result (t1,(S,X))):] is non empty set
t2 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (t1,(S,X))
(Den (t1,(S,X))) . t2 is Element of Result (t1,(S,X))
t1 is Element of the carrier of S
[((Den (t1,(S,X))) . t2),t1] is V26() set
{((Den (t1,(S,X))) . t2),t1} is non empty set
{((Den (t1,(S,X))) . t2)} is non empty set
{{((Den (t1,(S,X))) . t2),t1},{((Den (t1,(S,X))) . t2)}} is non empty set
the_arity_of t1 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t1) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t1 is Element of the carrier of S
the Sorts of (S,X) . (the_result_sort_of t1) is non empty set
t2 is Element of the carrier' of S
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
the_arity_of t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t2) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t2 is Element of the carrier of S
tb is Element of the carrier of S
[(R -tree i),tb] is V26() set
{(R -tree i),tb} is non empty set
{(R -tree i)} is non empty functional set
{{(R -tree i),tb},{(R -tree i)}} is non empty set
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[t1,tb] is V26() set
{t1,tb} is non empty set
{t1} is non empty functional set
{{t1,tb},{t1}} is non empty set
(S,X) . t1 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
t2 is Element of the carrier' of S
Args (t2,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Result (t2,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (t2,(S,X)) is Relation-like Args (t2,(S,X)) -defined Result (t2,(S,X)) -valued Function-like V29( Args (t2,(S,X)), Result (t2,(S,X))) Element of bool [:(Args (t2,(S,X))),(Result (t2,(S,X))):]
[:(Args (t2,(S,X))),(Result (t2,(S,X))):] is non empty Relation-like set
bool [:(Args (t2,(S,X))),(Result (t2,(S,X))):] is non empty set
t1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (t2,(S,X))
(Den (t2,(S,X))) . t1 is Element of Result (t2,(S,X))
t2 is Element of the carrier of S
[((Den (t2,(S,X))) . t1),t2] is V26() set
{((Den (t2,(S,X))) . t1),t2} is non empty set
{((Den (t2,(S,X))) . t1)} is non empty set
{{((Den (t2,(S,X))) . t1),t2},{((Den (t2,(S,X))) . t1)}} is non empty set
the_arity_of t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t2) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t2 is Element of the carrier of S
t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom t2 is Element of bool K32()
t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom t2 is Element of bool K32()
s3 is Element of the carrier' of S
[s3, the carrier of S] is V26() set
{s3, the carrier of S} is non empty set
{s3} is non empty set
{{s3, the carrier of S},{s3}} is non empty set
the_arity_of s3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of s3) is V4() V5() V6() V10() Element of K32()
the_result_sort_of s3 is Element of the carrier of S
s3 is Element of the carrier' of S
[s3, the carrier of S] is V26() set
{s3, the carrier of S} is non empty set
{s3} is non empty set
{{s3, the carrier of S},{s3}} is non empty set
the_arity_of s3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of s3) is V4() V5() V6() V10() Element of K32()
the_result_sort_of s3 is Element of the carrier of S
o1 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
(S,X) * o1 is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like Element of (bool [:(TS (S,X)), the carrier of S:]) *
(S,X,t2) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
roots t1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
(S,X,t2) -tree o1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
o3 is Element of the carrier' of S
[o3, the carrier of S] is V26() set
{o3, the carrier of S} is non empty set
{o3} is non empty set
{{o3, the carrier of S},{o3}} is non empty set
Args (o3,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Den (o3,(S,X)) is Relation-like Args (o3,(S,X)) -defined Result (o3,(S,X)) -valued Function-like V29( Args (o3,(S,X)), Result (o3,(S,X))) Element of bool [:(Args (o3,(S,X))),(Result (o3,(S,X))):]
Result (o3,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (o3,(S,X))),(Result (o3,(S,X))):] is non empty Relation-like set
bool [:(Args (o3,(S,X))),(Result (o3,(S,X))):] is non empty set
(Den (o3,(S,X))) . o1 is set
the_result_sort_of o3 is Element of the carrier of S
ts3 is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of bool [:(TS (S,X)), the carrier of S:]
(S,X,(S,X,t2),ts3) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
dom ts3 is Element of bool K32()
{ [((Den (b₁,(S,X))) . b₂),b₃] where b₁ is Element of the carrier' of S, b₂ is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (b₁,(S,X)), b₃ is Element of the carrier of S : ( ex b₄ being Element of the carrier' of S st
( (S,X,t2) = [b₄, the carrier of S] & b₄ ~= b₁ & len (the_arity_of b₄) = len (the_arity_of b₁) & the_result_sort_of b₄ <= b₃ & the_result_sort_of b₁ <= b₃ ) & ex b₄ being Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S * st
( dom b₄ = dom ts3 & ( for b₅ being V4() V5() V6() V10() set holds
( not b₅ in dom ts3 or [(b₂ . b₅),(b₄ /. b₅)] in ts3 . b₅ ) ) ) ) } is set
proj2 o1 is set
len ts3 is V4() V5() V6() V10() Element of K32()
len o1 is V4() V5() V6() V10() Element of K32()
dom o1 is Element of bool K32()
dom (the_arity_of t2) is Element of bool K32()
dom t1 is Element of bool K32()
k is V4() V5() V6() V10() set
b . k is set
t2 /. k is Element of the carrier of S
[(b . k),(t2 /. k)] is V26() set
{(b . k),(t2 /. k)} is non empty set
{(b . k)} is non empty set
{{(b . k),(t2 /. k)},{(b . k)}} is non empty set
ts3 . k is set
proj2 b is set
t1 . k is set
[(t1 . k),(t2 /. k)] is V26() set
{(t1 . k),(t2 /. k)} is non empty set
{(t1 . k)} is non empty set
{{(t1 . k),(t2 /. k)},{(t1 . k)}} is non empty set
a . k is set
(S,X) . (b . k) is set
tk1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[tk1,(t2 /. k)] is V26() set
{tk1,(t2 /. k)} is non empty set
{tk1} is non empty functional set
{{tk1,(t2 /. k)},{tk1}} is non empty set
tk3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . tk3 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
R is Element of the carrier of (S,X)
root-tree R is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) . (root-tree R) is set
a is set
s is Element of the carrier of S
X . s is non empty set
[a,s] is V26() set
{a,s} is non empty set
{a} is non empty set
{{a,s},{a}} is non empty set
(S,X,R) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
{ [(root-tree R),b₁] where b₁ is Element of the carrier of S : ex b₂ being Element of the carrier of S ex b₃ being set st
( b₃ in X . b₂ & R = [b₃,b₂] & b₂ <= b₁ ) } is set
i is Element of Terminals (S,X)
root-tree i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= s & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= s ) ) } is set
the Sorts of (S,X) . s is non empty set
b is Element of the carrier of S
the Sorts of (S,X) . b is non empty set
[(root-tree R),b] is V26() set
{(root-tree R),b} is non empty set
{(root-tree R)} is non empty functional set
{{(root-tree R),b},{(root-tree R)}} is non empty set
ta is Element of the carrier of S
[(root-tree R),ta] is V26() set
{(root-tree R),ta} is non empty set
{{(root-tree R),ta},{(root-tree R)}} is non empty set
t1 is set
tb is Element of the carrier of S
X . tb is non empty set
[t1,tb] is V26() set
{t1,tb} is non empty set
{t1} is non empty set
{{t1,tb},{t1}} is non empty set
t1 is set
tb is Element of the carrier of S
X . tb is non empty set
[t1,tb] is V26() set
{t1,tb} is non empty set
{t1} is non empty set
{{t1,tb},{t1}} is non empty set
b is Element of the carrier of S
[(root-tree R),b] is V26() set
{(root-tree R),b} is non empty set
{(root-tree R)} is non empty functional set
{{(root-tree R),b},{(root-tree R)}} is non empty set
ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[ta,b] is V26() set
{ta,b} is non empty set
{ta} is non empty functional set
{{ta,b},{ta}} is non empty set
(S,X) . ta is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
tb is Element of the carrier of S
[(root-tree R),tb] is V26() set
{(root-tree R),tb} is non empty set
{{(root-tree R),tb},{(root-tree R)}} is non empty set
t2 is set
t1 is Element of the carrier of S
X . t1 is non empty set
[t2,t1] is V26() set
{t2,t1} is non empty set
{t2} is non empty set
{{t2,t1},{t2}} is non empty set
R is Element of the carrier of S
the Sorts of (S,X) . R is non empty set
[x,R] is V26() set
{x,R} is non empty set
{x} is non empty functional set
{{x,R},{x}} is non empty set
i is Element of the carrier of S
[x,i] is V26() set
{x,i} is non empty set
{{x,i},{x}} is non empty set
the Sorts of (S,X) . i is non empty set
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
s is Element of the carrier of S
[a,s] is V26() set
{a,s} is non empty set
{a} is non empty functional set
{{a,s},{a}} is non empty set
[x,s] is V26() set
{x,s} is non empty set
{{x,s},{x}} is non empty set
(S,X) . a is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
(S,X) is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
O1 is Element of the carrier of (S,X)
R is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots R is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
proj2 R is set
O1 -tree R is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) . (O1 -tree R) is set
i is Element of the carrier' of S
[i, the carrier of S] is V26() set
{i, the carrier of S} is non empty set
{i} is non empty set
{{i, the carrier of S},{i}} is non empty set
Args (i,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (i,(S,X)) is Relation-like Args (i,(S,X)) -defined Result (i,(S,X)) -valued Function-like V29( Args (i,(S,X)), Result (i,(S,X))) Element of bool [:(Args (i,(S,X))),(Result (i,(S,X))):]
Result (i,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (i,(S,X))),(Result (i,(S,X))):] is non empty Relation-like set
bool [:(Args (i,(S,X))),(Result (i,(S,X))):] is non empty set
(Den (i,(S,X))) . R is set
the_result_sort_of i is Element of the carrier of S
(S,X) * R is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like Element of (bool [:(TS (S,X)), the carrier of S:]) *
(bool [:(TS (S,X)), the carrier of S:]) * is non empty functional FinSequence-membered M10( bool [:(TS (S,X)), the carrier of S:])
s is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of bool [:(TS (S,X)), the carrier of S:]
(S,X,O1,s) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
dom s is Element of bool K32()
{ [((Den (b₁,(S,X))) . b₂),b₃] where b₁ is Element of the carrier' of S, b₂ is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (b₁,(S,X)), b₃ is Element of the carrier of S : ( ex b₄ being Element of the carrier' of S st
( O1 = [b₄, the carrier of S] & b₄ ~= b₁ & len (the_arity_of b₄) = len (the_arity_of b₁) & the_result_sort_of b₄ <= b₃ & the_result_sort_of b₁ <= b₃ ) & ex b₄ being Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S * st
( dom b₄ = dom s & ( for b₅ being V4() V5() V6() V10() set holds
( not b₅ in dom s or [(b₂ . b₅),(b₄ /. b₅)] in s . b₅ ) ) ) ) } is set
the_arity_of i is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of i) is V4() V5() V6() V10() Element of K32()
ta is Element of the carrier of S
[(O1 -tree R),ta] is V26() set
{(O1 -tree R),ta} is non empty set
{(O1 -tree R)} is non empty functional set
{{(O1 -tree R),ta},{(O1 -tree R)}} is non empty set
dom (S,X) is functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
len s is V4() V5() V6() V10() Element of K32()
len R is V4() V5() V6() V10() Element of K32()
dom R is Element of bool K32()
dom (the_arity_of i) is Element of bool K32()
a is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (i,(S,X))
tb is V4() V5() V6() V10() set
a . tb is set
(the_arity_of i) /. tb is Element of the carrier of S
[(a . tb),((the_arity_of i) /. tb)] is V26() set
{(a . tb),((the_arity_of i) /. tb)} is non empty set
{(a . tb)} is non empty set
{{(a . tb),((the_arity_of i) /. tb)},{(a . tb)}} is non empty set
s . tb is set
proj2 a is set
the Sorts of (S,X) . ((the_arity_of i) /. tb) is non empty set
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[t1,((the_arity_of i) /. tb)] is V26() set
{t1,((the_arity_of i) /. tb)} is non empty set
{t1} is non empty functional set
{{t1,((the_arity_of i) /. tb)},{t1}} is non empty set
(S,X) . t1 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
tb is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[tb,ta] is V26() set
{tb,ta} is non empty set
{tb} is non empty functional set
{{tb,ta},{tb}} is non empty set
tb is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[tb,ta] is V26() set
{tb,ta} is non empty set
{tb} is non empty functional set
{{tb,ta},{tb}} is non empty set
t1 is Element of the carrier' of S
Args (t1,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Result (t1,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (t1,(S,X)) is Relation-like Args (t1,(S,X)) -defined Result (t1,(S,X)) -valued Function-like V29( Args (t1,(S,X)), Result (t1,(S,X))) Element of bool [:(Args (t1,(S,X))),(Result (t1,(S,X))):]
[:(Args (t1,(S,X))),(Result (t1,(S,X))):] is non empty Relation-like set
bool [:(Args (t1,(S,X))),(Result (t1,(S,X))):] is non empty set
t2 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (t1,(S,X))
(Den (t1,(S,X))) . t2 is Element of Result (t1,(S,X))
t1 is Element of the carrier of S
[((Den (t1,(S,X))) . t2),t1] is V26() set
{((Den (t1,(S,X))) . t2),t1} is non empty set
{((Den (t1,(S,X))) . t2)} is non empty set
{{((Den (t1,(S,X))) . t2),t1},{((Den (t1,(S,X))) . t2)}} is non empty set
the_arity_of t1 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t1) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t1 is Element of the carrier of S
t2 is Element of the carrier' of S
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
the_arity_of t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t2) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t2 is Element of the carrier of S
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
O1 is Element of the carrier of (S,X)
root-tree O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) . (root-tree O1) is set
(S,X,O1) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
{ [(root-tree O1),b₁] where b₁ is Element of the carrier of S : ex b₂ being Element of the carrier of S ex b₃ being set st
( b₃ in X . b₂ & O1 = [b₃,b₂] & b₂ <= b₁ ) } is set
R is Element of the carrier of S
[(root-tree O1),R] is V26() set
{(root-tree O1),R} is non empty set
{(root-tree O1)} is non empty functional set
{{(root-tree O1),R},{(root-tree O1)}} is non empty set
i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[i,R] is V26() set
{i,R} is non empty set
{i} is non empty functional set
{{i,R},{i}} is non empty set
i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[i,R] is V26() set
{i,R} is non empty set
{i} is non empty functional set
{{i,R},{i}} is non empty set
s is Element of the carrier of S
[(root-tree O1),s] is V26() set
{(root-tree O1),s} is non empty set
{{(root-tree O1),s},{(root-tree O1)}} is non empty set
b is set
a is Element of the carrier of S
X . a is non empty set
[b,a] is V26() set
{b,a} is non empty set
{b} is non empty set
{{b,a},{b}} is non empty set
i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
R is Element of the carrier of S
[i,R] is V26() set
{i,R} is non empty set
{i} is non empty functional set
{{i,R},{i}} is non empty set
O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . O1 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[O1,R] is V26() set
{O1,R} is non empty set
{O1} is non empty functional set
{{O1,R},{O1}} is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
(S,X) is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
O1 is Element of the carrier of (S,X)
R is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots R is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
proj2 R is set
O1 -tree R is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) . (O1 -tree R) is set
i is Element of the carrier' of S
[i, the carrier of S] is V26() set
{i, the carrier of S} is non empty set
{i} is non empty set
{{i, the carrier of S},{i}} is non empty set
Args (i,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (i,(S,X)) is Relation-like Args (i,(S,X)) -defined Result (i,(S,X)) -valued Function-like V29( Args (i,(S,X)), Result (i,(S,X))) Element of bool [:(Args (i,(S,X))),(Result (i,(S,X))):]
Result (i,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (i,(S,X))),(Result (i,(S,X))):] is non empty Relation-like set
bool [:(Args (i,(S,X))),(Result (i,(S,X))):] is non empty set
(Den (i,(S,X))) . R is set
the_result_sort_of i is Element of the carrier of S
(S,X) * R is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like Element of (bool [:(TS (S,X)), the carrier of S:]) *
(bool [:(TS (S,X)), the carrier of S:]) * is non empty functional FinSequence-membered M10( bool [:(TS (S,X)), the carrier of S:])
a is Element of the carrier of S
b is Element of the carrier of S
the Sorts of (S,X) . a is non empty set
ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[ta,a] is V26() set
{ta,a} is non empty set
{ta} is non empty functional set
{{ta,a},{ta}} is non empty set
[ta,b] is V26() set
{ta,b} is non empty set
{{ta,b},{ta}} is non empty set
s is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of bool [:(TS (S,X)), the carrier of S:]
(S,X,O1,s) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
dom s is Element of bool K32()
{ [((Den (b₁,(S,X))) . b₂),b₃] where b₁ is Element of the carrier' of S, b₂ is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (b₁,(S,X)), b₃ is Element of the carrier of S : ( ex b₄ being Element of the carrier' of S st
( O1 = [b₄, the carrier of S] & b₄ ~= b₁ & len (the_arity_of b₄) = len (the_arity_of b₁) & the_result_sort_of b₄ <= b₃ & the_result_sort_of b₁ <= b₃ ) & ex b₄ being Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S * st
( dom b₄ = dom s & ( for b₅ being V4() V5() V6() V10() set holds
( not b₅ in dom s or [(b₂ . b₅),(b₄ /. b₅)] in s . b₅ ) ) ) ) } is set
t1 is Element of the carrier' of S
Args (t1,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Result (t1,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (t1,(S,X)) is Relation-like Args (t1,(S,X)) -defined Result (t1,(S,X)) -valued Function-like V29( Args (t1,(S,X)), Result (t1,(S,X))) Element of bool [:(Args (t1,(S,X))),(Result (t1,(S,X))):]
[:(Args (t1,(S,X))),(Result (t1,(S,X))):] is non empty Relation-like set
bool [:(Args (t1,(S,X))),(Result (t1,(S,X))):] is non empty set
t2 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (t1,(S,X))
(Den (t1,(S,X))) . t2 is Element of Result (t1,(S,X))
t1 is Element of the carrier of S
[((Den (t1,(S,X))) . t2),t1] is V26() set
{((Den (t1,(S,X))) . t2),t1} is non empty set
{((Den (t1,(S,X))) . t2)} is non empty set
{{((Den (t1,(S,X))) . t2),t1},{((Den (t1,(S,X))) . t2)}} is non empty set
the_arity_of t1 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t1) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t1 is Element of the carrier of S
t2 is Element of the carrier' of S
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
the_arity_of t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t2) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t2 is Element of the carrier of S
t2 is Element of the carrier' of S
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
the_arity_of t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t2) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t2 is Element of the carrier of S
tb is Element of the carrier of S
t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom t2 is Element of bool K32()
tb is Element of the carrier' of S
Args (tb,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Result (tb,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (tb,(S,X)) is Relation-like Args (tb,(S,X)) -defined Result (tb,(S,X)) -valued Function-like V29( Args (tb,(S,X)), Result (tb,(S,X))) Element of bool [:(Args (tb,(S,X))),(Result (tb,(S,X))):]
[:(Args (tb,(S,X))),(Result (tb,(S,X))):] is non empty Relation-like set
bool [:(Args (tb,(S,X))),(Result (tb,(S,X))):] is non empty set
t1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (tb,(S,X))
(Den (tb,(S,X))) . t1 is Element of Result (tb,(S,X))
t2 is Element of the carrier of S
[((Den (tb,(S,X))) . t1),t2] is V26() set
{((Den (tb,(S,X))) . t1),t2} is non empty set
{((Den (tb,(S,X))) . t1)} is non empty set
{{((Den (tb,(S,X))) . t1),t2},{((Den (tb,(S,X))) . t1)}} is non empty set
the_arity_of tb is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of tb) is V4() V5() V6() V10() Element of K32()
the_result_sort_of tb is Element of the carrier of S
(S,X,tb) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
[tb, the carrier of S] is V26() set
{tb, the carrier of S} is non empty set
{tb} is non empty set
{{tb, the carrier of S},{tb}} is non empty set
roots t1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
t1 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
(S,X,tb) -tree t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
t2 is Element of the carrier' of S
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
Args (t2,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Den (t2,(S,X)) is Relation-like Args (t2,(S,X)) -defined Result (t2,(S,X)) -valued Function-like V29( Args (t2,(S,X)), Result (t2,(S,X))) Element of bool [:(Args (t2,(S,X))),(Result (t2,(S,X))):]
Result (t2,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (t2,(S,X))),(Result (t2,(S,X))):] is non empty Relation-like set
bool [:(Args (t2,(S,X))),(Result (t2,(S,X))):] is non empty set
(Den (t2,(S,X))) . t1 is set
the_result_sort_of t2 is Element of the carrier of S
t2 is Element of the carrier' of S
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
the_arity_of t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t2) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t2 is Element of the carrier of S
t2 is Element of the carrier' of S
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
the_arity_of t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t2) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t2 is Element of the carrier of S
s3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom s3 is Element of bool K32()
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
O1 is Element of the carrier of (S,X)
root-tree O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) . (root-tree O1) is set
(S,X,O1) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
{ [(root-tree O1),b₁] where b₁ is Element of the carrier of S : ex b₂ being Element of the carrier of S ex b₃ being set st
( b₃ in X . b₂ & O1 = [b₃,b₂] & b₂ <= b₁ ) } is set
i is Element of the carrier of S
s is Element of the carrier of S
the Sorts of (S,X) . i is non empty set
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[a,i] is V26() set
{a,i} is non empty set
{a} is non empty functional set
{{a,i},{a}} is non empty set
[a,s] is V26() set
{a,s} is non empty set
{{a,s},{a}} is non empty set
the Sorts of (S,X) . s is non empty set
R is Element of Terminals (S,X)
root-tree R is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[(root-tree R),s] is V26() set
{(root-tree R),s} is non empty set
{(root-tree R)} is non empty functional set
{{(root-tree R),s},{(root-tree R)}} is non empty set
b is Element of the carrier of S
[(root-tree O1),b] is V26() set
{(root-tree O1),b} is non empty set
{(root-tree O1)} is non empty functional set
{{(root-tree O1),b},{(root-tree O1)}} is non empty set
tb is set
ta is Element of the carrier of S
X . ta is non empty set
[tb,ta] is V26() set
{tb,ta} is non empty set
{tb} is non empty set
{{tb,ta},{tb}} is non empty set
[(root-tree R),i] is V26() set
{(root-tree R),i} is non empty set
{{(root-tree R),i},{(root-tree R)}} is non empty set
b is Element of the carrier of S
[(root-tree O1),b] is V26() set
{(root-tree O1),b} is non empty set
{(root-tree O1)} is non empty functional set
{{(root-tree O1),b},{(root-tree O1)}} is non empty set
tb is set
ta is Element of the carrier of S
X . ta is non empty set
[tb,ta] is V26() set
{tb,ta} is non empty set
{tb} is non empty set
{{tb,ta},{tb}} is non empty set
i is Element of the carrier of S
s is Element of the carrier of S
O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
the Sorts of (S,X) . i is non empty set
R is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[R,i] is V26() set
{R,i} is non empty set
{R} is non empty functional set
{{R,i},{R}} is non empty set
(S,X) . O1 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[R,s] is V26() set
{R,s} is non empty set
{{R,s},{R}} is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
(S,X) is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
O1 is Element of the carrier of (S,X)
R is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots R is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
proj2 R is set
O1 -tree R is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) . (O1 -tree R) is set
i is Element of the carrier' of S
[i, the carrier of S] is V26() set
{i, the carrier of S} is non empty set
{i} is non empty set
{{i, the carrier of S},{i}} is non empty set
Args (i,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (i,(S,X)) is Relation-like Args (i,(S,X)) -defined Result (i,(S,X)) -valued Function-like V29( Args (i,(S,X)), Result (i,(S,X))) Element of bool [:(Args (i,(S,X))),(Result (i,(S,X))):]
Result (i,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (i,(S,X))),(Result (i,(S,X))):] is non empty Relation-like set
bool [:(Args (i,(S,X))),(Result (i,(S,X))):] is non empty set
(Den (i,(S,X))) . R is set
the_result_sort_of i is Element of the carrier of S
the_arity_of i is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom (the_arity_of i) is Element of bool K32()
dom R is Element of bool K32()
(S,X) * R is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like Element of (bool [:(TS (S,X)), the carrier of S:]) *
(bool [:(TS (S,X)), the carrier of S:]) * is non empty functional FinSequence-membered M10( bool [:(TS (S,X)), the carrier of S:])
dom (S,X) is functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
b is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of bool [:(TS (S,X)), the carrier of S:]
len b is V4() V5() V6() V10() Element of K32()
len R is V4() V5() V6() V10() Element of K32()
dom b is Element of bool K32()
(S,X,O1,b) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
{ [((Den (b₁,(S,X))) . b₂),b₃] where b₁ is Element of the carrier' of S, b₂ is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (b₁,(S,X)), b₃ is Element of the carrier of S : ( ex b₄ being Element of the carrier' of S st
( O1 = [b₄, the carrier of S] & b₄ ~= b₁ & len (the_arity_of b₄) = len (the_arity_of b₁) & the_result_sort_of b₄ <= b₃ & the_result_sort_of b₁ <= b₃ ) & ex b₄ being Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S * st
( dom b₄ = dom b & ( for b₅ being V4() V5() V6() V10() set holds
( not b₅ in dom b or [(b₂ . b₅),(b₄ /. b₅)] in b . b₅ ) ) ) ) } is set
ta is Element of the carrier of S
[(O1 -tree R),ta] is V26() set
{(O1 -tree R),ta} is non empty set
{(O1 -tree R)} is non empty functional set
{{(O1 -tree R),ta},{(O1 -tree R)}} is non empty set
tb is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[tb,ta] is V26() set
{tb,ta} is non empty set
{tb} is non empty functional set
{{tb,ta},{tb}} is non empty set
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[t1,ta] is V26() set
{t1,ta} is non empty set
{t1} is non empty functional set
{{t1,ta},{t1}} is non empty set
(S,X) . tb is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
(S,X) . t1 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
t2 is Element of the carrier' of S
Args (t2,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Result (t2,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (t2,(S,X)) is Relation-like Args (t2,(S,X)) -defined Result (t2,(S,X)) -valued Function-like V29( Args (t2,(S,X)), Result (t2,(S,X))) Element of bool [:(Args (t2,(S,X))),(Result (t2,(S,X))):]
[:(Args (t2,(S,X))),(Result (t2,(S,X))):] is non empty Relation-like set
bool [:(Args (t2,(S,X))),(Result (t2,(S,X))):] is non empty set
t1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (t2,(S,X))
(Den (t2,(S,X))) . t1 is Element of Result (t2,(S,X))
t2 is Element of the carrier of S
[((Den (t2,(S,X))) . t1),t2] is V26() set
{((Den (t2,(S,X))) . t1),t2} is non empty set
{((Den (t2,(S,X))) . t1)} is non empty set
{{((Den (t2,(S,X))) . t1),t2},{((Den (t2,(S,X))) . t1)}} is non empty set
the_arity_of t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t2) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t2 is Element of the carrier of S
t2 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
(S,X) * t2 is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like Element of (bool [:(TS (S,X)), the carrier of S:]) *
(S,X,t2) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
roots t1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
(S,X,t2) -tree t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
o1 is Element of the carrier' of S
[o1, the carrier of S] is V26() set
{o1, the carrier of S} is non empty set
{o1} is non empty set
{{o1, the carrier of S},{o1}} is non empty set
Args (o1,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Den (o1,(S,X)) is Relation-like Args (o1,(S,X)) -defined Result (o1,(S,X)) -valued Function-like V29( Args (o1,(S,X)), Result (o1,(S,X))) Element of bool [:(Args (o1,(S,X))),(Result (o1,(S,X))):]
Result (o1,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (o1,(S,X))),(Result (o1,(S,X))):] is non empty Relation-like set
bool [:(Args (o1,(S,X))),(Result (o1,(S,X))):] is non empty set
(Den (o1,(S,X))) . t2 is set
the_result_sort_of o1 is Element of the carrier of S
s3 is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of bool [:(TS (S,X)), the carrier of S:]
(S,X,(S,X,t2),s3) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
dom s3 is Element of bool K32()
{ [((Den (b₁,(S,X))) . b₂),b₃] where b₁ is Element of the carrier' of S, b₂ is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (b₁,(S,X)), b₃ is Element of the carrier of S : ( ex b₄ being Element of the carrier' of S st
( (S,X,t2) = [b₄, the carrier of S] & b₄ ~= b₁ & len (the_arity_of b₄) = len (the_arity_of b₁) & the_result_sort_of b₄ <= b₃ & the_result_sort_of b₁ <= b₃ ) & ex b₄ being Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S * st
( dom b₄ = dom s3 & ( for b₅ being V4() V5() V6() V10() set holds
( not b₅ in dom s3 or [(b₂ . b₅),(b₄ /. b₅)] in s3 . b₅ ) ) ) ) } is set
ts3 is Element of the carrier' of S
Args (ts3,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Result (ts3,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (ts3,(S,X)) is Relation-like Args (ts3,(S,X)) -defined Result (ts3,(S,X)) -valued Function-like V29( Args (ts3,(S,X)), Result (ts3,(S,X))) Element of bool [:(Args (ts3,(S,X))),(Result (ts3,(S,X))):]
[:(Args (ts3,(S,X))),(Result (ts3,(S,X))):] is non empty Relation-like set
bool [:(Args (ts3,(S,X))),(Result (ts3,(S,X))):] is non empty set
o3 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (ts3,(S,X))
(Den (ts3,(S,X))) . o3 is Element of Result (ts3,(S,X))
k is Element of the carrier of S
[((Den (ts3,(S,X))) . o3),k] is V26() set
{((Den (ts3,(S,X))) . o3),k} is non empty set
{((Den (ts3,(S,X))) . o3)} is non empty set
{{((Den (ts3,(S,X))) . o3),k},{((Den (ts3,(S,X))) . o3)}} is non empty set
the_arity_of ts3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of ts3) is V4() V5() V6() V10() Element of K32()
the_result_sort_of ts3 is Element of the carrier of S
tk1 is Element of the carrier' of S
[tk1, the carrier of S] is V26() set
{tk1, the carrier of S} is non empty set
{tk1} is non empty set
{{tk1, the carrier of S},{tk1}} is non empty set
the_arity_of tk1 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of tk1) is V4() V5() V6() V10() Element of K32()
the_result_sort_of tk1 is Element of the carrier of S
tk1 is Element of the carrier' of S
[tk1, the carrier of S] is V26() set
{tk1, the carrier of S} is non empty set
{tk1} is non empty set
{{tk1, the carrier of S},{tk1}} is non empty set
the_arity_of tk1 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of tk1) is V4() V5() V6() V10() Element of K32()
the_result_sort_of tk1 is Element of the carrier of S
tk3 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
(S,X) * tk3 is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like Element of (bool [:(TS (S,X)), the carrier of S:]) *
s is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (i,(S,X))
tak is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of bool [:(TS (S,X)), the carrier of S:]
proj2 t2 is set
len s3 is V4() V5() V6() V10() Element of K32()
len t2 is V4() V5() V6() V10() Element of K32()
dom t2 is Element of bool K32()
tk2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom tk2 is Element of bool K32()
tk2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom tk2 is Element of bool K32()
rt is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom rt is Element of bool K32()
rt is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom rt is Element of bool K32()
(S,X,ts3) is Element of NonTerminals (S,X)
[ts3, the carrier of S] is V26() set
{ts3, the carrier of S} is non empty set
{ts3} is non empty set
{{ts3, the carrier of S},{ts3}} is non empty set
roots o3 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
(S,X,ts3) -tree tk3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
a is Element of the carrier' of S
[a, the carrier of S] is V26() set
{a, the carrier of S} is non empty set
{a} is non empty set
{{a, the carrier of S},{a}} is non empty set
Args (a,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Den (a,(S,X)) is Relation-like Args (a,(S,X)) -defined Result (a,(S,X)) -valued Function-like V29( Args (a,(S,X)), Result (a,(S,X))) Element of bool [:(Args (a,(S,X))),(Result (a,(S,X))):]
Result (a,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (a,(S,X))),(Result (a,(S,X))):] is non empty Relation-like set
bool [:(Args (a,(S,X))),(Result (a,(S,X))):] is non empty set
(Den (a,(S,X))) . tk3 is set
the_result_sort_of a is Element of the carrier of S
(S,X,(S,X,ts3),tak) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
dom tak is Element of bool K32()
{ [((Den (b₁,(S,X))) . b₂),b₃] where b₁ is Element of the carrier' of S, b₂ is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (b₁,(S,X)), b₃ is Element of the carrier of S : ( ex b₄ being Element of the carrier' of S st
( (S,X,ts3) = [b₄, the carrier of S] & b₄ ~= b₁ & len (the_arity_of b₄) = len (the_arity_of b₁) & the_result_sort_of b₄ <= b₃ & the_result_sort_of b₁ <= b₃ ) & ex b₄ being Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S * st
( dom b₄ = dom tak & ( for b₅ being V4() V5() V6() V10() set holds
( not b₅ in dom tak or [(b₂ . b₅),(b₄ /. b₅)] in tak . b₅ ) ) ) ) } is set
n is Element of the carrier' of S
[n, the carrier of S] is V26() set
{n, the carrier of S} is non empty set
{n} is non empty set
{{n, the carrier of S},{n}} is non empty set
the_arity_of n is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of n) is V4() V5() V6() V10() Element of K32()
the_result_sort_of n is Element of the carrier of S
n is Element of the carrier' of S
[n, the carrier of S] is V26() set
{n, the carrier of S} is non empty set
{n} is non empty set
{{n, the carrier of S},{n}} is non empty set
the_arity_of n is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of n) is V4() V5() V6() V10() Element of K32()
the_result_sort_of n is Element of the carrier of S
dom (the_arity_of t2) is Element of bool K32()
dom t1 is Element of bool K32()
proj2 tk3 is set
len tak is V4() V5() V6() V10() Element of K32()
len tk3 is V4() V5() V6() V10() Element of K32()
dom tk3 is Element of bool K32()
dom (the_arity_of ts3) is Element of bool K32()
dom o3 is Element of bool K32()
rt is set
s . rt is set
tak . rt is set
o3 . rt is set
t1 . rt is set
proj2 s is set
t2 . rt is Relation-like Function-like set
rt /. rt is Element of the carrier of S
[(t1 . rt),(rt /. rt)] is V26() set
{(t1 . rt),(rt /. rt)} is non empty set
{(t1 . rt)} is non empty set
{{(t1 . rt),(rt /. rt)},{(t1 . rt)}} is non empty set
b . rt is set
dom s is Element of bool K32()
s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[s,(rt /. rt)] is V26() set
{s,(rt /. rt)} is non empty set
{s} is non empty functional set
{{s,(rt /. rt)},{s}} is non empty set
t is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . t is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[t,(rt /. rt)] is V26() set
{t,(rt /. rt)} is non empty set
{t} is non empty functional set
{{t,(rt /. rt)},{t}} is non empty set
the Sorts of (S,X) . (rt /. rt) is non empty set
(S,X) . s is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
(S,X,s) is Element of the carrier of S
tk2 /. rt is Element of the carrier of S
[(o3 . rt),(tk2 /. rt)] is V26() set
{(o3 . rt),(tk2 /. rt)} is non empty set
{(o3 . rt)} is non empty set
{{(o3 . rt),(tk2 /. rt)},{(o3 . rt)}} is non empty set
s3 . rt is set
x is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[x,(tk2 /. rt)] is V26() set
{x,(tk2 /. rt)} is non empty set
{x} is non empty functional set
{{x,(tk2 /. rt)},{x}} is non empty set
[s,(tk2 /. rt)] is V26() set
{s,(tk2 /. rt)} is non empty set
{{s,(tk2 /. rt)},{s}} is non empty set
the Sorts of (S,X) . (tk2 /. rt) is non empty set
x1 is Element of the carrier of S
(S,X) . x is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[x,x1] is V26() set
{x,x1} is non empty set
{{x,x1},{x}} is non empty set
[(s . rt),x1] is V26() set
{(s . rt),x1} is non empty set
{(s . rt)} is non empty set
{{(s . rt),x1},{(s . rt)}} is non empty set
(S,X) . (s . rt) is set
[s,x1] is V26() set
{s,x1} is non empty set
{{s,x1},{s}} is non empty set
[t,x1] is V26() set
{t,x1} is non empty set
{{t,x1},{t}} is non empty set
[:(dom tak), the carrier of S:] is Relation-like set
bool [:(dom tak), the carrier of S:] is non empty set
rt is Relation-like dom tak -defined the carrier of S -valued Function-like V29( dom tak, the carrier of S) Element of bool [:(dom tak), the carrier of S:]
dom rt is Element of bool (dom tak)
bool (dom tak) is non empty set
s is V4() V5() V6() V10() set
Seg s is V34() V41(s) Element of bool K32()
proj2 rt is set
t is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
s is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom s is Element of bool K32()
x is V4() V5() V6() V10() set
s . x is set
s /. x is Element of the carrier of S
[(s . x),(s /. x)] is V26() set
{(s . x),(s /. x)} is non empty set
{(s . x)} is non empty set
{{(s . x),(s /. x)},{(s . x)}} is non empty set
tak . x is set
s . x is set
[(s . x),(s . x)] is V26() set
{(s . x),(s . x)} is non empty set
{{(s . x),(s . x)},{(s . x)}} is non empty set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
O1 is Element of the carrier of (S,X)
root-tree O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) . (root-tree O1) is set
(S,X,O1) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
{ [(root-tree O1),b₁] where b₁ is Element of the carrier of S : ex b₂ being Element of the carrier of S ex b₃ being set st
( b₃ in X . b₂ & O1 = [b₃,b₂] & b₂ <= b₁ ) } is set
R is Element of the carrier of S
[(root-tree O1),R] is V26() set
{(root-tree O1),R} is non empty set
{(root-tree O1)} is non empty functional set
{{(root-tree O1),R},{(root-tree O1)}} is non empty set
i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[i,R] is V26() set
{i,R} is non empty set
{i} is non empty functional set
{{i,R},{i}} is non empty set
s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[s,R] is V26() set
{s,R} is non empty set
{s} is non empty functional set
{{s,R},{s}} is non empty set
(S,X) . i is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
(S,X) . s is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
a is Element of the carrier of S
[(root-tree O1),a] is V26() set
{(root-tree O1),a} is non empty set
{{(root-tree O1),a},{(root-tree O1)}} is non empty set
ta is set
b is Element of the carrier of S
X . b is non empty set
[ta,b] is V26() set
{ta,b} is non empty set
{ta} is non empty set
{{ta,b},{ta}} is non empty set
a is Element of the carrier of S
[(root-tree O1),a] is V26() set
{(root-tree O1),a} is non empty set
{{(root-tree O1),a},{(root-tree O1)}} is non empty set
ta is set
b is Element of the carrier of S
X . b is non empty set
[ta,b] is V26() set
{ta,b} is non empty set
{ta} is non empty set
{{ta,b},{ta}} is non empty set
R is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
s is Element of the carrier of S
[R,s] is V26() set
{R,s} is non empty set
{R} is non empty functional set
{{R,s},{R}} is non empty set
O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . O1 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[i,s] is V26() set
{i,s} is non empty set
{i} is non empty functional set
{{i,s},{i}} is non empty set
(S,X) . R is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[O1,s] is V26() set
{O1,s} is non empty set
{O1} is non empty functional set
{{O1,s},{O1}} is non empty set
(S,X) . i is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
(S,X) is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,a₁] in (S,X) . b₂ } is set
P is non empty Relation-like the carrier of S -defined Function-like total set
O1 is set
P . O1 is set
the Sorts of (S,X) . O1 is set
[:( the Sorts of (S,X) . O1),( the Sorts of (S,X) . O1):] is Relation-like set
bool [:( the Sorts of (S,X) . O1),( the Sorts of (S,X) . O1):] is non empty set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,O1] in (S,X) . b₂ } is set
R is Element of the carrier of S
P . R is set
the Sorts of (S,X) . R is non empty set
[:( the Sorts of (S,X) . R),( the Sorts of (S,X) . R):] is non empty Relation-like set
i is set
s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[s,a] is V26() set
{s,a} is non empty functional set
{s} is non empty functional set
{{s,a},{s}} is non empty set
[s,R] is V26() set
{s,R} is non empty set
{{s,R},{s}} is non empty set
(S,X) . a is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[a,R] is V26() set
{a,R} is non empty set
{a} is non empty functional set
{{a,R},{a}} is non empty set
(S,X) . s is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
O1 is non empty Relation-like the carrier of S -defined Function-like total V33() ManySortedRelation of the Sorts of (S,X), the Sorts of (S,X)
R is Element of the carrier of S
i is Element of the carrier of S
the Sorts of (S,X) . R is non empty set
O1 . R is Relation-like the Sorts of (S,X) . R -defined the Sorts of (S,X) . R -valued Element of bool [:( the Sorts of (S,X) . R),( the Sorts of (S,X) . R):]
[:( the Sorts of (S,X) . R),( the Sorts of (S,X) . R):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . R),( the Sorts of (S,X) . R):] is non empty set
O1 . i is Relation-like the Sorts of (S,X) . i -defined the Sorts of (S,X) . i -valued Element of bool [:( the Sorts of (S,X) . i),( the Sorts of (S,X) . i):]
the Sorts of (S,X) . i is non empty set
[:( the Sorts of (S,X) . i),( the Sorts of (S,X) . i):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . i),( the Sorts of (S,X) . i):] is non empty set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,R] in (S,X) . b₂ } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,i] in (S,X) . b₂ } is set
s is set
a is set
[s,a] is V26() set
{s,a} is non empty set
{s} is non empty set
{{s,a},{s}} is non empty set
b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[b,ta] is V26() set
{b,ta} is non empty functional set
{b} is non empty functional set
{{b,ta},{b}} is non empty set
[b,R] is V26() set
{b,R} is non empty set
{{b,R},{b}} is non empty set
(S,X) . ta is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[b,i] is V26() set
{b,i} is non empty set
{{b,i},{b}} is non empty set
b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[b,ta] is V26() set
{b,ta} is non empty functional set
{b} is non empty functional set
{{b,ta},{b}} is non empty set
[b,i] is V26() set
{b,i} is non empty set
{{b,i},{b}} is non empty set
(S,X) . ta is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[b,R] is V26() set
{b,R} is non empty set
{{b,R},{b}} is non empty set
R is non empty Relation-like the carrier of S -defined Function-like total V33() OrderSortedRelation of (S,X)
i is set
the Sorts of (S,X) . i is set
[:( the Sorts of (S,X) . i),( the Sorts of (S,X) . i):] is Relation-like set
bool [:( the Sorts of (S,X) . i),( the Sorts of (S,X) . i):] is non empty set
R . i is set
s is Relation-like the Sorts of (S,X) . i -defined the Sorts of (S,X) . i -valued Element of bool [:( the Sorts of (S,X) . i),( the Sorts of (S,X) . i):]
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,i] in (S,X) . b₂ } is set
b is set
ta is set
[b,ta] is V26() set
{b,ta} is non empty set
{b} is non empty set
{{b,ta},{b}} is non empty set
[ta,b] is V26() set
{ta,b} is non empty set
{ta} is non empty set
{{ta,b},{ta}} is non empty set
a is Element of the carrier of S
tb is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[tb,t1] is V26() set
{tb,t1} is non empty functional set
{tb} is non empty functional set
{{tb,t1},{tb}} is non empty set
[tb,a] is V26() set
{tb,a} is non empty set
{{tb,a},{tb}} is non empty set
(S,X) . t1 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[t1,a] is V26() set
{t1,a} is non empty set
{t1} is non empty functional set
{{t1,a},{t1}} is non empty set
(S,X) . tb is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
b is set
ta is set
tb is set
[b,ta] is V26() set
{b,ta} is non empty set
{b} is non empty set
{{b,ta},{b}} is non empty set
[ta,tb] is V26() set
{ta,tb} is non empty set
{ta} is non empty set
{{ta,tb},{ta}} is non empty set
a is Element of the carrier of S
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[t1,t2] is V26() set
{t1,t2} is non empty functional set
{t1} is non empty functional set
{{t1,t2},{t1}} is non empty set
[t1,a] is V26() set
{t1,a} is non empty set
{{t1,a},{t1}} is non empty set
(S,X) . t2 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[t2,a] is V26() set
{t2,a} is non empty set
{t2} is non empty functional set
{{t2,a},{t2}} is non empty set
(S,X) . t1 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[t1,t2] is V26() set
{t1,t2} is non empty functional set
{t1} is non empty functional set
{{t1,t2},{t1}} is non empty set
[t1,a] is V26() set
{t1,a} is non empty set
{{t1,a},{t1}} is non empty set
(S,X) . t2 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[t2,a] is V26() set
{t2,a} is non empty set
{t2} is non empty functional set
{{t2,a},{t2}} is non empty set
[b,tb] is V26() set
{b,tb} is non empty set
{{b,tb},{b}} is non empty set
the Sorts of (S,X) . a is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : S₁[b₁,a] } is set
b is set
ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
ta . {} is set
[ta,a] is V26() set
{ta,a} is non empty set
{ta} is non empty functional set
{{ta,a},{ta}} is non empty set
(S,X) . ta is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[b,b] is V26() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
field s is set
dom s is Element of bool ( the Sorts of (S,X) . i)
bool ( the Sorts of (S,X) . i) is non empty set
i is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like OrderSortedRelation of (S,X)
s is set
i . s is set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,s] in (S,X) . b₂ } is set
t is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like OrderSortedRelation of (S,X)
tx is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like OrderSortedRelation of (S,X)
P is set
t . P is set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,P] in (S,X) . b₂ } is set
tx . P is set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
proj2 (S,X) is set
t is set
P is set
[t,P] is V26() set
{t,P} is non empty set
{t} is non empty set
{{t,P},{t}} is non empty set
tx is set
(S,X) . tx is set
dom (S,X) is functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
dom (S,X) is functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like OrderSortedRelation of (S,X)
(S,X) is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
x is non empty Element of K539(S)
CompClass ((S,X),x) is Relation-like K541(S, the Sorts of (S,X),x) -defined K541(S, the Sorts of (S,X),x) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),x),K541(S, the Sorts of (S,X),x):]
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
K541(S, the Sorts of (S,X),x) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in x } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in x } is set
[:K541(S, the Sorts of (S,X),x),K541(S, the Sorts of (S,X),x):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),x),K541(S, the Sorts of (S,X),x):] is non empty set
y is set
t is set
[y,t] is V26() set
{y,t} is non empty set
{y} is non empty set
{{y,t},{y}} is non empty set
(S,X) . t is set
tx is Element of the carrier of S
(S,X) . tx is Relation-like the Sorts of (S,X) . tx -defined the Sorts of (S,X) . tx -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . tx),( the Sorts of (S,X) . tx):]
the Sorts of (S,X) . tx is non empty set
[:( the Sorts of (S,X) . tx),( the Sorts of (S,X) . tx):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . tx),( the Sorts of (S,X) . tx):] is non empty set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,tx] in (S,X) . b₂ } is set
P is Element of the carrier of S
O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
R is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[O1,R] is V26() set
{O1,R} is non empty functional set
{O1} is non empty functional set
{{O1,R},{O1}} is non empty set
[O1,P] is V26() set
{O1,P} is non empty set
{{O1,P},{O1}} is non empty set
(S,X) . R is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[y,P] is V26() set
{y,P} is non empty set
{{y,P},{y}} is non empty set
tx is Element of the carrier of S
[y,tx] is V26() set
{y,tx} is non empty set
{{y,tx},{y}} is non empty set
P is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[P,O1] is V26() set
{P,O1} is non empty functional set
{P} is non empty functional set
{{P,O1},{P}} is non empty set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,tx] in (S,X) . b₂ } is set
(S,X) . tx is Relation-like the Sorts of (S,X) . tx -defined the Sorts of (S,X) . tx -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . tx),( the Sorts of (S,X) . tx):]
the Sorts of (S,X) . tx is non empty set
[:( the Sorts of (S,X) . tx),( the Sorts of (S,X) . tx):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . tx),( the Sorts of (S,X) . tx):] is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like OrderSortedRelation of (S,X)
(S,X) is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
x is Element of the carrier of S
the Sorts of (S,X) . x is non empty set
y is Element of the Sorts of (S,X) . x
OSClass ((S,X),y) is Element of OSClass ((S,X),x)
OSClass ((S,X),x) is non empty Element of bool (Class (CompClass ((S,X),(CComp x))))
CComp x is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),x) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp x)) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp x } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp x } is set
CompClass ((S,X),(CComp x)) is Relation-like K541(S, the Sorts of (S,X),(CComp x)) -defined K541(S, the Sorts of (S,X),(CComp x)) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp x)),K541(S, the Sorts of (S,X),(CComp x)):]
[:K541(S, the Sorts of (S,X),(CComp x)),K541(S, the Sorts of (S,X),(CComp x)):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp x)),K541(S, the Sorts of (S,X),(CComp x)):] is non empty set
Class (CompClass ((S,X),(CComp x))) is a_partition of K541(S, the Sorts of (S,X),(CComp x))
bool (Class (CompClass ((S,X),(CComp x)))) is non empty set
Class ((CompClass ((S,X),(CComp x))),y) is Element of bool K541(S, the Sorts of (S,X),(CComp x))
bool K541(S, the Sorts of (S,X),(CComp x)) is non empty set
(S,X) . y is set
proj1 ((S,X) . y) is set
O1 is set
[O1,y] is V26() set
{O1,y} is non empty set
{O1} is non empty set
{{O1,y},{O1}} is non empty set
R is Element of the carrier of S
[O1,R] is V26() set
{O1,R} is non empty set
{{O1,R},{O1}} is non empty set
R is set
[O1,R] is V26() set
{O1,R} is non empty set
{{O1,R},{O1}} is non empty set
s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,s) is Element of the carrier of S
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
i is Element of the carrier of S
[a,i] is V26() set
{a,i} is non empty set
{a} is non empty functional set
{{a,i},{a}} is non empty set
(S,X) . s is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[s,i] is V26() set
{s,i} is non empty set
{s} is non empty functional set
{{s,i},{s}} is non empty set
the Sorts of (S,X) . R is set
CComp i is non empty Element of K539(S)
Class ((Path_Rel S),i) is Element of bool the carrier of S
CComp (S,X,s) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,s)) is Element of bool the carrier of S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like OrderSortedRelation of (S,X)
x is non empty Relation-like the carrier of S -defined Function-like total V33() ManySortedRelation of the Sorts of (S,X), the Sorts of (S,X)
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
(S,X) is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
s is non empty Relation-like the carrier of S -defined Function-like total V33() ManySortedRelation of the Sorts of (S,X), the Sorts of (S,X)
a is non empty Relation-like the carrier of S -defined Function-like total V33() ManySortedRelation of the Sorts of (S,X), the Sorts of (S,X)
b is Element of the carrier of (S,X)
ta is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots ta is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
proj2 ta is set
b -tree ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
{ b₁ where b₁ is Element of the carrier of (S,X) : ex b₂ being Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set st b₁ ==> b₂ } is set
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
tb is Element of NonTerminals (S,X)
t2 is set
[(b -tree ta),t2] is V26() set
{(b -tree ta),t2} is non empty set
{(b -tree ta)} is non empty functional set
{{(b -tree ta),t2},{(b -tree ta)}} is non empty set
t1 is Element of the carrier of S
s . t1 is Relation-like the Sorts of (S,X) . t1 -defined the Sorts of (S,X) . t1 -valued Element of bool [:( the Sorts of (S,X) . t1),( the Sorts of (S,X) . t1):]
the Sorts of (S,X) . t1 is non empty set
[:( the Sorts of (S,X) . t1),( the Sorts of (S,X) . t1):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . t1),( the Sorts of (S,X) . t1):] is non empty set
a . t1 is Relation-like the Sorts of (S,X) . t1 -defined the Sorts of (S,X) . t1 -valued Element of bool [:( the Sorts of (S,X) . t1),( the Sorts of (S,X) . t1):]
[b,(roots ta)] is V26() set
{b,(roots ta)} is non empty set
{b} is non empty set
{{b,(roots ta)},{b}} is non empty set
the Rules of (S,X) is Relation-like the carrier of (S,X) -defined the carrier of (S,X) * -valued Element of bool [: the carrier of (S,X),( the carrier of (S,X) *):]
the carrier of (S,X) * is non empty functional FinSequence-membered M10( the carrier of (S,X))
[: the carrier of (S,X),( the carrier of (S,X) *):] is non empty Relation-like set
bool [: the carrier of (S,X),( the carrier of (S,X) *):] is non empty set
t2 is Element of [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))
t2 is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
[t2,t2] is V26() set
{t2,t2} is non empty set
{t2} is non empty set
{{t2,t2},{t2}} is non empty set
s3 is Element of the carrier' of S
o1 is Element of { the carrier of S}
[s3,o1] is V26() set
{s3,o1} is non empty set
{s3} is non empty set
{{s3,o1},{s3}} is non empty set
t1 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding SubtreeSeq of tb
b -tree t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(b -tree t1) . {} is set
[s3, the carrier of S] is V26() set
{s3, the carrier of S} is non empty set
{{s3, the carrier of S},{s3}} is non empty set
(S,X,s3) is Element of NonTerminals (S,X)
tb -tree t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
Args (s3,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (s3,(S,X)) is Relation-like Args (s3,(S,X)) -defined Result (s3,(S,X)) -valued Function-like V29( Args (s3,(S,X)), Result (s3,(S,X))) Element of bool [:(Args (s3,(S,X))),(Result (s3,(S,X))):]
Result (s3,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (s3,(S,X))),(Result (s3,(S,X))):] is non empty Relation-like set
bool [:(Args (s3,(S,X))),(Result (s3,(S,X))):] is non empty set
ts3 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding SubtreeSeq of (S,X,s3)
(S,X,s3) -tree ts3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
roots ts3 is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
(Den (s3,(S,X))) . ts3 is set
(S,X,t1) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= t1 & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= t1 ) ) } is set
o3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
o3 . {} is set
k is Element of the carrier of S
tk1 is set
X . k is non empty set
[tk1,k] is V26() set
{tk1,k} is non empty set
{tk1} is non empty set
{{tk1,k},{tk1}} is non empty set
root-tree [tk1,k] is Relation-like Function-like DecoratedTree-like set
k is Element of the carrier of S
tk1 is set
X . k is non empty set
[tk1,k] is V26() set
{tk1,k} is non empty set
{tk1} is non empty set
{{tk1,k},{tk1}} is non empty set
root-tree [tk1,k] is Relation-like Function-like DecoratedTree-like set
tk3 is Element of the carrier' of S
[tk3, the carrier of S] is V26() set
{tk3, the carrier of S} is non empty set
{tk3} is non empty set
{{tk3, the carrier of S},{tk3}} is non empty set
the_result_sort_of tk3 is Element of the carrier of S
k is Element of the carrier' of S
[k, the carrier of S] is V26() set
{k, the carrier of S} is non empty set
{k} is non empty set
{{k, the carrier of S},{k}} is non empty set
the_result_sort_of k is Element of the carrier of S
(S,X,k) is Element of NonTerminals (S,X)
Args (k,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Den (k,(S,X)) is Relation-like Args (k,(S,X)) -defined Result (k,(S,X)) -valued Function-like V29( Args (k,(S,X)), Result (k,(S,X))) Element of bool [:(Args (k,(S,X))),(Result (k,(S,X))):]
Result (k,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (k,(S,X))),(Result (k,(S,X))):] is non empty Relation-like set
bool [:(Args (k,(S,X))),(Result (k,(S,X))):] is non empty set
tk1 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding SubtreeSeq of (S,X,k)
(S,X,k) -tree tk1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
roots tk1 is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
(Den (k,(S,X))) . tk1 is set
tk3 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding SubtreeSeq of (S,X,s3)
(S,X,s3) -tree tk3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
roots tk3 is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
(Den (s3,(S,X))) . tk3 is set
the_arity_of s3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of s3) is V4() V5() V6() V10() Element of K32()
the_arity_of k is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of k) is V4() V5() V6() V10() Element of K32()
tak is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (s3,(S,X))
dom tak is Element of bool K32()
tk2 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (k,(S,X))
rt is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom rt is Element of bool K32()
a is V4() V5() V6() V10() set
tak . a is set
tk2 . a is set
[(tak . a),(tk2 . a)] is V26() set
{(tak . a),(tk2 . a)} is non empty set
{(tak . a)} is non empty set
{{(tak . a),(tk2 . a)},{(tak . a)}} is non empty set
rt /. a is Element of the carrier of S
a . (rt /. a) is Relation-like the Sorts of (S,X) . (rt /. a) -defined the Sorts of (S,X) . (rt /. a) -valued Element of bool [:( the Sorts of (S,X) . (rt /. a)),( the Sorts of (S,X) . (rt /. a)):]
the Sorts of (S,X) . (rt /. a) is non empty set
[:( the Sorts of (S,X) . (rt /. a)),( the Sorts of (S,X) . (rt /. a)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (rt /. a)),( the Sorts of (S,X) . (rt /. a)):] is non empty set
n is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[n,(tk2 . a)] is V26() set
{n,(tk2 . a)} is non empty set
{n} is non empty functional set
{{n,(tk2 . a)},{n}} is non empty set
s . (rt /. a) is Relation-like the Sorts of (S,X) . (rt /. a) -defined the Sorts of (S,X) . (rt /. a) -valued Element of bool [:( the Sorts of (S,X) . (rt /. a)),( the Sorts of (S,X) . (rt /. a)):]
the_result_sort_of s3 is Element of the carrier of S
k is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
k . {} is set
tk1 is Element of the carrier of S
tk3 is set
X . tk1 is non empty set
[tk3,tk1] is V26() set
{tk3,tk1} is non empty set
{tk3} is non empty set
{{tk3,tk1},{tk3}} is non empty set
root-tree [tk3,tk1] is Relation-like Function-like DecoratedTree-like set
tk1 is Element of the carrier of S
tk3 is set
X . tk1 is non empty set
[tk3,tk1] is V26() set
{tk3,tk1} is non empty set
{tk3} is non empty set
{{tk3,tk1},{tk3}} is non empty set
root-tree [tk3,tk1] is Relation-like Function-like DecoratedTree-like set
tak is Element of the carrier' of S
[tak, the carrier of S] is V26() set
{tak, the carrier of S} is non empty set
{tak} is non empty set
{{tak, the carrier of S},{tak}} is non empty set
the_result_sort_of tak is Element of the carrier of S
tk1 is Element of the carrier' of S
[tk1, the carrier of S] is V26() set
{tk1, the carrier of S} is non empty set
{tk1} is non empty set
{{tk1, the carrier of S},{tk1}} is non empty set
the_result_sort_of tk1 is Element of the carrier of S
(S,X,tk1) is Element of NonTerminals (S,X)
Args (tk1,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Den (tk1,(S,X)) is Relation-like Args (tk1,(S,X)) -defined Result (tk1,(S,X)) -valued Function-like V29( Args (tk1,(S,X)), Result (tk1,(S,X))) Element of bool [:(Args (tk1,(S,X))),(Result (tk1,(S,X))):]
Result (tk1,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (tk1,(S,X))),(Result (tk1,(S,X))):] is non empty Relation-like set
bool [:(Args (tk1,(S,X))),(Result (tk1,(S,X))):] is non empty set
tk3 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding SubtreeSeq of (S,X,tk1)
(S,X,tk1) -tree tk3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
roots tk3 is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
(Den (tk1,(S,X))) . tk3 is set
the_arity_of tk1 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of tk1) is V4() V5() V6() V10() Element of K32()
o3 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (s3,(S,X))
dom o3 is Element of bool K32()
tak is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (tk1,(S,X))
tk2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom tk2 is Element of bool K32()
rt is V4() V5() V6() V10() set
o3 . rt is set
tak . rt is set
[(o3 . rt),(tak . rt)] is V26() set
{(o3 . rt),(tak . rt)} is non empty set
{(o3 . rt)} is non empty set
{{(o3 . rt),(tak . rt)},{(o3 . rt)}} is non empty set
tk2 /. rt is Element of the carrier of S
s . (tk2 /. rt) is Relation-like the Sorts of (S,X) . (tk2 /. rt) -defined the Sorts of (S,X) . (tk2 /. rt) -valued Element of bool [:( the Sorts of (S,X) . (tk2 /. rt)),( the Sorts of (S,X) . (tk2 /. rt)):]
the Sorts of (S,X) . (tk2 /. rt) is non empty set
[:( the Sorts of (S,X) . (tk2 /. rt)),( the Sorts of (S,X) . (tk2 /. rt)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (tk2 /. rt)),( the Sorts of (S,X) . (tk2 /. rt)):] is non empty set
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[a,(tak . rt)] is V26() set
{a,(tak . rt)} is non empty set
{a} is non empty functional set
{{a,(tak . rt)},{a}} is non empty set
a . (tk2 /. rt) is Relation-like the Sorts of (S,X) . (tk2 /. rt) -defined the Sorts of (S,X) . (tk2 /. rt) -valued Element of bool [:( the Sorts of (S,X) . (tk2 /. rt)),( the Sorts of (S,X) . (tk2 /. rt)):]
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
b is Element of the carrier of (S,X)
root-tree b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
tb is set
ta is Element of the carrier of S
X . ta is non empty set
[tb,ta] is V26() set
{tb,ta} is non empty set
{tb} is non empty set
{{tb,ta},{tb}} is non empty set
t1 is set
[(root-tree b),t1] is V26() set
{(root-tree b),t1} is non empty set
{(root-tree b)} is non empty functional set
{{(root-tree b),t1},{(root-tree b)}} is non empty set
t2 is Element of the carrier of S
s . t2 is Relation-like the Sorts of (S,X) . t2 -defined the Sorts of (S,X) . t2 -valued Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of (S,X) . t2):]
the Sorts of (S,X) . t2 is non empty set
[:( the Sorts of (S,X) . t2),( the Sorts of (S,X) . t2):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . t2),( the Sorts of (S,X) . t2):] is non empty set
a . t2 is Relation-like the Sorts of (S,X) . t2 -defined the Sorts of (S,X) . t2 -valued Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of (S,X) . t2):]
root-tree [tb,ta] is Relation-like Function-like DecoratedTree-like set
b is set
s . b is set
a . b is set
ta is Element of the carrier of S
s . ta is Relation-like the Sorts of (S,X) . ta -defined the Sorts of (S,X) . ta -valued Element of bool [:( the Sorts of (S,X) . ta),( the Sorts of (S,X) . ta):]
the Sorts of (S,X) . ta is non empty set
[:( the Sorts of (S,X) . ta),( the Sorts of (S,X) . ta):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . ta),( the Sorts of (S,X) . ta):] is non empty set
a . ta is Relation-like the Sorts of (S,X) . ta -defined the Sorts of (S,X) . ta -valued Element of bool [:( the Sorts of (S,X) . ta),( the Sorts of (S,X) . ta):]
tb is set
t1 is set
[tb,t1] is V26() set
{tb,t1} is non empty set
{tb} is non empty set
{{tb,t1},{tb}} is non empty set
(S,X,ta) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= ta & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= ta ) ) } is set
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t1 is Element of the carrier of S
t2 is set
X . t1 is non empty set
[t2,t1] is V26() set
{t2,t1} is non empty set
{t2} is non empty set
{{t2,t1},{t2}} is non empty set
root-tree [t2,t1] is Relation-like Function-like DecoratedTree-like set
t2 is Element of the carrier' of S
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
t2 . {} is set
the_result_sort_of t2 is Element of the carrier of S
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t1 is Element of the carrier of S
t2 is set
X . t1 is non empty set
[t2,t1] is V26() set
{t2,t1} is non empty set
{t2} is non empty set
{{t2,t1},{t2}} is non empty set
root-tree [t2,t1] is Relation-like Function-like DecoratedTree-like set
t2 is Element of the carrier' of S
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
t2 . {} is set
the_result_sort_of t2 is Element of the carrier of S
s is Element of the carrier' of S
Args (s,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
a is Element of the carrier' of S
Args (a,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Result (s,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
Den (s,(S,X)) is Relation-like Args (s,(S,X)) -defined Result (s,(S,X)) -valued Function-like V29( Args (s,(S,X)), Result (s,(S,X))) Element of bool [:(Args (s,(S,X))),(Result (s,(S,X))):]
[:(Args (s,(S,X))),(Result (s,(S,X))):] is non empty Relation-like set
bool [:(Args (s,(S,X))),(Result (s,(S,X))):] is non empty set
Result (a,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (a,(S,X)) is Relation-like Args (a,(S,X)) -defined Result (a,(S,X)) -valued Function-like V29( Args (a,(S,X)), Result (a,(S,X))) Element of bool [:(Args (a,(S,X))),(Result (a,(S,X))):]
[:(Args (a,(S,X))),(Result (a,(S,X))):] is non empty Relation-like set
bool [:(Args (a,(S,X))),(Result (a,(S,X))):] is non empty set
the_arity_of s is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of s) is V4() V5() V6() V10() Element of K32()
the_arity_of a is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of a) is V4() V5() V6() V10() Element of K32()
the_result_sort_of s is Element of the carrier of S
the_result_sort_of a is Element of the carrier of S
b is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (s,(S,X))
(Den (s,(S,X))) . b is Element of Result (s,(S,X))
dom b is Element of bool K32()
ta is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (a,(S,X))
(Den (a,(S,X))) . ta is Element of Result (a,(S,X))
[((Den (s,(S,X))) . b),((Den (a,(S,X))) . ta)] is V26() set
{((Den (s,(S,X))) . b),((Den (a,(S,X))) . ta)} is non empty set
{((Den (s,(S,X))) . b)} is non empty set
{{((Den (s,(S,X))) . b),((Den (a,(S,X))) . ta)},{((Den (s,(S,X))) . b)}} is non empty set
tb is Element of the carrier of S
(S,X) . tb is set
dom (the_arity_of a) is Element of bool K32()
dom ta is Element of bool K32()
(S,X) . tb is Relation-like the Sorts of (S,X) . tb -defined the Sorts of (S,X) . tb -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . tb),( the Sorts of (S,X) . tb):]
the Sorts of (S,X) . tb is non empty set
[:( the Sorts of (S,X) . tb),( the Sorts of (S,X) . tb):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . tb),( the Sorts of (S,X) . tb):] is non empty set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,tb] in (S,X) . b₂ } is set
dom (the_arity_of s) is Element of bool K32()
t2 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
proj2 t2 is set
(S,X) * t2 is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like Element of (bool [:(TS (S,X)), the carrier of S:]) *
(bool [:(TS (S,X)), the carrier of S:]) * is non empty functional FinSequence-membered M10( bool [:(TS (S,X)), the carrier of S:])
dom (S,X) is functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
t1 is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of bool [:(TS (S,X)), the carrier of S:]
len t1 is V4() V5() V6() V10() Element of K32()
len t2 is V4() V5() V6() V10() Element of K32()
dom t1 is Element of bool K32()
dom t2 is Element of bool K32()
(S,X,s) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
[s, the carrier of S] is V26() set
{s, the carrier of S} is non empty set
{s} is non empty set
{{s, the carrier of S},{s}} is non empty set
roots b is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
(S,X,s) -tree t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) . ((S,X,s) -tree t2) is set
(S,X,(S,X,s),t1) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
{ [((Den (b₁,(S,X))) . b₂),b₃] where b₁ is Element of the carrier' of S, b₂ is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (b₁,(S,X)), b₃ is Element of the carrier of S : ( ex b₄ being Element of the carrier' of S st
( (S,X,s) = [b₄, the carrier of S] & b₄ ~= b₁ & len (the_arity_of b₄) = len (the_arity_of b₁) & the_result_sort_of b₄ <= b₃ & the_result_sort_of b₁ <= b₃ ) & ex b₄ being Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S * st
( dom b₄ = dom t1 & ( for b₅ being V4() V5() V6() V10() set holds
( not b₅ in dom t1 or [(b₂ . b₅),(b₄ /. b₅)] in t1 . b₅ ) ) ) ) } is set
(S,X,a) is Element of NonTerminals (S,X)
[a, the carrier of S] is V26() set
{a, the carrier of S} is non empty set
{a} is non empty set
{{a, the carrier of S},{a}} is non empty set
roots ta is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
t1 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
(S,X,a) -tree t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) . a is Relation-like ( the Arity of S * ((S,X) #)) . a -defined ( the ResultSort of S * (S,X)) . a -valued Function-like V29(( the Arity of S * ((S,X) #)) . a,( the ResultSort of S * (S,X)) . a) Element of bool [:(( the Arity of S * ((S,X) #)) . a),(( the ResultSort of S * (S,X)) . a):]
( the Arity of S * ((S,X) #)) . a is set
( the ResultSort of S * (S,X)) . a is non empty set
[:(( the Arity of S * ((S,X) #)) . a),(( the ResultSort of S * (S,X)) . a):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . a),(( the ResultSort of S * (S,X)) . a):] is non empty set
((S,X) . a) . ta is set
(S,X,a) is Relation-like ( the Arity of S * ((S,X) #)) . a -defined ( the ResultSort of S * (S,X)) . a -valued Function-like V29(( the Arity of S * ((S,X) #)) . a,( the ResultSort of S * (S,X)) . a) Element of bool [:(( the Arity of S * ((S,X) #)) . a),(( the ResultSort of S * (S,X)) . a):]
(S,X,a) . t1 is set
(S,X) . s is Relation-like ( the Arity of S * ((S,X) #)) . s -defined ( the ResultSort of S * (S,X)) . s -valued Function-like V29(( the Arity of S * ((S,X) #)) . s,( the ResultSort of S * (S,X)) . s) Element of bool [:(( the Arity of S * ((S,X) #)) . s),(( the ResultSort of S * (S,X)) . s):]
( the Arity of S * ((S,X) #)) . s is set
( the ResultSort of S * (S,X)) . s is non empty set
[:(( the Arity of S * ((S,X) #)) . s),(( the ResultSort of S * (S,X)) . s):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . s),(( the ResultSort of S * (S,X)) . s):] is non empty set
((S,X) . s) . b is set
(S,X,s) is Relation-like ( the Arity of S * ((S,X) #)) . s -defined ( the ResultSort of S * (S,X)) . s -valued Function-like V29(( the Arity of S * ((S,X) #)) . s,( the ResultSort of S * (S,X)) . s) Element of bool [:(( the Arity of S * ((S,X) #)) . s),(( the ResultSort of S * (S,X)) . s):]
(S,X,s) . t2 is set
proj2 t1 is set
s3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
o1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[s3,o1] is V26() set
{s3,o1} is non empty functional set
{s3} is non empty functional set
{{s3,o1},{s3}} is non empty set
[s3,tb] is V26() set
{s3,tb} is non empty set
{{s3,tb},{s3}} is non empty set
(S,X) . o1 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[o1,tb] is V26() set
{o1,tb} is non empty set
{o1} is non empty functional set
{{o1,tb},{o1}} is non empty set
(S,X) . s3 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
ts3 is Element of the carrier' of S
Args (ts3,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Result (ts3,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (ts3,(S,X)) is Relation-like Args (ts3,(S,X)) -defined Result (ts3,(S,X)) -valued Function-like V29( Args (ts3,(S,X)), Result (ts3,(S,X))) Element of bool [:(Args (ts3,(S,X))),(Result (ts3,(S,X))):]
[:(Args (ts3,(S,X))),(Result (ts3,(S,X))):] is non empty Relation-like set
bool [:(Args (ts3,(S,X))),(Result (ts3,(S,X))):] is non empty set
o3 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (ts3,(S,X))
(Den (ts3,(S,X))) . o3 is Element of Result (ts3,(S,X))
k is Element of the carrier of S
[((Den (ts3,(S,X))) . o3),k] is V26() set
{((Den (ts3,(S,X))) . o3),k} is non empty set
{((Den (ts3,(S,X))) . o3)} is non empty set
{{((Den (ts3,(S,X))) . o3),k},{((Den (ts3,(S,X))) . o3)}} is non empty set
the_arity_of ts3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of ts3) is V4() V5() V6() V10() Element of K32()
the_result_sort_of ts3 is Element of the carrier of S
tk1 is Element of the carrier' of S
[tk1, the carrier of S] is V26() set
{tk1, the carrier of S} is non empty set
{tk1} is non empty set
{{tk1, the carrier of S},{tk1}} is non empty set
the_arity_of tk1 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of tk1) is V4() V5() V6() V10() Element of K32()
the_result_sort_of tk1 is Element of the carrier of S
tk1 is Element of the carrier' of S
[tk1, the carrier of S] is V26() set
{tk1, the carrier of S} is non empty set
{tk1} is non empty set
{{tk1, the carrier of S},{tk1}} is non empty set
the_arity_of tk1 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of tk1) is V4() V5() V6() V10() Element of K32()
the_result_sort_of tk1 is Element of the carrier of S
(S,X,ts3) is Element of NonTerminals (S,X)
[ts3, the carrier of S] is V26() set
{ts3, the carrier of S} is non empty set
{ts3} is non empty set
{{ts3, the carrier of S},{ts3}} is non empty set
roots o3 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
(S,X) . ts3 is Relation-like ( the Arity of S * ((S,X) #)) . ts3 -defined ( the ResultSort of S * (S,X)) . ts3 -valued Function-like V29(( the Arity of S * ((S,X) #)) . ts3,( the ResultSort of S * (S,X)) . ts3) Element of bool [:(( the Arity of S * ((S,X) #)) . ts3),(( the ResultSort of S * (S,X)) . ts3):]
( the Arity of S * ((S,X) #)) . ts3 is set
( the ResultSort of S * (S,X)) . ts3 is non empty set
[:(( the Arity of S * ((S,X) #)) . ts3),(( the ResultSort of S * (S,X)) . ts3):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . ts3),(( the ResultSort of S * (S,X)) . ts3):] is non empty set
((S,X) . ts3) . o3 is set
(S,X,ts3) is Relation-like ( the Arity of S * ((S,X) #)) . ts3 -defined ( the ResultSort of S * (S,X)) . ts3 -valued Function-like V29(( the Arity of S * ((S,X) #)) . ts3,( the ResultSort of S * (S,X)) . ts3) Element of bool [:(( the Arity of S * ((S,X) #)) . ts3),(( the ResultSort of S * (S,X)) . ts3):]
tk3 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
(S,X,ts3) . tk3 is set
(S,X,ts3) -tree tk3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
tak is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom tak is Element of bool K32()
tak is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom tak is Element of bool K32()
tk2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom tk2 is Element of bool K32()
rt is V4() V5() V6() V10() set
t2 . rt is Relation-like Function-like set
t1 . rt is Relation-like Function-like set
o3 . rt is set
tk2 /. rt is Element of the carrier of S
[(o3 . rt),(tk2 /. rt)] is V26() set
{(o3 . rt),(tk2 /. rt)} is non empty set
{(o3 . rt)} is non empty set
{{(o3 . rt),(tk2 /. rt)},{(o3 . rt)}} is non empty set
t1 . rt is set
[(t1 . rt),(tk2 /. rt)] is V26() set
{(t1 . rt),(tk2 /. rt)} is non empty set
{(t1 . rt)} is non empty functional set
{{(t1 . rt),(tk2 /. rt)},{(t1 . rt)}} is non empty set
(S,X) . (t2 . rt) is set
n is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[n,(tk2 /. rt)] is V26() set
{n,(tk2 /. rt)} is non empty set
{n} is non empty functional set
{{n,(tk2 /. rt)},{n}} is non empty set
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . a is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
(S,X) . (tk2 /. rt) is Relation-like the Sorts of (S,X) . (tk2 /. rt) -defined the Sorts of (S,X) . (tk2 /. rt) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (tk2 /. rt)),( the Sorts of (S,X) . (tk2 /. rt)):]
the Sorts of (S,X) . (tk2 /. rt) is non empty set
[:( the Sorts of (S,X) . (tk2 /. rt)),( the Sorts of (S,X) . (tk2 /. rt)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (tk2 /. rt)),( the Sorts of (S,X) . (tk2 /. rt)):] is non empty set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,(tk2 /. rt)] in (S,X) . b₂ } is set
b . rt is set
ta . rt is set
[(b . rt),(ta . rt)] is V26() set
{(b . rt),(ta . rt)} is non empty set
{(b . rt)} is non empty set
{{(b . rt),(ta . rt)},{(b . rt)}} is non empty set
s3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom s3 is Element of bool K32()
s3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom s3 is Element of bool K32()
o1 is V4() V5() V6() V10() set
ta . o1 is set
s3 /. o1 is Element of the carrier of S
[(ta . o1),(s3 /. o1)] is V26() set
{(ta . o1),(s3 /. o1)} is non empty set
{(ta . o1)} is non empty set
{{(ta . o1),(s3 /. o1)},{(ta . o1)}} is non empty set
t1 . o1 is set
(S,X) . (s3 /. o1) is Relation-like the Sorts of (S,X) . (s3 /. o1) -defined the Sorts of (S,X) . (s3 /. o1) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (s3 /. o1)),( the Sorts of (S,X) . (s3 /. o1)):]
the Sorts of (S,X) . (s3 /. o1) is non empty set
[:( the Sorts of (S,X) . (s3 /. o1)),( the Sorts of (S,X) . (s3 /. o1)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (s3 /. o1)),( the Sorts of (S,X) . (s3 /. o1)):] is non empty set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,(s3 /. o1)] in (S,X) . b₂ } is set
b . o1 is set
[(b . o1),(ta . o1)] is V26() set
{(b . o1),(ta . o1)} is non empty set
{(b . o1)} is non empty set
{{(b . o1),(ta . o1)},{(b . o1)}} is non empty set
ts3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
o3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[ts3,o3] is V26() set
{ts3,o3} is non empty functional set
{ts3} is non empty functional set
{{ts3,o3},{ts3}} is non empty set
[ts3,(s3 /. o1)] is V26() set
{ts3,(s3 /. o1)} is non empty set
{{ts3,(s3 /. o1)},{ts3}} is non empty set
(S,X) . o3 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[o3,(s3 /. o1)] is V26() set
{o3,(s3 /. o1)} is non empty set
{o3} is non empty functional set
{{o3,(s3 /. o1)},{o3}} is non empty set
(S,X) . ts3 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[((Den (a,(S,X))) . ta),tb] is V26() set
{((Den (a,(S,X))) . ta),tb} is non empty set
{((Den (a,(S,X))) . ta)} is non empty set
{{((Den (a,(S,X))) . ta),tb},{((Den (a,(S,X))) . ta)}} is non empty set
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[t2,tb] is V26() set
{t2,tb} is non empty set
{t2} is non empty functional set
{{t2,tb},{t2}} is non empty set
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . t2 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
s is Element of the carrier of S
X . s is non empty set
a is Element of the carrier of S
(S,X) . a is set
b is set
[b,s] is V26() set
{b,s} is non empty set
{b} is non empty set
{{b,s},{b}} is non empty set
root-tree [b,s] is Relation-like Function-like DecoratedTree-like set
[(root-tree [b,s]),(root-tree [b,s])] is V26() set
{(root-tree [b,s]),(root-tree [b,s])} is non empty functional set
{(root-tree [b,s])} is non empty functional set
{{(root-tree [b,s]),(root-tree [b,s])},{(root-tree [b,s])}} is non empty set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
(S,X) . a is Relation-like the Sorts of (S,X) . a -defined the Sorts of (S,X) . a -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . a),( the Sorts of (S,X) . a):]
the Sorts of (S,X) . a is non empty set
[:( the Sorts of (S,X) . a),( the Sorts of (S,X) . a):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . a),( the Sorts of (S,X) . a):] is non empty set
{ [b₁,b₂] where b₁, b₂ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : [b₁,a] in (S,X) . b₂ } is set
the Sorts of (S,X) . s is non empty set
ta is Element of Terminals (S,X)
root-tree ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[(root-tree ta),s] is V26() set
{(root-tree ta),s} is non empty set
{(root-tree ta)} is non empty functional set
{{(root-tree ta),s},{(root-tree ta)}} is non empty set
(S,X) . (root-tree ta) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
[(root-tree ta),a] is V26() set
{(root-tree ta),a} is non empty set
{{(root-tree ta),a},{(root-tree ta)}} is non empty set
tb is set
[(root-tree [b,s]),tb] is V26() set
{(root-tree [b,s]),tb} is non empty set
{{(root-tree [b,s]),tb},{(root-tree [b,s])}} is non empty set
[tb,(root-tree [b,s])] is V26() set
{tb,(root-tree [b,s])} is non empty set
{tb} is non empty set
{{tb,(root-tree [b,s])},{tb}} is non empty set
field ((S,X) . a) is set
(S,X,ta) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
root-tree ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
{ [(root-tree ta),b₁] where b₁ is Element of the carrier of S : ex b₂ being Element of the carrier of S ex b₃ being set st
( b₃ in X . b₂ & ta = [b₃,b₂] & b₂ <= b₁ ) } is set
{ [(root-tree ta),b₁] where b₁ is Element of the carrier of S : ex b₂ being Element of the carrier of S ex b₃ being set st
( b₃ in X . b₂ & ta = [b₃,b₂] & b₂ <= b₁ ) } is set
[tb,(root-tree ta)] is V26() set
{tb,(root-tree ta)} is non empty set
{{tb,(root-tree ta)},{tb}} is non empty set
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
[t1,t2] is V26() set
{t1,t2} is non empty functional set
{t1} is non empty functional set
{{t1,t2},{t1}} is non empty set
[t1,a] is V26() set
{t1,a} is non empty set
{{t1,a},{t1}} is non empty set
(S,X) . t2 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
t1 is Element of the carrier of S
[(root-tree ta),t1] is V26() set
{(root-tree ta),t1} is non empty set
{{(root-tree ta),t1},{(root-tree ta)}} is non empty set
t2 is set
t2 is Element of the carrier of S
X . t2 is non empty set
[t2,t2] is V26() set
{t2,t2} is non empty set
{t2} is non empty set
{{t2,t2},{t2}} is non empty set
tb is Element of the carrier' of S
Args (tb,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
t1 is Element of the carrier' of S
Args (t1,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
t2 is Element of the carrier' of S
Args (t2,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
s3 is Element of the carrier' of S
Args (s3,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
b is set
s is Element of the carrier of S
X . s is non empty set
a is Element of the carrier of S
[b,s] is V26() set
{b,s} is non empty set
{b} is non empty set
{{b,s},{b}} is non empty set
root-tree [b,s] is Relation-like Function-like DecoratedTree-like set
[(root-tree [b,s]),(root-tree [b,s])] is V26() set
{(root-tree [b,s]),(root-tree [b,s])} is non empty functional set
{(root-tree [b,s])} is non empty functional set
{{(root-tree [b,s]),(root-tree [b,s])},{(root-tree [b,s])}} is non empty set
x . a is Relation-like the Sorts of (S,X) . a -defined the Sorts of (S,X) . a -valued Element of bool [:( the Sorts of (S,X) . a),( the Sorts of (S,X) . a):]
the Sorts of (S,X) . a is non empty set
[:( the Sorts of (S,X) . a),( the Sorts of (S,X) . a):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . a),( the Sorts of (S,X) . a):] is non empty set
ta is set
[(root-tree [b,s]),ta] is V26() set
{(root-tree [b,s]),ta} is non empty set
{{(root-tree [b,s]),ta},{(root-tree [b,s])}} is non empty set
[ta,(root-tree [b,s])] is V26() set
{ta,(root-tree [b,s])} is non empty set
{ta} is non empty set
{{ta,(root-tree [b,s])},{ta}} is non empty set
Result (tb,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
Den (tb,(S,X)) is Relation-like Args (tb,(S,X)) -defined Result (tb,(S,X)) -valued Function-like V29( Args (tb,(S,X)), Result (tb,(S,X))) Element of bool [:(Args (tb,(S,X))),(Result (tb,(S,X))):]
[:(Args (tb,(S,X))),(Result (tb,(S,X))):] is non empty Relation-like set
bool [:(Args (tb,(S,X))),(Result (tb,(S,X))):] is non empty set
t2 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (tb,(S,X))
(Den (tb,(S,X))) . t2 is Element of Result (tb,(S,X))
Result (t1,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (t1,(S,X)) is Relation-like Args (t1,(S,X)) -defined Result (t1,(S,X)) -valued Function-like V29( Args (t1,(S,X)), Result (t1,(S,X))) Element of bool [:(Args (t1,(S,X))),(Result (t1,(S,X))):]
[:(Args (t1,(S,X))),(Result (t1,(S,X))):] is non empty Relation-like set
bool [:(Args (t1,(S,X))),(Result (t1,(S,X))):] is non empty set
t1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (t1,(S,X))
(Den (t1,(S,X))) . t1 is Element of Result (t1,(S,X))
[((Den (tb,(S,X))) . t2),((Den (t1,(S,X))) . t1)] is V26() set
{((Den (tb,(S,X))) . t2),((Den (t1,(S,X))) . t1)} is non empty set
{((Den (tb,(S,X))) . t2)} is non empty set
{{((Den (tb,(S,X))) . t2),((Den (t1,(S,X))) . t1)},{((Den (tb,(S,X))) . t2)}} is non empty set
t2 is Element of the carrier of S
x . t2 is Relation-like the Sorts of (S,X) . t2 -defined the Sorts of (S,X) . t2 -valued Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of (S,X) . t2):]
the Sorts of (S,X) . t2 is non empty set
[:( the Sorts of (S,X) . t2),( the Sorts of (S,X) . t2):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . t2),( the Sorts of (S,X) . t2):] is non empty set
the_arity_of tb is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of tb) is V4() V5() V6() V10() Element of K32()
the_arity_of t1 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t1) is V4() V5() V6() V10() Element of K32()
the_result_sort_of tb is Element of the carrier of S
the_result_sort_of t1 is Element of the carrier of S
dom t2 is Element of bool K32()
the_arity_of t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t2) is V4() V5() V6() V10() Element of K32()
the_arity_of s3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of s3) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t2 is Element of the carrier of S
o3 is Element of the carrier of S
the_result_sort_of s3 is Element of the carrier of S
k is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom k is Element of bool K32()
o1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (t2,(S,X))
dom o1 is Element of bool K32()
ts3 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (s3,(S,X))
Result (t2,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (t2,(S,X)) is Relation-like Args (t2,(S,X)) -defined Result (t2,(S,X)) -valued Function-like V29( Args (t2,(S,X)), Result (t2,(S,X))) Element of bool [:(Args (t2,(S,X))),(Result (t2,(S,X))):]
[:(Args (t2,(S,X))),(Result (t2,(S,X))):] is non empty Relation-like set
bool [:(Args (t2,(S,X))),(Result (t2,(S,X))):] is non empty set
(Den (t2,(S,X))) . o1 is Element of Result (t2,(S,X))
Result (s3,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (s3,(S,X)) is Relation-like Args (s3,(S,X)) -defined Result (s3,(S,X)) -valued Function-like V29( Args (s3,(S,X)), Result (s3,(S,X))) Element of bool [:(Args (s3,(S,X))),(Result (s3,(S,X))):]
[:(Args (s3,(S,X))),(Result (s3,(S,X))):] is non empty Relation-like set
bool [:(Args (s3,(S,X))),(Result (s3,(S,X))):] is non empty set
(Den (s3,(S,X))) . ts3 is Element of Result (s3,(S,X))
[((Den (t2,(S,X))) . o1),((Den (s3,(S,X))) . ts3)] is V26() set
{((Den (t2,(S,X))) . o1),((Den (s3,(S,X))) . ts3)} is non empty set
{((Den (t2,(S,X))) . o1)} is non empty set
{{((Den (t2,(S,X))) . o1),((Den (s3,(S,X))) . ts3)},{((Den (t2,(S,X))) . o1)}} is non empty set
x . o3 is Relation-like the Sorts of (S,X) . o3 -defined the Sorts of (S,X) . o3 -valued Element of bool [:( the Sorts of (S,X) . o3),( the Sorts of (S,X) . o3):]
the Sorts of (S,X) . o3 is non empty set
[:( the Sorts of (S,X) . o3),( the Sorts of (S,X) . o3):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . o3),( the Sorts of (S,X) . o3):] is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like OrderSortedRelation of (S,X)
t is Element of the carrier' of S
tx is Element of the carrier' of S
Args (t,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Args (tx,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the_arity_of tx is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
Result (t,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
Den (t,(S,X)) is Relation-like Args (t,(S,X)) -defined Result (t,(S,X)) -valued Function-like V29( Args (t,(S,X)), Result (t,(S,X))) Element of bool [:(Args (t,(S,X))),(Result (t,(S,X))):]
[:(Args (t,(S,X))),(Result (t,(S,X))):] is non empty Relation-like set
bool [:(Args (t,(S,X))),(Result (t,(S,X))):] is non empty set
Result (tx,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (tx,(S,X)) is Relation-like Args (tx,(S,X)) -defined Result (tx,(S,X)) -valued Function-like V29( Args (tx,(S,X)), Result (tx,(S,X))) Element of bool [:(Args (tx,(S,X))),(Result (tx,(S,X))):]
[:(Args (tx,(S,X))),(Result (tx,(S,X))):] is non empty Relation-like set
bool [:(Args (tx,(S,X))),(Result (tx,(S,X))):] is non empty set
the_result_sort_of tx is Element of the carrier of S
(S,X) . (the_result_sort_of tx) is Relation-like the Sorts of (S,X) . (the_result_sort_of tx) -defined the Sorts of (S,X) . (the_result_sort_of tx) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (the_result_sort_of tx)),( the Sorts of (S,X) . (the_result_sort_of tx)):]
the Sorts of (S,X) . (the_result_sort_of tx) is non empty set
[:( the Sorts of (S,X) . (the_result_sort_of tx)),( the Sorts of (S,X) . (the_result_sort_of tx)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (the_result_sort_of tx)),( the Sorts of (S,X) . (the_result_sort_of tx)):] is non empty set
the_result_sort_of t is Element of the carrier of S
P is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (t,(S,X))
proj1 P is set
(Den (t,(S,X))) . P is Element of Result (t,(S,X))
O1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (tx,(S,X))
(Den (tx,(S,X))) . O1 is Element of Result (tx,(S,X))
[((Den (t,(S,X))) . P),((Den (tx,(S,X))) . O1)] is V26() set
{((Den (t,(S,X))) . P),((Den (tx,(S,X))) . O1)} is non empty set
{((Den (t,(S,X))) . P)} is non empty set
{{((Den (t,(S,X))) . P),((Den (tx,(S,X))) . O1)},{((Den (t,(S,X))) . P)}} is non empty set
dom P is Element of bool K32()
the_arity_of t is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t) is V4() V5() V6() V10() Element of K32()
len (the_arity_of tx) is V4() V5() V6() V10() Element of K32()
dom (the_arity_of tx) is Element of bool K32()
dom (the_arity_of t) is Element of bool K32()
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like OrderSortedRelation of (S,X)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is Element of the carrier of S
the Sorts of (S,X) . x is non empty set
bool ( the Sorts of (S,X) . x) is non empty set
X . x is non empty set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
P is set
O1 is set
O1 is Element of bool ( the Sorts of (S,X) . x)
dom (coprod X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
(coprod X) . x is non empty set
proj2 (coprod X) is non empty V205() set
coprod (x,X) is set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
the carrier of (S,X) is non empty set
bool the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= x & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= x ) ) } is set
i is set
s is set
[s,x] is V26() set
{s,x} is non empty set
{s} is non empty set
{{s,x},{s}} is non empty set
root-tree [s,x] is Relation-like Function-like DecoratedTree-like set
s is set
[s,x] is V26() set
{s,x} is non empty set
{s} is non empty set
{{s,x},{s}} is non empty set
root-tree [s,x] is Relation-like Function-like DecoratedTree-like set
(S,X) . x is non empty set
(S,X,x) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
union (proj2 (coprod X)) is set
b is Element of the carrier of (S,X)
root-tree b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
tb is set
[tb,x] is V26() set
{tb,x} is non empty set
{tb} is non empty set
{{tb,x},{tb}} is non empty set
root-tree [tb,x] is Relation-like Function-like DecoratedTree-like set
tx is Element of bool ( the Sorts of (S,X) . x)
P is Element of bool ( the Sorts of (S,X) . x)
O1 is set
R is set
[R,x] is V26() set
{R,x} is non empty set
{R} is non empty set
{{R,x},{R}} is non empty set
root-tree [R,x] is Relation-like Function-like DecoratedTree-like set
O1 is set
R is set
[R,x] is V26() set
{R,x} is non empty set
{R} is non empty set
{{R,x},{R}} is non empty set
root-tree [R,x] is Relation-like Function-like DecoratedTree-like set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is Element of the carrier of S
(S,X,x) is Element of bool ( the Sorts of (S,X) . x)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . x is non empty set
bool ( the Sorts of (S,X) . x) is non empty set
X . x is non empty set
y is set
[y,x] is V26() set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
root-tree [y,x] is Relation-like Function-like DecoratedTree-like set
t is set
[t,x] is V26() set
{t,x} is non empty set
{t} is non empty set
{{t,x},{t}} is non empty set
root-tree [t,x] is Relation-like Function-like DecoratedTree-like set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
x is Element of the carrier of S
(S,X,x) is non empty Element of bool ( the Sorts of (S,X) . x)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . x is non empty set
bool ( the Sorts of (S,X) . x) is non empty set
{ (root-tree b₁) where b₁ is Element of the carrier of (S,X) : ( b₁ in Terminals (S,X) & b₁ `2 = x ) } is set
tx is set
X . x is non empty set
P is set
[P,x] is V26() set
{P,x} is non empty set
{P} is non empty set
{{P,x},{P}} is non empty set
root-tree [P,x] is Relation-like Function-like DecoratedTree-like set
O1 is Element of the carrier of (S,X)
O1 `2 is set
tx is set
P is Element of the carrier of (S,X)
root-tree P is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
P `2 is set
R is set
O1 is Element of the carrier of S
X . O1 is non empty set
[R,O1] is V26() set
{R,O1} is non empty set
{R} is non empty set
{{R,O1},{R}} is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
y is Relation-like Function-like set
proj1 y is set
t is non empty Relation-like the carrier of S -defined Function-like total set
tx is set
t . tx is set
the Sorts of (S,X) . tx is set
P is Element of the carrier of S
t . P is set
(S,X,P) is non empty Element of bool ( the Sorts of (S,X) . P)
the Sorts of (S,X) . P is non empty set
bool ( the Sorts of (S,X) . P) is non empty set
tx is non empty Relation-like the carrier of S -defined Function-like total ManySortedSubset of the Sorts of (S,X)
P is Element of the carrier of S
tx . P is set
(S,X,P) is non empty Element of bool ( the Sorts of (S,X) . P)
the Sorts of (S,X) . P is non empty set
bool ( the Sorts of (S,X) . P) is non empty set
x is non empty Relation-like the carrier of S -defined Function-like total ManySortedSubset of the Sorts of (S,X)
y is non empty Relation-like the carrier of S -defined Function-like total ManySortedSubset of the Sorts of (S,X)
t is set
x . t is set
y . t is set
tx is Element of the carrier of S
x . tx is set
(S,X,tx) is non empty Element of bool ( the Sorts of (S,X) . tx)
the Sorts of (S,X) . tx is non empty set
bool ( the Sorts of (S,X) . tx) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total ManySortedSubset of the Sorts of (S,X)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is set
(S,X) . x is set
y is Element of the carrier of S
(S,X) . y is set
(S,X,y) is non empty Element of bool ( the Sorts of (S,X) . y)
the Sorts of (S,X) . y is non empty set
bool ( the Sorts of (S,X) . y) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted monotone MSAlgebra over S
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
QuotOSAlg ((S,X),(S,X)) is strict non-empty order-sorted monotone MSAlgebra over S
OSClass (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
OSQuotCharact (S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((OSClass (S,X)) #), the ResultSort of S * (OSClass (S,X))
(OSClass (S,X)) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((OSClass (S,X)) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * (OSClass (S,X)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (OSClass (S,X)),(OSQuotCharact (S,X)) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is Element of the carrier of S
the Sorts of (S,X) . x is non empty set
bool ( the Sorts of (S,X) . x) is non empty set
X . x is non empty set
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (QuotOSAlg ((S,X),(S,X))) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
OSNat_Hom ((S,X),(S,X)) is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of the Sorts of (S,X), the Sorts of (QuotOSAlg ((S,X),(S,X)))
(OSNat_Hom ((S,X),(S,X))) . x is Relation-like the Sorts of (S,X) . x -defined the Sorts of (QuotOSAlg ((S,X),(S,X))) . x -valued Function-like V29( the Sorts of (S,X) . x, the Sorts of (QuotOSAlg ((S,X),(S,X))) . x) Element of bool [:( the Sorts of (S,X) . x),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . x):]
the Sorts of (S,X) . x is non empty set
the Sorts of (QuotOSAlg ((S,X),(S,X))) . x is non empty set
[:( the Sorts of (S,X) . x),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . x):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . x),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . x):] is non empty set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
R is set
i is set
i is Element of bool ( the Sorts of (S,X) . x)
dom (coprod X) is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
(coprod X) . x is non empty set
proj2 (coprod X) is non empty V205() set
coprod (x,X) is set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
the carrier of (S,X) is non empty set
bool the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b<sub>2</sub> being Element of the carrier of S ex b<sub>3</sub> being set st
( b<sub>2</sub> <= x & b<sub>3</sub> in X . b<sub>2</sub> & b<sub>1</sub> = root-tree [b<sub>3</sub>,b<sub>2</sub>] ) or ex b<sub>2</sub> being Element of the carrier' of S st
( [b<sub>2</sub>, the carrier of S] = b<sub>1</sub> . {} & the_result_sort_of b<sub>2</sub> <= x ) ) } is set
a is set
b is set
[b,x] is V26() set
{b,x} is non empty set
{b} is non empty set
{{b,x},{b}} is non empty set
root-tree [b,x] is Relation-like Function-like DecoratedTree-like set
((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree [b,x]) is set
b is set
[b,x] is V26() set
{b,x} is non empty set
{b} is non empty set
{{b,x},{b}} is non empty set
root-tree [b,x] is Relation-like Function-like DecoratedTree-like set
((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree [b,x]) is set
(S,X) . x is non empty set
(S,X,x) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
union (proj2 (coprod X)) is set
tb is Element of the carrier of (S,X)
root-tree tb is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
((OSNat_Hom ((S,X),(S,X))) . x) . t1 is set
tx is Element of bool ( the Sorts of (S,X) . x)
P is Element of bool ( the Sorts of (S,X) . x)
O1 is set
R is set
[R,x] is V26() set
{R,x} is non empty set
{R} is non empty set
{{R,x},{R}} is non empty set
root-tree [R,x] is Relation-like Function-like DecoratedTree-like set
((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree [R,x]) is set
O1 is set
R is set
[R,x] is V26() set
{R,x} is non empty set
{R} is non empty set
{{R,x},{R}} is non empty set
root-tree [R,x] is Relation-like Function-like DecoratedTree-like set
((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree [R,x]) is set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is Element of the carrier of S
(S,X,x) is Element of bool ( the Sorts of (S,X) . x)
(S,X) is strict non-empty order-sorted monotone MSAlgebra over S
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
QuotOSAlg ((S,X),(S,X)) is strict non-empty order-sorted monotone MSAlgebra over S
OSClass (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
OSQuotCharact (S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((OSClass (S,X)) #), the ResultSort of S * (OSClass (S,X))
(OSClass (S,X)) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((OSClass (S,X)) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * (OSClass (S,X)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (OSClass (S,X)),(OSQuotCharact (S,X)) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . x is non empty set
bool ( the Sorts of (S,X) . x) is non empty set
OSNat_Hom ((S,X),(S,X)) is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of the Sorts of (S,X), the Sorts of (QuotOSAlg ((S,X),(S,X)))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (QuotOSAlg ((S,X),(S,X))) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
X . x is non empty set
(OSNat_Hom ((S,X),(S,X))) . x is Relation-like the Sorts of (S,X) . x -defined the Sorts of (QuotOSAlg ((S,X),(S,X))) . x -valued Function-like V29( the Sorts of (S,X) . x, the Sorts of (QuotOSAlg ((S,X),(S,X))) . x) Element of bool [:( the Sorts of (S,X) . x),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . x):]
the Sorts of (S,X) . x is non empty set
the Sorts of (QuotOSAlg ((S,X),(S,X))) . x is non empty set
[:( the Sorts of (S,X) . x),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . x):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . x),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . x):] is non empty set
t is set
[t,x] is V26() set
{t,x} is non empty set
{t} is non empty set
{{t,x},{t}} is non empty set
root-tree [t,x] is Relation-like Function-like DecoratedTree-like set
((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree [t,x]) is set
tx is set
[tx,x] is V26() set
{tx,x} is non empty set
{tx} is non empty set
{{tx,x},{tx}} is non empty set
root-tree [tx,x] is Relation-like Function-like DecoratedTree-like set
((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree [tx,x]) is set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
QuotOSAlg ((S,X),(S,X)) is strict non-empty order-sorted monotone MSAlgebra over S
OSClass (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
OSQuotCharact (S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((OSClass (S,X)) #), the ResultSort of S * (OSClass (S,X))
(OSClass (S,X)) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((OSClass (S,X)) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * (OSClass (S,X)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (OSClass (S,X)),(OSQuotCharact (S,X)) #) is strict MSAlgebra over S
the Sorts of (QuotOSAlg ((S,X),(S,X))) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
OSNat_Hom ((S,X),(S,X)) is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of the Sorts of (S,X), the Sorts of (QuotOSAlg ((S,X),(S,X)))
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
x is Element of the carrier of S
(S,X,x) is non empty Element of bool ( the Sorts of (S,X) . x)
(S,X) is strict non-empty order-sorted monotone MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . x is non empty set
bool ( the Sorts of (S,X) . x) is non empty set
(OSNat_Hom ((S,X),(S,X))) . x is Relation-like the Sorts of (S,X) . x -defined the Sorts of (QuotOSAlg ((S,X),(S,X))) . x -valued Function-like V29( the Sorts of (S,X) . x, the Sorts of (QuotOSAlg ((S,X),(S,X))) . x) Element of bool [:( the Sorts of (S,X) . x),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . x):]
the Sorts of (S,X) . x is non empty set
the Sorts of (QuotOSAlg ((S,X),(S,X))) . x is non empty set
[:( the Sorts of (S,X) . x),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . x):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . x),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . x):] is non empty set
{ (((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree b<sub>1</sub>)) where b<sub>1</sub> is Element of the carrier of (S,X) : ( b<sub>1</sub> in Terminals (S,X) & b<sub>1</sub> `2 = x ) } is set
P is set
X . x is non empty set
O1 is set
[O1,x] is V26() set
{O1,x} is non empty set
{O1} is non empty set
{{O1,x},{O1}} is non empty set
root-tree [O1,x] is Relation-like Function-like DecoratedTree-like set
((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree [O1,x]) is set
R is Element of the carrier of (S,X)
R `2 is set
P is set
O1 is Element of the carrier of (S,X)
root-tree O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree O1) is set
O1 `2 is set
i is set
R is Element of the carrier of S
X . R is non empty set
[i,R] is V26() set
{i,R} is non empty set
{i} is non empty set
{{i,R},{i}} is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted monotone MSAlgebra over S
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
QuotOSAlg ((S,X),(S,X)) is strict non-empty order-sorted monotone MSAlgebra over S
OSClass (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
OSQuotCharact (S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((OSClass (S,X)) #), the ResultSort of S * (OSClass (S,X))
(OSClass (S,X)) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((OSClass (S,X)) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * (OSClass (S,X)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (OSClass (S,X)),(OSQuotCharact (S,X)) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
OSNat_Hom ((S,X),(S,X)) is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of the Sorts of (S,X), the Sorts of (QuotOSAlg ((S,X),(S,X)))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (QuotOSAlg ((S,X),(S,X))) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
O1 is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of the Sorts of (S,X), the Sorts of (S,X)
i is Relation-like Function-like set
proj1 i is set
s is non empty Relation-like the carrier of S -defined Function-like total set
a is set
s . a is set
the Sorts of (S,X) . a is set
b is Element of the carrier of S
s . b is set
(S,X,b) is non empty Element of bool ( the Sorts of (S,X) . b)
the Sorts of (S,X) . b is non empty set
bool ( the Sorts of (S,X) . b) is non empty set
a is non empty Relation-like the carrier of S -defined Function-like total ManySortedSubset of the Sorts of (S,X)
OSCl a is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
R is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
b is non empty Relation-like the carrier of S -defined Function-like total OSSubset of (S,X)
GenOSAlg b is strict order-sorted MSSubAlgebra of (S,X)
the Sorts of (GenOSAlg b) is non empty Relation-like the carrier of S -defined Function-like total set
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
t2 is Element of the carrier of (S,X)
t1 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots t1 is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
proj2 t1 is set
t2 -tree t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
[t2,(roots t1)] is V26() set
{t2,(roots t1)} is non empty set
{t2} is non empty set
{{t2,(roots t1)},{t2}} is non empty set
the Rules of (S,X) is Relation-like the carrier of (S,X) -defined the carrier of (S,X) * -valued Element of bool [: the carrier of (S,X),( the carrier of (S,X) *):]
the carrier of (S,X) * is non empty functional FinSequence-membered M10( the carrier of (S,X))
[: the carrier of (S,X),( the carrier of (S,X) *):] is non empty Relation-like set
bool [: the carrier of (S,X),( the carrier of (S,X) *):] is non empty set
t2 is Element of [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))
t2 is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
[t2,t2] is V26() set
{t2,t2} is non empty set
{t2} is non empty set
{{t2,t2},{t2}} is non empty set
s3 is Element of the carrier' of S
o1 is Element of { the carrier of S}
[s3,o1] is V26() set
{s3,o1} is non empty set
{s3} is non empty set
{{s3,o1},{s3}} is non empty set
ts3 is Element of the carrier of S
the Sorts of (S,X) . ts3 is non empty set
O1 . ts3 is Relation-like the Sorts of (S,X) . ts3 -defined the Sorts of (S,X) . ts3 -valued Function-like V29( the Sorts of (S,X) . ts3, the Sorts of (S,X) . ts3) Element of bool [:( the Sorts of (S,X) . ts3),( the Sorts of (S,X) . ts3):]
the Sorts of (S,X) . ts3 is non empty set
[:( the Sorts of (S,X) . ts3),( the Sorts of (S,X) . ts3):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . ts3),( the Sorts of (S,X) . ts3):] is non empty set
dom (O1 . ts3) is Element of bool ( the Sorts of (S,X) . ts3)
bool ( the Sorts of (S,X) . ts3) is non empty set
(O1 . ts3) . (t2 -tree t1) is set
the Sorts of (GenOSAlg b) . ts3 is set
(S,X,ts3) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= ts3 & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= ts3 ) ) } is set
o3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
o3 . {} is set
len t2 is V4() V5() V6() V10() Element of K32()
Seg (len t2) is V34() V41( len t2) Element of bool K32()
dom t2 is Element of bool K32()
k is Element of the carrier of S
tk1 is set
X . k is non empty set
[tk1,k] is V26() set
{tk1,k} is non empty set
{tk1} is non empty set
{{tk1,k},{tk1}} is non empty set
root-tree [tk1,k] is Relation-like Function-like DecoratedTree-like set
(t2 -tree t1) . {} is set
k is Element of the carrier of S
tk1 is set
X . k is non empty set
[tk1,k] is V26() set
{tk1,k} is non empty set
{tk1} is non empty set
{{tk1,k},{tk1}} is non empty set
root-tree [tk1,k] is Relation-like Function-like DecoratedTree-like set
tk3 is Element of the carrier' of S
[tk3, the carrier of S] is V26() set
{tk3, the carrier of S} is non empty set
{tk3} is non empty set
{{tk3, the carrier of S},{tk3}} is non empty set
the_result_sort_of tk3 is Element of the carrier of S
k is Element of the carrier' of S
[k, the carrier of S] is V26() set
{k, the carrier of S} is non empty set
{k} is non empty set
{{k, the carrier of S},{k}} is non empty set
the_result_sort_of k is Element of the carrier of S
the_arity_of s3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the_result_sort_of s3 is Element of the carrier of S
dom (roots t1) is Element of bool K32()
dom t1 is Element of bool K32()
len (the_arity_of s3) is V4() V5() V6() V10() Element of K32()
Seg (len (the_arity_of s3)) is V34() V41( len (the_arity_of s3)) Element of bool K32()
dom (the_arity_of s3) is Element of bool K32()
tak is non empty Relation-like the carrier of S -defined Function-like total ManySortedSubset of the Sorts of (S,X)
(the_arity_of s3) * tak is Relation-like K32() -defined dom (the_arity_of s3) -defined Function-like total V34() FinSequence-like FinSubsequence-like set
dom ((the_arity_of s3) * tak) is Element of bool K32()
tak # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * (tak #) is non empty Relation-like the carrier' of S -defined Function-like total set
the Arity of S . s3 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
( the Arity of S * (tak #)) . s3 is set
product ((the_arity_of s3) * tak) is set
the ResultSort of S . s3 is Element of the carrier of S
Args (s3,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Result (s3,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
Den (s3,(S,X)) is Relation-like Args (s3,(S,X)) -defined Result (s3,(S,X)) -valued Function-like V29( Args (s3,(S,X)), Result (s3,(S,X))) Element of bool [:(Args (s3,(S,X))),(Result (s3,(S,X))):]
[:(Args (s3,(S,X))),(Result (s3,(S,X))):] is non empty Relation-like set
bool [:(Args (s3,(S,X))),(Result (s3,(S,X))):] is non empty set
(Den (s3,(S,X))) | (( the Arity of S * (tak #)) . s3) is Relation-like ( the Arity of S * (tak #)) . s3 -defined Args (s3,(S,X)) -defined Result (s3,(S,X)) -valued Function-like Element of bool [:(Args (s3,(S,X))),(Result (s3,(S,X))):]
proj2 ((Den (s3,(S,X))) | (( the Arity of S * (tak #)) . s3)) is set
the ResultSort of S * tak is non empty Relation-like the carrier' of S -defined Function-like total set
( the ResultSort of S * tak) . s3 is set
(S,X,s3) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
[s3, the carrier of S] is V26() set
{s3, the carrier of S} is non empty set
{{s3, the carrier of S},{s3}} is non empty set
( the Arity of S * ((S,X) #)) . s3 is set
Args (s3,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (s3,(S,X)) is Relation-like Args (s3,(S,X)) -defined Result (s3,(S,X)) -valued Function-like V29( Args (s3,(S,X)), Result (s3,(S,X))) Element of bool [:(Args (s3,(S,X))),(Result (s3,(S,X))):]
Result (s3,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (s3,(S,X))),(Result (s3,(S,X))):] is non empty Relation-like set
bool [:(Args (s3,(S,X))),(Result (s3,(S,X))):] is non empty set
(S,X) . s3 is Relation-like ( the Arity of S * ((S,X) #)) . s3 -defined ( the ResultSort of S * (S,X)) . s3 -valued Function-like V29(( the Arity of S * ((S,X) #)) . s3,( the ResultSort of S * (S,X)) . s3) Element of bool [:(( the Arity of S * ((S,X) #)) . s3),(( the ResultSort of S * (S,X)) . s3):]
( the ResultSort of S * (S,X)) . s3 is non empty set
[:(( the Arity of S * ((S,X) #)) . s3),(( the ResultSort of S * (S,X)) . s3):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . s3),(( the ResultSort of S * (S,X)) . s3):] is non empty set
(S,X,s3) is Relation-like ( the Arity of S * ((S,X) #)) . s3 -defined ( the ResultSort of S * (S,X)) . s3 -valued Function-like V29(( the Arity of S * ((S,X) #)) . s3,( the ResultSort of S * (S,X)) . s3) Element of bool [:(( the Arity of S * ((S,X) #)) . s3),(( the ResultSort of S * (S,X)) . s3):]
(Den (s3,(S,X))) . t1 is set
(the_arity_of s3) * the Sorts of (S,X) is Relation-like non-empty K32() -defined dom (the_arity_of s3) -defined Function-like total V34() FinSequence-like FinSubsequence-like set
dom ((the_arity_of s3) * the Sorts of (S,X)) is Element of bool K32()
s is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (s3,(S,X))
O1 # s is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (s3,(S,X))
x is set
(O1 # s) . x is set
((the_arity_of s3) * tak) . x is set
x1 is V4() V5() V6() V10() set
t1 . x1 is Relation-like Function-like set
t1 . x is Relation-like Function-like set
s . x is set
((the_arity_of s3) * the Sorts of (S,X)) . x is set
(the_arity_of s3) . x is set
the Sorts of (S,X) . ((the_arity_of s3) . x) is set
(the_arity_of s3) /. x is Element of the carrier of S
the Sorts of (S,X) . ((the_arity_of s3) /. x) is non empty set
s . x1 is set
(the_arity_of s3) /. x1 is Element of the carrier of S
the Sorts of (S,X) . ((the_arity_of s3) /. x1) is non empty set
O1 . ((the_arity_of s3) /. x1) is Relation-like the Sorts of (S,X) . ((the_arity_of s3) /. x1) -defined the Sorts of (S,X) . ((the_arity_of s3) /. x1) -valued Function-like V29( the Sorts of (S,X) . ((the_arity_of s3) /. x1), the Sorts of (S,X) . ((the_arity_of s3) /. x1)) Element of bool [:( the Sorts of (S,X) . ((the_arity_of s3) /. x1)),( the Sorts of (S,X) . ((the_arity_of s3) /. x1)):]
the Sorts of (S,X) . ((the_arity_of s3) /. x1) is non empty set
[:( the Sorts of (S,X) . ((the_arity_of s3) /. x1)),( the Sorts of (S,X) . ((the_arity_of s3) /. x1)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . ((the_arity_of s3) /. x1)),( the Sorts of (S,X) . ((the_arity_of s3) /. x1)):] is non empty set
dom (O1 . ((the_arity_of s3) /. x1)) is Element of bool ( the Sorts of (S,X) . ((the_arity_of s3) /. x1))
bool ( the Sorts of (S,X) . ((the_arity_of s3) /. x1)) is non empty set
t is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(O1 . ((the_arity_of s3) /. x1)) . t is set
the Sorts of (GenOSAlg b) . ((the_arity_of s3) /. x1) is set
(O1 . ((the_arity_of s3) /. x1)) . (s . x1) is set
tak . ((the_arity_of s3) . x) is set
(O1 # s) . x1 is set
dom (Den (s3,(S,X))) is functional Element of bool (Args (s3,(S,X)))
bool (Args (s3,(S,X))) is non empty set
t is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
n is Element of the carrier of S
t . n is set
rt is Element of the carrier of S
t . rt is set
dom (O1 # s) is Element of bool K32()
(Den (s3,(S,X))) . (O1 # s) is Element of Result (s3,(S,X))
the ResultSort of S * the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
( the ResultSort of S * the Sorts of (S,X)) . s3 is non empty set
the Sorts of (S,X) . (the_result_sort_of s3) is non empty set
O1 . (the_result_sort_of s3) is Relation-like the Sorts of (S,X) . (the_result_sort_of s3) -defined the Sorts of (S,X) . (the_result_sort_of s3) -valued Function-like V29( the Sorts of (S,X) . (the_result_sort_of s3), the Sorts of (S,X) . (the_result_sort_of s3)) Element of bool [:( the Sorts of (S,X) . (the_result_sort_of s3)),( the Sorts of (S,X) . (the_result_sort_of s3)):]
the Sorts of (S,X) . (the_result_sort_of s3) is non empty set
[:( the Sorts of (S,X) . (the_result_sort_of s3)),( the Sorts of (S,X) . (the_result_sort_of s3)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (the_result_sort_of s3)),( the Sorts of (S,X) . (the_result_sort_of s3)):] is non empty set
dom (O1 . (the_result_sort_of s3)) is Element of bool ( the Sorts of (S,X) . (the_result_sort_of s3))
bool ( the Sorts of (S,X) . (the_result_sort_of s3)) is non empty set
O1 . rt is Relation-like the Sorts of (S,X) . rt -defined the Sorts of (S,X) . rt -valued Function-like V29( the Sorts of (S,X) . rt, the Sorts of (S,X) . rt) Element of bool [:( the Sorts of (S,X) . rt),( the Sorts of (S,X) . rt):]
the Sorts of (S,X) . rt is non empty set
the Sorts of (S,X) . rt is non empty set
[:( the Sorts of (S,X) . rt),( the Sorts of (S,X) . rt):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . rt),( the Sorts of (S,X) . rt):] is non empty set
(O1 . rt) . (t2 -tree t1) is set
O1 . n is Relation-like the Sorts of (S,X) . n -defined the Sorts of (S,X) . n -valued Function-like V29( the Sorts of (S,X) . n, the Sorts of (S,X) . n) Element of bool [:( the Sorts of (S,X) . n),( the Sorts of (S,X) . n):]
the Sorts of (S,X) . n is non empty set
the Sorts of (S,X) . n is non empty set
[:( the Sorts of (S,X) . n),( the Sorts of (S,X) . n):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . n),( the Sorts of (S,X) . n):] is non empty set
(O1 . n) . (t2 -tree t1) is set
(Den (s3,(S,X))) . s is Element of Result (s3,(S,X))
(O1 . (the_result_sort_of s3)) . ((Den (s3,(S,X))) . s) is set
(O1 . (the_result_sort_of s3)) . (t2 -tree t1) is set
tak . (the_result_sort_of s3) is set
tb is Element of the carrier of S
the Sorts of (GenOSAlg b) . tb is set
the Sorts of (S,X) . tb is non empty set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
t2 is Element of the carrier of (S,X)
root-tree t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
t1 is Element of the carrier of S
the Sorts of (S,X) . t1 is non empty set
O1 . t1 is Relation-like the Sorts of (S,X) . t1 -defined the Sorts of (S,X) . t1 -valued Function-like V29( the Sorts of (S,X) . t1, the Sorts of (S,X) . t1) Element of bool [:( the Sorts of (S,X) . t1),( the Sorts of (S,X) . t1):]
the Sorts of (S,X) . t1 is non empty set
[:( the Sorts of (S,X) . t1),( the Sorts of (S,X) . t1):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . t1),( the Sorts of (S,X) . t1):] is non empty set
dom (O1 . t1) is Element of bool ( the Sorts of (S,X) . t1)
bool ( the Sorts of (S,X) . t1) is non empty set
(O1 . t1) . (root-tree t2) is set
the Sorts of (GenOSAlg b) . t1 is set
(S,X,t1) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= t1 & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= t1 ) ) } is set
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t2 . {} is set
s3 is set
t2 is Element of the carrier of S
X . t2 is non empty set
[s3,t2] is V26() set
{s3,t2} is non empty set
{s3} is non empty set
{{s3,t2},{s3}} is non empty set
o1 is Element of the carrier' of S
[o1, the carrier of S] is V26() set
{o1, the carrier of S} is non empty set
{o1} is non empty set
{{o1, the carrier of S},{o1}} is non empty set
the_result_sort_of o1 is Element of the carrier of S
t2 is Element of the carrier of S
s3 is set
X . t2 is non empty set
[s3,t2] is V26() set
{s3,t2} is non empty set
{s3} is non empty set
{{s3,t2},{s3}} is non empty set
root-tree [s3,t2] is Relation-like Function-like DecoratedTree-like set
o1 is Element of the carrier' of S
[o1, the carrier of S] is V26() set
{o1, the carrier of S} is non empty set
{o1} is non empty set
{{o1, the carrier of S},{o1}} is non empty set
the_result_sort_of o1 is Element of the carrier of S
t2 is Element of the carrier of S
s3 is set
X . t2 is non empty set
[s3,t2] is V26() set
{s3,t2} is non empty set
{s3} is non empty set
{{s3,t2},{s3}} is non empty set
root-tree [s3,t2] is Relation-like Function-like DecoratedTree-like set
(S,X,t2) is non empty functional constituted-DTrees Element of bool (TS (S,X))
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= t2 & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= t2 ) ) } is set
(S,X) . t2 is non empty set
the Sorts of (S,X) . t2 is non empty set
O1 . t2 is Relation-like the Sorts of (S,X) . t2 -defined the Sorts of (S,X) . t2 -valued Function-like V29( the Sorts of (S,X) . t2, the Sorts of (S,X) . t2) Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of (S,X) . t2):]
the Sorts of (S,X) . t2 is non empty set
[:( the Sorts of (S,X) . t2),( the Sorts of (S,X) . t2):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . t2),( the Sorts of (S,X) . t2):] is non empty set
dom (O1 . t2) is Element of bool ( the Sorts of (S,X) . t2)
bool ( the Sorts of (S,X) . t2) is non empty set
ts3 is Element of the carrier of S
O1 . ts3 is Relation-like the Sorts of (S,X) . ts3 -defined the Sorts of (S,X) . ts3 -valued Function-like V29( the Sorts of (S,X) . ts3, the Sorts of (S,X) . ts3) Element of bool [:( the Sorts of (S,X) . ts3),( the Sorts of (S,X) . ts3):]
the Sorts of (S,X) . ts3 is non empty set
the Sorts of (S,X) . ts3 is non empty set
[:( the Sorts of (S,X) . ts3),( the Sorts of (S,X) . ts3):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . ts3),( the Sorts of (S,X) . ts3):] is non empty set
(O1 . ts3) . (root-tree [s3,t2]) is set
o1 is Element of the carrier of S
O1 . o1 is Relation-like the Sorts of (S,X) . o1 -defined the Sorts of (S,X) . o1 -valued Function-like V29( the Sorts of (S,X) . o1, the Sorts of (S,X) . o1) Element of bool [:( the Sorts of (S,X) . o1),( the Sorts of (S,X) . o1):]
the Sorts of (S,X) . o1 is non empty set
the Sorts of (S,X) . o1 is non empty set
[:( the Sorts of (S,X) . o1),( the Sorts of (S,X) . o1):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . o1),( the Sorts of (S,X) . o1):] is non empty set
(O1 . o1) . (root-tree [s3,t2]) is set
a . t2 is set
the Sorts of (GenOSAlg b) . t2 is set
(S,X,t2) is non empty Element of bool ( the Sorts of (S,X) . t2)
bool ( the Sorts of (S,X) . t2) is non empty set
ta is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
ta . ts3 is set
ta . o1 is set
(O1 . t2) . (root-tree [s3,t2]) is set
t2 is set
the Sorts of (S,X) . tb is non empty set
(S,X,tb) is non empty functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) : ( ex b₂ being Element of the carrier of S ex b₃ being set st
( b₂ <= tb & b₃ in X . b₂ & b₁ = root-tree [b₃,b₂] ) or ex b₂ being Element of the carrier' of S st
( [b₂, the carrier of S] = b₁ . {} & the_result_sort_of b₂ <= tb ) ) } is set
O1 . tb is Relation-like the Sorts of (S,X) . tb -defined the Sorts of (S,X) . tb -valued Function-like V29( the Sorts of (S,X) . tb, the Sorts of (S,X) . tb) Element of bool [:( the Sorts of (S,X) . tb),( the Sorts of (S,X) . tb):]
[:( the Sorts of (S,X) . tb),( the Sorts of (S,X) . tb):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . tb),( the Sorts of (S,X) . tb):] is non empty set
proj2 (O1 . tb) is set
dom (O1 . tb) is Element of bool ( the Sorts of (S,X) . tb)
bool ( the Sorts of (S,X) . tb) is non empty set
t1 is set
(O1 . tb) . t1 is set
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t2 is Element of the carrier of S
s3 is set
X . t2 is non empty set
[s3,t2] is V26() set
{s3,t2} is non empty set
{s3} is non empty set
{{s3,t2},{s3}} is non empty set
root-tree [s3,t2] is Relation-like Function-like DecoratedTree-like set
o1 is Element of the carrier' of S
[o1, the carrier of S] is V26() set
{o1, the carrier of S} is non empty set
{o1} is non empty set
{{o1, the carrier of S},{o1}} is non empty set
t2 . {} is set
the_result_sort_of o1 is Element of the carrier of S
ta is non empty Relation-like the carrier of S -defined Function-like total OSSubset of (S,X)
GenOSAlg ta is strict order-sorted MSSubAlgebra of (S,X)
the Sorts of (GenOSAlg ta) is non empty Relation-like the carrier of S -defined Function-like total set
ta is non empty Relation-like the carrier of S -defined Function-like total (S,(S,X))
tb is Element of the carrier of S
ta . tb is set
(S,X,tb) is non empty Element of bool ( the Sorts of (S,X) . tb)
the Sorts of (S,X) . tb is non empty set
bool ( the Sorts of (S,X) . tb) is non empty set
x is non empty Relation-like the carrier of S -defined Function-like total (S,(S,X))
y is non empty Relation-like the carrier of S -defined Function-like total (S,(S,X))
t is set
x . t is set
y . t is set
tx is Element of the carrier of S
x . tx is set
(S,X,tx) is non empty Element of bool ( the Sorts of (S,X) . tx)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . tx is non empty set
bool ( the Sorts of (S,X) . tx) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total (S,(S,X))
(S,X) is strict non-empty order-sorted monotone MSAlgebra over S
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
QuotOSAlg ((S,X),(S,X)) is strict non-empty order-sorted monotone MSAlgebra over S
OSClass (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
OSQuotCharact (S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((OSClass (S,X)) #), the ResultSort of S * (OSClass (S,X))
(OSClass (S,X)) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((OSClass (S,X)) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * (OSClass (S,X)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (OSClass (S,X)),(OSQuotCharact (S,X)) #) is strict MSAlgebra over S
x is set
(S,X) . x is set
y is Element of the carrier of S
(S,X) . y is set
(S,X,y) is non empty Element of bool ( the Sorts of (S,X) . y)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . y is non empty set
bool ( the Sorts of (S,X) . y) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total (S,(S,X))
(S,X) is strict non-empty order-sorted monotone MSAlgebra over S
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
QuotOSAlg ((S,X),(S,X)) is strict non-empty order-sorted monotone MSAlgebra over S
OSClass (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
OSQuotCharact (S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((OSClass (S,X)) #), the ResultSort of S * (OSClass (S,X))
(OSClass (S,X)) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((OSClass (S,X)) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * (OSClass (S,X)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (OSClass (S,X)),(OSQuotCharact (S,X)) #) is strict MSAlgebra over S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like OrderSortedRelation of (S,X)
y is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,y) is Element of the carrier of S
OSClass (x,(S,X,y)) is non empty Element of bool (Class (CompClass (x,(CComp (S,X,y)))))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
CComp (S,X,y) is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),(S,X,y)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,y))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,y) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,y) } is set
CompClass (x,(CComp (S,X,y))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,y))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,y))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):] is non empty set
Class (CompClass (x,(CComp (S,X,y)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,y)))
bool (Class (CompClass (x,(CComp (S,X,y))))) is non empty set
the Sorts of (S,X) . (S,X,y) is non empty set
P is Element of the Sorts of (S,X) . (S,X,y)
OSClass (x,P) is Element of OSClass (x,(S,X,y))
Class ((CompClass (x,(CComp (S,X,y)))),P) is Element of bool K541(S, the Sorts of (S,X),(CComp (S,X,y)))
bool K541(S, the Sorts of (S,X),(CComp (S,X,y))) is non empty set
O1 is Element of the carrier of S
the Sorts of (S,X) . O1 is non empty set
R is Element of the Sorts of (S,X) . O1
OSClass (x,R) is Element of OSClass (x,O1)
OSClass (x,O1) is non empty Element of bool (Class (CompClass (x,(CComp O1))))
CComp O1 is non empty Element of K539(S)
Class ((Path_Rel S),O1) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp O1)) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp O1 } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp O1 } is set
CompClass (x,(CComp O1)) is Relation-like K541(S, the Sorts of (S,X),(CComp O1)) -defined K541(S, the Sorts of (S,X),(CComp O1)) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp O1)),K541(S, the Sorts of (S,X),(CComp O1)):]
[:K541(S, the Sorts of (S,X),(CComp O1)),K541(S, the Sorts of (S,X),(CComp O1)):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp O1)),K541(S, the Sorts of (S,X),(CComp O1)):] is non empty set
Class (CompClass (x,(CComp O1))) is a_partition of K541(S, the Sorts of (S,X),(CComp O1))
bool (Class (CompClass (x,(CComp O1)))) is non empty set
Class ((CompClass (x,(CComp O1))),R) is Element of bool K541(S, the Sorts of (S,X),(CComp O1))
bool K541(S, the Sorts of (S,X),(CComp O1)) is non empty set
the Sorts of (S,X) . (S,X,y) is non empty set
O1 is Element of OSClass (x,(S,X,y))
R is Element of OSClass (x,(S,X,y))
P is Element of the Sorts of (S,X) . (S,X,y)
OSClass (x,P) is Element of OSClass (x,(S,X,y))
Class ((CompClass (x,(CComp (S,X,y)))),P) is Element of bool K541(S, the Sorts of (S,X),(CComp (S,X,y)))
bool K541(S, the Sorts of (S,X),(CComp (S,X,y))) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like OrderSortedRelation of (S,X)
y is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,x,y) is Element of OSClass (x,(S,X,y))
(S,X,y) is Element of the carrier of S
OSClass (x,(S,X,y)) is non empty Element of bool (Class (CompClass (x,(CComp (S,X,y)))))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
CComp (S,X,y) is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),(S,X,y)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,y))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,y) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,y) } is set
CompClass (x,(CComp (S,X,y))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,y))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,y))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):] is non empty set
Class (CompClass (x,(CComp (S,X,y)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,y)))
bool (Class (CompClass (x,(CComp (S,X,y))))) is non empty set
the Sorts of (S,X) . (S,X,y) is non empty set
tx is Element of the Sorts of (S,X) . (S,X,y)
OSClass (x,tx) is Element of OSClass (x,(S,X,y))
Class ((CompClass (x,(CComp (S,X,y)))),tx) is Element of bool K541(S, the Sorts of (S,X),(CComp (S,X,y)))
bool K541(S, the Sorts of (S,X),(CComp (S,X,y))) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
x is Element of the carrier of S
X . x is non empty set
y is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),y) is Element of OSClass ((S,X),(S,X,y))
(S,X,y) is Element of the carrier of S
OSClass ((S,X),(S,X,y)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,y)))))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
CComp (S,X,y) is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),(S,X,y)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,y))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,y) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,y) } is set
CompClass ((S,X),(CComp (S,X,y))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,y))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,y))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,y)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,y)))
bool (Class (CompClass ((S,X),(CComp (S,X,y))))) is non empty set
the Sorts of (S,X) . (S,X,y) is non empty set
R is set
[R,x] is V26() set
{R,x} is non empty set
{R} is non empty set
{{R,x},{R}} is non empty set
root-tree [R,x] is Relation-like Function-like DecoratedTree-like set
i is set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
O1 is Element of the Sorts of (S,X) . (S,X,y)
OSClass ((S,X),O1) is Element of OSClass ((S,X),(S,X,y))
Class ((CompClass ((S,X),(CComp (S,X,y)))),O1) is Element of bool K541(S, the Sorts of (S,X),(CComp (S,X,y)))
bool K541(S, the Sorts of (S,X),(CComp (S,X,y))) is non empty set
(S,X) is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
(S,X) . O1 is set
proj1 ((S,X) . O1) is set
s is Element of the carrier of (S,X)
root-tree s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) . (root-tree s) is set
(S,X,s) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
{ [(root-tree s),b₁] where b₁ is Element of the carrier of S : ex b₂ being Element of the carrier of S ex b₃ being set st
( b₃ in X . b₂ & s = [b₃,b₂] & b₂ <= b₁ ) } is set
a is set
[i,a] is V26() set
{i,a} is non empty set
{i} is non empty set
{{i,a},{i}} is non empty set
b is Element of the carrier of S
[(root-tree s),b] is V26() set
{(root-tree s),b} is non empty set
{(root-tree s)} is non empty functional set
{{(root-tree s),b},{(root-tree s)}} is non empty set
tb is set
ta is Element of the carrier of S
X . ta is non empty set
[tb,ta] is V26() set
{tb,ta} is non empty set
{tb} is non empty set
{{tb,ta},{tb}} is non empty set
[i,x] is V26() set
{i,x} is non empty set
{{i,x},{i}} is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like OrderSortedRelation of (S,X)
t is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
y is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,x,y) is Element of OSClass (x,(S,X,y))
(S,X,y) is Element of the carrier of S
OSClass (x,(S,X,y)) is non empty Element of bool (Class (CompClass (x,(CComp (S,X,y)))))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
CComp (S,X,y) is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),(S,X,y)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,y))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,y) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,y) } is set
CompClass (x,(CComp (S,X,y))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,y))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,y))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):] is non empty set
Class (CompClass (x,(CComp (S,X,y)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,y)))
bool (Class (CompClass (x,(CComp (S,X,y))))) is non empty set
(S,X,x,t) is Element of OSClass (x,(S,X,t))
(S,X,t) is Element of the carrier of S
OSClass (x,(S,X,t)) is non empty Element of bool (Class (CompClass (x,(CComp (S,X,t)))))
CComp (S,X,t) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,t)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,t))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,t) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,t) } is set
CompClass (x,(CComp (S,X,t))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,t))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,t))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t))),K541(S, the Sorts of (S,X),(CComp (S,X,t))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,t))),K541(S, the Sorts of (S,X),(CComp (S,X,t))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t))),K541(S, the Sorts of (S,X),(CComp (S,X,t))):] is non empty set
Class (CompClass (x,(CComp (S,X,t)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,t)))
bool (Class (CompClass (x,(CComp (S,X,t))))) is non empty set
the Sorts of (S,X) . (S,X,y) is non empty set
O1 is Element of the Sorts of (S,X) . (S,X,y)
OSClass (x,O1) is Element of OSClass (x,(S,X,y))
Class ((CompClass (x,(CComp (S,X,y)))),O1) is Element of bool K541(S, the Sorts of (S,X),(CComp (S,X,y)))
bool K541(S, the Sorts of (S,X),(CComp (S,X,y))) is non empty set
[t,O1] is V26() set
{t,O1} is non empty set
{t} is non empty functional set
{{t,O1},{t}} is non empty set
s is Element of the carrier of S
x . s is Relation-like the Sorts of (S,X) . s -defined the Sorts of (S,X) . s -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):]
the Sorts of (S,X) . s is non empty set
[:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):] is non empty set
a is Element of the Sorts of (S,X) . s
OSClass (x,a) is Element of OSClass (x,s)
OSClass (x,s) is non empty Element of bool (Class (CompClass (x,(CComp s))))
CComp s is non empty Element of K539(S)
Class ((Path_Rel S),s) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp s)) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp s } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp s } is set
CompClass (x,(CComp s)) is Relation-like K541(S, the Sorts of (S,X),(CComp s)) -defined K541(S, the Sorts of (S,X),(CComp s)) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp s)),K541(S, the Sorts of (S,X),(CComp s)):]
[:K541(S, the Sorts of (S,X),(CComp s)),K541(S, the Sorts of (S,X),(CComp s)):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp s)),K541(S, the Sorts of (S,X),(CComp s)):] is non empty set
Class (CompClass (x,(CComp s))) is a_partition of K541(S, the Sorts of (S,X),(CComp s))
bool (Class (CompClass (x,(CComp s)))) is non empty set
Class ((CompClass (x,(CComp s))),a) is Element of bool K541(S, the Sorts of (S,X),(CComp s))
bool K541(S, the Sorts of (S,X),(CComp s)) is non empty set
b is Element of the Sorts of (S,X) . s
OSClass (x,b) is Element of OSClass (x,s)
Class ((CompClass (x,(CComp s))),b) is Element of bool K541(S, the Sorts of (S,X),(CComp s))
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
x is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like OrderSortedRelation of (S,X)
y is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like OrderSortedRelation of (S,X)
t is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,x,t) is Element of OSClass (x,(S,X,t))
(S,X,t) is Element of the carrier of S
OSClass (x,(S,X,t)) is non empty Element of bool (Class (CompClass (x,(CComp (S,X,t)))))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
CComp (S,X,t) is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),(S,X,t)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,t))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,t) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,t) } is set
CompClass (x,(CComp (S,X,t))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,t))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,t))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t))),K541(S, the Sorts of (S,X),(CComp (S,X,t))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,t))),K541(S, the Sorts of (S,X),(CComp (S,X,t))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t))),K541(S, the Sorts of (S,X),(CComp (S,X,t))):] is non empty set
Class (CompClass (x,(CComp (S,X,t)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,t)))
bool (Class (CompClass (x,(CComp (S,X,t))))) is non empty set
(S,X,y,t) is Element of OSClass (y,(S,X,t))
OSClass (y,(S,X,t)) is non empty Element of bool (Class (CompClass (y,(CComp (S,X,t)))))
CompClass (y,(CComp (S,X,t))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,t))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,t))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t))),K541(S, the Sorts of (S,X),(CComp (S,X,t))):]
Class (CompClass (y,(CComp (S,X,t)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,t)))
bool (Class (CompClass (y,(CComp (S,X,t))))) is non empty set
the Sorts of (S,X) . (S,X,t) is non empty set
a is Element of the Sorts of (S,X) . (S,X,t)
OSClass (x,a) is Element of OSClass (x,(S,X,t))
Class ((CompClass (x,(CComp (S,X,t)))),a) is Element of bool K541(S, the Sorts of (S,X),(CComp (S,X,t)))
bool K541(S, the Sorts of (S,X),(CComp (S,X,t))) is non empty set
b is set
[b,a] is V26() set
{b,a} is non empty set
{b} is non empty set
{{b,a},{b}} is non empty set
ta is Element of the carrier of S
x . ta is Relation-like the Sorts of (S,X) . ta -defined the Sorts of (S,X) . ta -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . ta),( the Sorts of (S,X) . ta):]
the Sorts of (S,X) . ta is non empty set
[:( the Sorts of (S,X) . ta),( the Sorts of (S,X) . ta):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . ta),( the Sorts of (S,X) . ta):] is non empty set
y . ta is Relation-like the Sorts of (S,X) . ta -defined the Sorts of (S,X) . ta -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . ta),( the Sorts of (S,X) . ta):]
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,y,t2) is Element of OSClass (y,(S,X,t2))
(S,X,t2) is Element of the carrier of S
OSClass (y,(S,X,t2)) is non empty Element of bool (Class (CompClass (y,(CComp (S,X,t2)))))
CComp (S,X,t2) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,t2)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,t2))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,t2) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,t2) } is set
CompClass (y,(CComp (S,X,t2))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,t2))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,t2))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t2))),K541(S, the Sorts of (S,X),(CComp (S,X,t2))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,t2))),K541(S, the Sorts of (S,X),(CComp (S,X,t2))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t2))),K541(S, the Sorts of (S,X),(CComp (S,X,t2))):] is non empty set
Class (CompClass (y,(CComp (S,X,t2)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,t2)))
bool (Class (CompClass (y,(CComp (S,X,t2))))) is non empty set
t1 is Element of the Sorts of (S,X) . ta
OSClass (y,t1) is Element of OSClass (y,ta)
OSClass (y,ta) is non empty Element of bool (Class (CompClass (y,(CComp ta))))
CComp ta is non empty Element of K539(S)
Class ((Path_Rel S),ta) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp ta)) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp ta } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp ta } is set
CompClass (y,(CComp ta)) is Relation-like K541(S, the Sorts of (S,X),(CComp ta)) -defined K541(S, the Sorts of (S,X),(CComp ta)) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp ta)),K541(S, the Sorts of (S,X),(CComp ta)):]
[:K541(S, the Sorts of (S,X),(CComp ta)),K541(S, the Sorts of (S,X),(CComp ta)):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp ta)),K541(S, the Sorts of (S,X),(CComp ta)):] is non empty set
Class (CompClass (y,(CComp ta))) is a_partition of K541(S, the Sorts of (S,X),(CComp ta))
bool (Class (CompClass (y,(CComp ta)))) is non empty set
Class ((CompClass (y,(CComp ta))),t1) is Element of bool K541(S, the Sorts of (S,X),(CComp ta))
bool K541(S, the Sorts of (S,X),(CComp ta)) is non empty set
tb is Element of the Sorts of (S,X) . ta
OSClass (y,tb) is Element of OSClass (y,ta)
Class ((CompClass (y,(CComp ta))),tb) is Element of bool K541(S, the Sorts of (S,X),(CComp ta))
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
x is Element of the carrier of S
X . x is non empty set
y is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),y) is Element of OSClass ((S,X),(S,X,y))
(S,X,y) is Element of the carrier of S
OSClass ((S,X),(S,X,y)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,y)))))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
CComp (S,X,y) is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),(S,X,y)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,y))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,y) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,y) } is set
CompClass ((S,X),(CComp (S,X,y))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,y))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,y))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,y)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,y)))
bool (Class (CompClass ((S,X),(CComp (S,X,y))))) is non empty set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
P is set
[P,x] is V26() set
{P,x} is non empty set
{P} is non empty set
{{P,x},{P}} is non empty set
root-tree [P,x] is Relation-like Function-like DecoratedTree-like set
O1 is set
(S,X,(S,X),y) is Element of OSClass ((S,X),(S,X,y))
OSClass ((S,X),(S,X,y)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,y)))))
CompClass ((S,X),(CComp (S,X,y))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,y))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,y))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):]
Class (CompClass ((S,X),(CComp (S,X,y)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,y)))
bool (Class (CompClass ((S,X),(CComp (S,X,y))))) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total ManySortedSubset of the Sorts of (S,X)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
t is Element of the carrier of (S,X)
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
Union x is non empty set
y is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of (S,X),x
t `2 is set
y . (t `2) is Relation-like Function-like set
root-tree t is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
R is set
O1 is Element of the carrier of S
X . O1 is non empty set
[R,O1] is V26() set
{R,O1} is non empty set
{R} is non empty set
{{R,O1},{R}} is non empty set
(S,X) . O1 is set
(S,X,O1) is non empty Element of bool ( the Sorts of (S,X) . O1)
the Sorts of (S,X) . O1 is non empty set
bool ( the Sorts of (S,X) . O1) is non empty set
y . O1 is Relation-like (S,X) . O1 -defined x . O1 -valued Function-like V29((S,X) . O1,x . O1) Element of bool [:((S,X) . O1),(x . O1):]
x . O1 is non empty set
[:((S,X) . O1),(x . O1):] is Relation-like set
bool [:((S,X) . O1),(x . O1):] is non empty set
dom (y . O1) is Element of bool ((S,X) . O1)
bool ((S,X) . O1) is non empty set
{ (root-tree b₁) where b₁ is Element of the carrier of (S,X) : ( b₁ in Terminals (S,X) & b₁ `2 = O1 ) } is set
(y . O1) . (root-tree t) is set
proj2 (y . O1) is set
dom x is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
proj2 x is non empty V205() set
union (proj2 x) is set
i is Element of Union x
s is Relation-like Function-like set
s . (root-tree t) is set
P is set
tx is Element of the carrier of S
X . tx is non empty set
[P,tx] is V26() set
{P,tx} is non empty set
{P} is non empty set
{{P,tx},{P}} is non empty set
y . tx is Relation-like (S,X) . tx -defined x . tx -valued Function-like V29((S,X) . tx,x . tx) Element of bool [:((S,X) . tx),(x . tx):]
(S,X) . tx is set
x . tx is non empty set
[:((S,X) . tx),(x . tx):] is Relation-like set
bool [:((S,X) . tx),(x . tx):] is non empty set
R is Element of Union x
i is Element of Union x
O1 is Relation-like Function-like set
O1 . (root-tree t) is set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total ManySortedSubset of the Sorts of (S,X)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
P is non-empty order-sorted monotone MSAlgebra over S
the Sorts of P is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
O1 is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of (S,X), the Sorts of P
the carrier of (S,X) is non empty set
Union the Sorts of P is non empty set
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)),(Union the Sorts of P):] is non empty Relation-like set
bool [:(TS (S,X)),(Union the Sorts of P):] is non empty set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
t1 is Relation-like TS (S,X) -defined Union the Sorts of P -valued Function-like V29( TS (S,X), Union the Sorts of P) Element of bool [:(TS (S,X)),(Union the Sorts of P):]
t2 is Relation-like Function-like set
proj1 t2 is set
t1 is non empty Relation-like the carrier of S -defined Function-like total set
dom t1 is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
t2 is set
t1 . t2 is set
the Sorts of (S,X) . t2 is set
t1 | ( the Sorts of (S,X) . t2) is Relation-like TS (S,X) -defined the Sorts of (S,X) . t2 -defined TS (S,X) -defined Union the Sorts of P -valued Function-like Element of bool [:(TS (S,X)),(Union the Sorts of P):]
t2 is non empty Relation-like the carrier of S -defined Function-like total V32() V33() set
t2 is Element of the carrier of (S,X)
s3 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots s3 is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
proj2 s3 is set
t2 -tree s3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
t1 * s3 is Relation-like K32() -defined Union the Sorts of P -valued Function-like V34() FinSequence-like FinSubsequence-like Element of (Union the Sorts of P) *
(Union the Sorts of P) * is non empty functional FinSequence-membered M10( Union the Sorts of P)
(S,X,t2) is Element of the carrier' of S
the_arity_of (S,X,t2) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the_result_sort_of (S,X,t2) is Element of the carrier of S
[(S,X,t2), the carrier of S] is V26() set
{(S,X,t2), the carrier of S} is non empty set
{(S,X,t2)} is non empty set
{{(S,X,t2), the carrier of S},{(S,X,t2)}} is non empty set
[[(S,X,t2), the carrier of S],(roots s3)] is V26() set
{[(S,X,t2), the carrier of S],(roots s3)} is non empty set
{[(S,X,t2), the carrier of S]} is non empty Relation-like Function-like set
{{[(S,X,t2), the carrier of S],(roots s3)},{[(S,X,t2), the carrier of S]}} is non empty set
the Rules of (S,X) is Relation-like the carrier of (S,X) -defined the carrier of (S,X) * -valued Element of bool [: the carrier of (S,X),( the carrier of (S,X) *):]
the carrier of (S,X) * is non empty functional FinSequence-membered M10( the carrier of (S,X))
[: the carrier of (S,X),( the carrier of (S,X) *):] is non empty Relation-like set
bool [: the carrier of (S,X),( the carrier of (S,X) *):] is non empty set
tak is Element of the carrier of S
the Sorts of (S,X) . tak is non empty set
t2 . tak is Relation-like Function-like set
(t2 . tak) . (t2 -tree s3) is set
the Sorts of P . tak is non empty set
rt is Element of the carrier' of S
[rt, the carrier of S] is V26() set
{rt, the carrier of S} is non empty set
{rt} is non empty set
{{rt, the carrier of S},{rt}} is non empty set
Args (rt,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (rt,(S,X)) is Relation-like Args (rt,(S,X)) -defined Result (rt,(S,X)) -valued Function-like V29( Args (rt,(S,X)), Result (rt,(S,X))) Element of bool [:(Args (rt,(S,X))),(Result (rt,(S,X))):]
Result (rt,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (rt,(S,X))),(Result (rt,(S,X))):] is non empty Relation-like set
bool [:(Args (rt,(S,X))),(Result (rt,(S,X))):] is non empty set
(Den (rt,(S,X))) . s3 is set
the_result_sort_of rt is Element of the carrier of S
tb is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
tb . (the_result_sort_of (S,X,t2)) is set
tk2 is Element of the carrier of S
tb . tk2 is set
Den ((S,X,t2),P) is Relation-like Args ((S,X,t2),P) -defined Result ((S,X,t2),P) -valued Function-like V29( Args ((S,X,t2),P), Result ((S,X,t2),P)) Element of bool [:(Args ((S,X,t2),P)),(Result ((S,X,t2),P)):]
Args ((S,X,t2),P) is non empty functional Element of proj2 ( the Sorts of P #)
the Sorts of P # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of P #) is non empty set
Result ((S,X,t2),P) is non empty Element of proj2 the Sorts of P
proj2 the Sorts of P is non empty V205() set
[:(Args ((S,X,t2),P)),(Result ((S,X,t2),P)):] is non empty Relation-like set
bool [:(Args ((S,X,t2),P)),(Result ((S,X,t2),P)):] is non empty set
proj2 (Den ((S,X,t2),P)) is set
(the_arity_of (S,X,t2)) * the Sorts of P is Relation-like non-empty K32() -defined dom (the_arity_of (S,X,t2)) -defined Function-like total V34() FinSequence-like FinSubsequence-like set
dom (the_arity_of (S,X,t2)) is Element of bool K32()
dom ((the_arity_of (S,X,t2)) * the Sorts of P) is Element of bool K32()
(S,X,(S,X,t2)) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
(S,X,(S,X,t2)) is Relation-like ( the Arity of S * ((S,X) #)) . (S,X,t2) -defined ( the ResultSort of S * (S,X)) . (S,X,t2) -valued Function-like V29(( the Arity of S * ((S,X) #)) . (S,X,t2),( the ResultSort of S * (S,X)) . (S,X,t2)) Element of bool [:(( the Arity of S * ((S,X) #)) . (S,X,t2)),(( the ResultSort of S * (S,X)) . (S,X,t2)):]
( the Arity of S * ((S,X) #)) . (S,X,t2) is set
( the ResultSort of S * (S,X)) . (S,X,t2) is non empty set
[:(( the Arity of S * ((S,X) #)) . (S,X,t2)),(( the ResultSort of S * (S,X)) . (S,X,t2)):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . (S,X,t2)),(( the ResultSort of S * (S,X)) . (S,X,t2)):] is non empty set
(S,X,(S,X,t2)) . s3 is set
(the_arity_of (S,X,t2)) * the Sorts of (S,X) is Relation-like non-empty K32() -defined dom (the_arity_of (S,X,t2)) -defined Function-like total V34() FinSequence-like FinSubsequence-like set
dom ((the_arity_of (S,X,t2)) * the Sorts of (S,X)) is Element of bool K32()
dom (S,X,(S,X,t2)) is Element of bool (( the Arity of S * ((S,X) #)) . (S,X,t2))
bool (( the Arity of S * ((S,X) #)) . (S,X,t2)) is non empty set
proj2 (S,X,(S,X,t2)) is set
t2 . (the_result_sort_of (S,X,t2)) is Relation-like Function-like set
the Sorts of (S,X) . (the_result_sort_of (S,X,t2)) is non empty set
t1 | ( the Sorts of (S,X) . (the_result_sort_of (S,X,t2))) is Relation-like TS (S,X) -defined the Sorts of (S,X) . (the_result_sort_of (S,X,t2)) -defined TS (S,X) -defined Union the Sorts of P -valued Function-like Element of bool [:(TS (S,X)),(Union the Sorts of P):]
len (the_arity_of (S,X,t2)) is V4() V5() V6() V10() Element of K32()
Seg (len (the_arity_of (S,X,t2))) is V34() V41( len (the_arity_of (S,X,t2))) Element of bool K32()
proj2 (the_arity_of (S,X,t2)) is set
the Arity of S . (S,X,t2) is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom (roots s3) is Element of bool K32()
dom s3 is Element of bool K32()
a is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
len a is V4() V5() V6() V10() Element of K32()
dom a is Element of bool K32()
Seg (len a) is V34() V41( len a) Element of bool K32()
dom (t1 * s3) is Element of bool K32()
n is set
(t1 * s3) . n is set
((the_arity_of (S,X,t2)) * the Sorts of P) . n is set
rt is V4() V5() V6() V10() set
s3 . rt is Relation-like Function-like set
(t1 * s3) . rt is set
t1 . (s3 . rt) is set
(the_arity_of (S,X,t2)) . n is set
s is Element of the carrier of S
t2 . s is Relation-like Function-like set
the Sorts of (S,X) . s is non empty set
t1 | ( the Sorts of (S,X) . s) is Relation-like TS (S,X) -defined the Sorts of (S,X) . s -defined TS (S,X) -defined Union the Sorts of P -valued Function-like Element of bool [:(TS (S,X)),(Union the Sorts of P):]
dom the Sorts of (S,X) is non empty Element of bool the carrier of S
dom t1 is functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
union (proj2 the Sorts of (S,X)) is set
proj1 (t2 . s) is set
(the_arity_of (S,X,t2)) * (S,X) is Relation-like non-empty K32() -defined dom (the_arity_of (S,X,t2)) -defined Function-like total V34() FinSequence-like FinSubsequence-like set
product ((the_arity_of (S,X,t2)) * (S,X)) is set
s3 . n is Relation-like Function-like set
((the_arity_of (S,X,t2)) * (S,X)) . n is set
(S,X) . ((the_arity_of (S,X,t2)) . n) is set
t is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(t2 . s) . t is set
the Sorts of P . s is non empty set
t1 . t is Element of Union the Sorts of P
pi ((S,X,t2),P,(t1 * s3)) is Element of Union the Sorts of P
dom (Den ((S,X,t2),P)) is functional Element of bool (Args ((S,X,t2),P))
bool (Args ((S,X,t2),P)) is non empty set
dom the ResultSort of S is Element of bool the carrier' of S
bool the carrier' of S is non empty set
the Arity of S * ( the Sorts of P #) is non empty Relation-like the carrier' of S -defined Function-like total set
( the Arity of S * ( the Sorts of P #)) . (S,X,t2) is set
product ((the_arity_of (S,X,t2)) * the Sorts of P) is set
(Den ((S,X,t2),P)) . (t1 * s3) is set
t1 | ( the Sorts of (S,X) . tak) is Relation-like TS (S,X) -defined the Sorts of (S,X) . tak -defined TS (S,X) -defined Union the Sorts of P -valued Function-like Element of bool [:(TS (S,X)),(Union the Sorts of P):]
t1 . (t2 -tree s3) is set
proj2 the ResultSort of S is set
dom the Sorts of (S,X) is non empty Element of bool the carrier of S
the ResultSort of S * the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
dom ( the ResultSort of S * the Sorts of (S,X)) is non empty Element of bool the carrier' of S
dom the Sorts of P is non empty Element of bool the carrier of S
the ResultSort of S * the Sorts of P is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
dom ( the ResultSort of S * the Sorts of P) is non empty Element of bool the carrier' of S
( the ResultSort of S * the Sorts of (S,X)) . (S,X,t2) is non empty set
the ResultSort of S . (S,X,t2) is Element of the carrier of S
the Sorts of (S,X) . ( the ResultSort of S . (S,X,t2)) is non empty set
(t1 | ( the Sorts of (S,X) . (the_result_sort_of (S,X,t2)))) . (t2 -tree s3) is set
( the ResultSort of S * the Sorts of P) . (S,X,t2) is non empty set
the Sorts of P . ( the ResultSort of S . (S,X,t2)) is non empty set
the Sorts of P . (the_result_sort_of (S,X,t2)) is non empty set
(t2 . (the_result_sort_of (S,X,t2))) . (t2 -tree s3) is set
t2 is Element of the carrier of (S,X)
root-tree t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
o1 is set
s3 is Element of the carrier of S
X . s3 is non empty set
[o1,s3] is V26() set
{o1,s3} is non empty set
{o1} is non empty set
{{o1,s3},{o1}} is non empty set
ts3 is Element of the carrier of S
{ (root-tree b<sub>1</sub>) where b<sub>1</sub> is Element of the carrier of (S,X) : ( b<sub>1</sub> in Terminals (S,X) & b<sub>1</sub> `2 = ts3 ) } is set
t2 `2 is set
(S,X) . ts3 is set
the Sorts of P . ts3 is non empty set
[:((S,X) . ts3),( the Sorts of P . ts3):] is Relation-like set
bool [:((S,X) . ts3),( the Sorts of P . ts3):] is non empty set
O1 . ts3 is Relation-like (S,X) . ts3 -defined the Sorts of P . ts3 -valued Function-like V29((S,X) . ts3, the Sorts of P . ts3) Element of bool [:((S,X) . ts3),( the Sorts of P . ts3):]
tk1 is Relation-like (S,X) . ts3 -defined the Sorts of P . ts3 -valued Function-like V29((S,X) . ts3, the Sorts of P . ts3) Element of bool [:((S,X) . ts3),( the Sorts of P . ts3):]
dom tk1 is Element of bool ((S,X) . ts3)
bool ((S,X) . ts3) is non empty set
proj2 tk1 is set
(S,X,ts3) is non empty Element of bool ( the Sorts of (S,X) . ts3)
the Sorts of (S,X) . ts3 is non empty set
bool ( the Sorts of (S,X) . ts3) is non empty set
tk1 . (root-tree t2) is set
tk3 is Element of the carrier of S
the Sorts of (S,X) . tk3 is non empty set
t2 . tk3 is Relation-like Function-like set
(t2 . tk3) . (root-tree t2) is set
the Sorts of P . tk3 is non empty set
tb is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
tak is Element of the carrier of S
tb . tak is set
tk2 is Element of the carrier of S
tb . tk2 is set
t2 . ts3 is Relation-like Function-like set
t1 | ( the Sorts of (S,X) . ts3) is Relation-like TS (S,X) -defined the Sorts of (S,X) . ts3 -defined TS (S,X) -defined Union the Sorts of P -valued Function-like Element of bool [:(TS (S,X)),(Union the Sorts of P):]
(t2 . ts3) . (root-tree t2) is set
t1 . (root-tree t2) is set
(S,X, the Sorts of P,O1,t2) is Element of Union the Sorts of P
t1 | ( the Sorts of (S,X) . tk3) is Relation-like TS (S,X) -defined the Sorts of (S,X) . tk3 -defined TS (S,X) -defined Union the Sorts of P -valued Function-like Element of bool [:(TS (S,X)),(Union the Sorts of P):]
t2 is set
t2 . t2 is Relation-like Function-like set
the Sorts of (S,X) . t2 is set
the Sorts of P . t2 is set
[:( the Sorts of (S,X) . t2),( the Sorts of P . t2):] is Relation-like set
bool [:( the Sorts of (S,X) . t2),( the Sorts of P . t2):] is non empty set
dom t1 is functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
proj2 the Sorts of (S,X) is non empty V205() set
union (proj2 the Sorts of (S,X)) is set
dom the Sorts of (S,X) is non empty Element of bool the carrier of S
s3 is Element of the carrier of S
the Sorts of (S,X) . s3 is non empty set
t2 . s3 is Relation-like Function-like set
t1 | ( the Sorts of (S,X) . s3) is Relation-like TS (S,X) -defined the Sorts of (S,X) . s3 -defined TS (S,X) -defined Union the Sorts of P -valued Function-like Element of bool [:(TS (S,X)),(Union the Sorts of P):]
proj1 (t2 . s3) is set
proj2 (t2 . s3) is set
the Sorts of P . s3 is non empty set
o1 is set
ts3 is set
(t2 . s3) . ts3 is set
o3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t2 is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of the Sorts of (S,X), the Sorts of P
t2 || (S,X) is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of (S,X), the Sorts of P
dom the Sorts of (S,X) is non empty Element of bool the carrier of S
proj2 the ResultSort of S is set
the ResultSort of S * the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
dom ( the ResultSort of S * the Sorts of (S,X)) is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
dom the ResultSort of S is Element of bool the carrier' of S
s3 is Element of the carrier' of S
Args (s3,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
the_result_sort_of s3 is Element of the carrier of S
t2 . (the_result_sort_of s3) is Relation-like the Sorts of (S,X) . (the_result_sort_of s3) -defined the Sorts of P . (the_result_sort_of s3) -valued Function-like V29( the Sorts of (S,X) . (the_result_sort_of s3), the Sorts of P . (the_result_sort_of s3)) Element of bool [:( the Sorts of (S,X) . (the_result_sort_of s3)),( the Sorts of P . (the_result_sort_of s3)):]
the Sorts of (S,X) . (the_result_sort_of s3) is non empty set
the Sorts of P . (the_result_sort_of s3) is non empty set
[:( the Sorts of (S,X) . (the_result_sort_of s3)),( the Sorts of P . (the_result_sort_of s3)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (the_result_sort_of s3)),( the Sorts of P . (the_result_sort_of s3)):] is non empty set
Den (s3,(S,X)) is Relation-like Args (s3,(S,X)) -defined Result (s3,(S,X)) -valued Function-like V29( Args (s3,(S,X)), Result (s3,(S,X))) Element of bool [:(Args (s3,(S,X))),(Result (s3,(S,X))):]
Result (s3,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (s3,(S,X))),(Result (s3,(S,X))):] is non empty Relation-like set
bool [:(Args (s3,(S,X))),(Result (s3,(S,X))):] is non empty set
Den (s3,P) is Relation-like Args (s3,P) -defined Result (s3,P) -valued Function-like V29( Args (s3,P), Result (s3,P)) Element of bool [:(Args (s3,P)),(Result (s3,P)):]
Args (s3,P) is non empty functional Element of proj2 ( the Sorts of P #)
the Sorts of P # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of P #) is non empty set
Result (s3,P) is non empty Element of proj2 the Sorts of P
proj2 the Sorts of P is non empty V205() set
[:(Args (s3,P)),(Result (s3,P)):] is non empty Relation-like set
bool [:(Args (s3,P)),(Result (s3,P)):] is non empty set
ts3 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (s3,(S,X))
(Den (s3,(S,X))) . ts3 is set
(t2 . (the_result_sort_of s3)) . ((Den (s3,(S,X))) . ts3) is set
t2 # ts3 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (s3,P)
(Den (s3,P)) . (t2 # ts3) is set
o1 is Element of the carrier' of S
the_result_sort_of o1 is Element of the carrier of S
Den (o1,(S,X)) is Relation-like Args (o1,(S,X)) -defined Result (o1,(S,X)) -valued Function-like V29( Args (o1,(S,X)), Result (o1,(S,X))) Element of bool [:(Args (o1,(S,X))),(Result (o1,(S,X))):]
Args (o1,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Result (o1,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (o1,(S,X))),(Result (o1,(S,X))):] is non empty Relation-like set
bool [:(Args (o1,(S,X))),(Result (o1,(S,X))):] is non empty set
Den (o1,P) is Relation-like Args (o1,P) -defined Result (o1,P) -valued Function-like V29( Args (o1,P), Result (o1,P)) Element of bool [:(Args (o1,P)),(Result (o1,P)):]
Args (o1,P) is non empty functional Element of proj2 ( the Sorts of P #)
Result (o1,P) is non empty Element of proj2 the Sorts of P
[:(Args (o1,P)),(Result (o1,P)):] is non empty Relation-like set
bool [:(Args (o1,P)),(Result (o1,P)):] is non empty set
the_arity_of o1 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the Arity of S . o1 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
( the Arity of S * ((S,X) #)) . o1 is set
(S,X,o1) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
[o1, the carrier of S] is V26() set
{o1, the carrier of S} is non empty set
{o1} is non empty set
{{o1, the carrier of S},{o1}} is non empty set
tk2 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots tk2 is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
(S,X,(S,X,o1)) is Element of the carrier' of S
t1 * tk2 is Relation-like K32() -defined Union the Sorts of P -valued Function-like V34() FinSequence-like FinSubsequence-like Element of (Union the Sorts of P) *
(Union the Sorts of P) * is non empty functional FinSequence-membered M10( Union the Sorts of P)
dom (t1 * tk2) is Element of bool K32()
dom tk2 is Element of bool K32()
a is set
(t1 * tk2) . a is set
(t2 # ts3) . a is set
(the_arity_of o1) * the Sorts of (S,X) is Relation-like non-empty K32() -defined dom (the_arity_of o1) -defined Function-like total V34() FinSequence-like FinSubsequence-like set
dom (the_arity_of o1) is Element of bool K32()
dom ((the_arity_of o1) * the Sorts of (S,X)) is Element of bool K32()
[[o1, the carrier of S],(roots tk2)] is V26() set
{[o1, the carrier of S],(roots tk2)} is non empty set
{[o1, the carrier of S]} is non empty Relation-like Function-like set
{{[o1, the carrier of S],(roots tk2)},{[o1, the carrier of S]}} is non empty set
the Rules of (S,X) is Relation-like the carrier of (S,X) -defined the carrier of (S,X) * -valued Element of bool [: the carrier of (S,X),( the carrier of (S,X) *):]
the carrier of (S,X) * is non empty functional FinSequence-membered M10( the carrier of (S,X))
[: the carrier of (S,X),( the carrier of (S,X) *):] is non empty Relation-like set
bool [: the carrier of (S,X),( the carrier of (S,X) *):] is non empty set
n is V4() V5() V6() V10() set
(t2 # ts3) . n is set
(the_arity_of o1) /. n is Element of the carrier of S
t2 . ((the_arity_of o1) /. n) is Relation-like the Sorts of (S,X) . ((the_arity_of o1) /. n) -defined the Sorts of P . ((the_arity_of o1) /. n) -valued Function-like V29( the Sorts of (S,X) . ((the_arity_of o1) /. n), the Sorts of P . ((the_arity_of o1) /. n)) Element of bool [:( the Sorts of (S,X) . ((the_arity_of o1) /. n)),( the Sorts of P . ((the_arity_of o1) /. n)):]
the Sorts of (S,X) . ((the_arity_of o1) /. n) is non empty set
the Sorts of P . ((the_arity_of o1) /. n) is non empty set
[:( the Sorts of (S,X) . ((the_arity_of o1) /. n)),( the Sorts of P . ((the_arity_of o1) /. n)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . ((the_arity_of o1) /. n)),( the Sorts of P . ((the_arity_of o1) /. n)):] is non empty set
ts3 . n is set
(t2 . ((the_arity_of o1) /. n)) . (ts3 . n) is set
(t1 * tk2) . n is set
t1 . (ts3 . n) is set
t1 | ( the Sorts of (S,X) . ((the_arity_of o1) /. n)) is Relation-like TS (S,X) -defined the Sorts of (S,X) . ((the_arity_of o1) /. n) -defined TS (S,X) -defined Union the Sorts of P -valued Function-like Element of bool [:(TS (S,X)),(Union the Sorts of P):]
dom (roots tk2) is Element of bool K32()
rt is Relation-like K32() -defined [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -valued Function-like V34() FinSequence-like FinSubsequence-like Element of ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *
len rt is V4() V5() V6() V10() Element of K32()
len (the_arity_of o1) is V4() V5() V6() V10() Element of K32()
Seg (len rt) is V34() V41( len rt) Element of bool K32()
dom rt is Element of bool K32()
Seg (len (the_arity_of o1)) is V34() V41( len (the_arity_of o1)) Element of bool K32()
(the_arity_of o1) * (S,X) is Relation-like non-empty K32() -defined dom (the_arity_of o1) -defined Function-like total V34() FinSequence-like FinSubsequence-like set
product ((the_arity_of o1) * (S,X)) is set
tk2 . n is Relation-like Function-like set
((the_arity_of o1) * (S,X)) . n is set
(the_arity_of o1) . n is set
the Sorts of (S,X) . ((the_arity_of o1) . n) is set
dom (t2 # ts3) is Element of bool K32()
dom (the_arity_of o1) is Element of bool K32()
t2 . (the_result_sort_of o1) is Relation-like the Sorts of (S,X) . (the_result_sort_of o1) -defined the Sorts of P . (the_result_sort_of o1) -valued Function-like V29( the Sorts of (S,X) . (the_result_sort_of o1), the Sorts of P . (the_result_sort_of o1)) Element of bool [:( the Sorts of (S,X) . (the_result_sort_of o1)),( the Sorts of P . (the_result_sort_of o1)):]
the Sorts of (S,X) . (the_result_sort_of o1) is non empty set
the Sorts of P . (the_result_sort_of o1) is non empty set
[:( the Sorts of (S,X) . (the_result_sort_of o1)),( the Sorts of P . (the_result_sort_of o1)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (the_result_sort_of o1)),( the Sorts of P . (the_result_sort_of o1)):] is non empty set
t1 | ( the Sorts of (S,X) . (the_result_sort_of o1)) is Relation-like TS (S,X) -defined the Sorts of (S,X) . (the_result_sort_of o1) -defined TS (S,X) -defined Union the Sorts of P -valued Function-like Element of bool [:(TS (S,X)),(Union the Sorts of P):]
(S,X,o1) is Relation-like ( the Arity of S * ((S,X) #)) . o1 -defined ( the ResultSort of S * (S,X)) . o1 -valued Function-like V29(( the Arity of S * ((S,X) #)) . o1,( the ResultSort of S * (S,X)) . o1) Element of bool [:(( the Arity of S * ((S,X) #)) . o1),(( the ResultSort of S * (S,X)) . o1):]
( the ResultSort of S * (S,X)) . o1 is non empty set
[:(( the Arity of S * ((S,X) #)) . o1),(( the ResultSort of S * (S,X)) . o1):] is Relation-like set
bool [:(( the Arity of S * ((S,X) #)) . o1),(( the ResultSort of S * (S,X)) . o1):] is non empty set
proj2 (S,X,o1) is set
dom (S,X,o1) is Element of bool (( the Arity of S * ((S,X) #)) . o1)
bool (( the Arity of S * ((S,X) #)) . o1) is non empty set
(S,X,o1) . tk2 is set
(S,X,o1) -tree tk2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
( the ResultSort of S * the Sorts of (S,X)) . o1 is non empty set
the ResultSort of S . o1 is Element of the carrier of S
the Sorts of (S,X) . ( the ResultSort of S . o1) is non empty set
dom t1 is functional constituted-DTrees Element of bool (TS (S,X))
bool (TS (S,X)) is non empty set
union (proj2 the Sorts of (S,X)) is set
dom (t2 . (the_result_sort_of o1)) is Element of bool ( the Sorts of (S,X) . (the_result_sort_of o1))
bool ( the Sorts of (S,X) . (the_result_sort_of o1)) is non empty set
(S,X) . o1 is Relation-like ( the Arity of S * ((S,X) #)) . o1 -defined ( the ResultSort of S * (S,X)) . o1 -valued Function-like V29(( the Arity of S * ((S,X) #)) . o1,( the ResultSort of S * (S,X)) . o1) Element of bool [:(( the Arity of S * ((S,X) #)) . o1),(( the ResultSort of S * (S,X)) . o1):]
(Den (o1,(S,X))) . ts3 is set
(t2 . (the_result_sort_of o1)) . ((Den (o1,(S,X))) . ts3) is set
t1 . ((S,X,o1) -tree tk2) is set
pi ((S,X,(S,X,o1)),P,(t1 * tk2)) is Element of Union the Sorts of P
(Den (o1,P)) . (t2 # ts3) is set
s3 is Element of the carrier of S
o1 is Element of the carrier of S
t2 . s3 is Relation-like Function-like set
proj1 (t2 . s3) is set
t2 . o1 is Relation-like Function-like set
proj1 (t2 . o1) is set
ta is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
ta . s3 is set
ta . o1 is set
ts3 is set
(t2 . s3) . ts3 is set
(t2 . o1) . ts3 is set
the Sorts of (S,X) . s3 is non empty set
t2 . s3 is Relation-like the Sorts of (S,X) . s3 -defined the Sorts of P . s3 -valued Function-like V29( the Sorts of (S,X) . s3, the Sorts of P . s3) Element of bool [:( the Sorts of (S,X) . s3),( the Sorts of P . s3):]
the Sorts of P . s3 is non empty set
[:( the Sorts of (S,X) . s3),( the Sorts of P . s3):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . s3),( the Sorts of P . s3):] is non empty set
dom (t2 . s3) is Element of bool ( the Sorts of (S,X) . s3)
bool ( the Sorts of (S,X) . s3) is non empty set
the Sorts of (S,X) . o1 is non empty set
t2 . o1 is Relation-like the Sorts of (S,X) . o1 -defined the Sorts of P . o1 -valued Function-like V29( the Sorts of (S,X) . o1, the Sorts of P . o1) Element of bool [:( the Sorts of (S,X) . o1),( the Sorts of P . o1):]
the Sorts of P . o1 is non empty set
[:( the Sorts of (S,X) . o1),( the Sorts of P . o1):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . o1),( the Sorts of P . o1):] is non empty set
dom (t2 . o1) is Element of bool ( the Sorts of (S,X) . o1)
bool ( the Sorts of (S,X) . o1) is non empty set
t1 | ( the Sorts of (S,X) . o1) is Relation-like TS (S,X) -defined the Sorts of (S,X) . o1 -defined TS (S,X) -defined Union the Sorts of P -valued Function-like Element of bool [:(TS (S,X)),(Union the Sorts of P):]
t1 | ( the Sorts of (S,X) . s3) is Relation-like TS (S,X) -defined the Sorts of (S,X) . s3 -defined TS (S,X) -defined Union the Sorts of P -valued Function-like Element of bool [:(TS (S,X)),(Union the Sorts of P):]
(t2 . s3) . ts3 is set
t1 . ts3 is set
(t2 . o1) . ts3 is set
o1 is set
(t2 || (S,X)) . o1 is Relation-like Function-like set
O1 . o1 is Relation-like Function-like set
ts3 is Element of the carrier of S
the Sorts of (S,X) . ts3 is non empty set
t2 . ts3 is Relation-like the Sorts of (S,X) . ts3 -defined the Sorts of P . ts3 -valued Function-like V29( the Sorts of (S,X) . ts3, the Sorts of P . ts3) Element of bool [:( the Sorts of (S,X) . ts3),( the Sorts of P . ts3):]
the Sorts of P . ts3 is non empty set
[:( the Sorts of (S,X) . ts3),( the Sorts of P . ts3):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . ts3),( the Sorts of P . ts3):] is non empty set
dom (t2 . ts3) is Element of bool ( the Sorts of (S,X) . ts3)
bool ( the Sorts of (S,X) . ts3) is non empty set
(S,X) . ts3 is set
(t2 || (S,X)) . ts3 is Relation-like (S,X) . ts3 -defined the Sorts of P . ts3 -valued Function-like V29((S,X) . ts3, the Sorts of P . ts3) Element of bool [:((S,X) . ts3),( the Sorts of P . ts3):]
[:((S,X) . ts3),( the Sorts of P . ts3):] is Relation-like set
bool [:((S,X) . ts3),( the Sorts of P . ts3):] is non empty set
dom ((t2 || (S,X)) . ts3) is Element of bool ((S,X) . ts3)
bool ((S,X) . ts3) is non empty set
(S,X,ts3) is non empty Element of bool ( the Sorts of (S,X) . ts3)
(t2 . ts3) | ((S,X) . ts3) is Relation-like the Sorts of (S,X) . ts3 -defined (S,X) . ts3 -defined the Sorts of (S,X) . ts3 -defined the Sorts of P . ts3 -valued Function-like Element of bool [:( the Sorts of (S,X) . ts3),( the Sorts of P . ts3):]
O1 . ts3 is Relation-like (S,X) . ts3 -defined the Sorts of P . ts3 -valued Function-like V29((S,X) . ts3, the Sorts of P . ts3) Element of bool [:((S,X) . ts3),( the Sorts of P . ts3):]
o3 is set
((t2 || (S,X)) . ts3) . o3 is set
(O1 . ts3) . o3 is set
t1 | ( the Sorts of (S,X) . ts3) is Relation-like TS (S,X) -defined the Sorts of (S,X) . ts3 -defined TS (S,X) -defined Union the Sorts of P -valued Function-like Element of bool [:(TS (S,X)),(Union the Sorts of P):]
{ (root-tree b<sub>1</sub>) where b<sub>1</sub> is Element of the carrier of (S,X) : ( b<sub>1</sub> in Terminals (S,X) & b<sub>1</sub> `2 = ts3 ) } is set
k is Element of the carrier of (S,X)
root-tree k is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
k `2 is set
(t2 . ts3) . o3 is set
t1 . o3 is set
(S,X, the Sorts of P,O1,k) is Element of Union the Sorts of P
dom (O1 . ts3) is Element of bool ((S,X) . ts3)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is Element of the carrier of S
(S,X,x) is non empty Element of bool ( the Sorts of (S,X) . x)
(S,X) is strict non-empty order-sorted monotone MSAlgebra over S
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
QuotOSAlg ((S,X),(S,X)) is strict non-empty order-sorted monotone MSAlgebra over S
OSClass (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
OSQuotCharact (S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((OSClass (S,X)) #), the ResultSort of S * (OSClass (S,X))
(OSClass (S,X)) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((OSClass (S,X)) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * (OSClass (S,X)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (OSClass (S,X)),(OSQuotCharact (S,X)) #) is strict MSAlgebra over S
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . x is non empty set
bool ( the Sorts of (S,X) . x) is non empty set
(S,X,x) is non empty Element of bool ( the Sorts of (S,X) . x)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . x is non empty set
bool ( the Sorts of (S,X) . x) is non empty set
[:(S,X,x),(S,X,x):] is non empty Relation-like set
bool [:(S,X,x),(S,X,x):] is non empty set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
the Sorts of (QuotOSAlg ((S,X),(S,X))) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
OSNat_Hom ((S,X),(S,X)) is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of the Sorts of (S,X), the Sorts of (QuotOSAlg ((S,X),(S,X)))
(OSNat_Hom ((S,X),(S,X))) . x is Relation-like the Sorts of (S,X) . x -defined the Sorts of (QuotOSAlg ((S,X),(S,X))) . x -valued Function-like V29( the Sorts of (S,X) . x, the Sorts of (QuotOSAlg ((S,X),(S,X))) . x) Element of bool [:( the Sorts of (S,X) . x),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . x):]
the Sorts of (QuotOSAlg ((S,X),(S,X))) . x is non empty set
[:( the Sorts of (S,X) . x),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . x):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . x),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . x):] is non empty set
OSNat_Hom ((S,X),(S,X),x) is Relation-like the Sorts of (S,X) . x -defined OSClass ((S,X),x) -valued Function-like V29( the Sorts of (S,X) . x, OSClass ((S,X),x)) Element of bool [:( the Sorts of (S,X) . x),(OSClass ((S,X),x)):]
OSClass ((S,X),x) is non empty Element of bool (Class (CompClass ((S,X),(CComp x))))
CComp x is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),x) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp x)) is set
{ ( the Sorts of (S,X) . b<sub>1</sub>) where b<sub>1</sub> is Element of the carrier of S : b<sub>1</sub> in CComp x } is set
union { ( the Sorts of (S,X) . b<sub>1</sub>) where b<sub>1</sub> is Element of the carrier of S : b<sub>1</sub> in CComp x } is set
CompClass ((S,X),(CComp x)) is Relation-like K541(S, the Sorts of (S,X),(CComp x)) -defined K541(S, the Sorts of (S,X),(CComp x)) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp x)),K541(S, the Sorts of (S,X),(CComp x)):]
[:K541(S, the Sorts of (S,X),(CComp x)),K541(S, the Sorts of (S,X),(CComp x)):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp x)),K541(S, the Sorts of (S,X),(CComp x)):] is non empty set
Class (CompClass ((S,X),(CComp x))) is a_partition of K541(S, the Sorts of (S,X),(CComp x))
bool (Class (CompClass ((S,X),(CComp x)))) is non empty set
[:( the Sorts of (S,X) . x),(OSClass ((S,X),x)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . x),(OSClass ((S,X),x)):] is non empty set
s is set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
{ (((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree b<sub>1</sub>)) where b<sub>1</sub> is Element of the carrier of (S,X) : ( b<sub>1</sub> in Terminals (S,X) & b<sub>1</sub> `2 = x ) } is set
a is Element of the carrier of (S,X)
root-tree a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree a) is set
a `2 is set
(OSNat_Hom ((S,X),(S,X),x)) . (root-tree a) is set
ta is set
b is Element of the carrier of S
X . b is non empty set
[ta,b] is V26() set
{ta,b} is non empty set
{ta} is non empty set
{{ta,b},{ta}} is non empty set
tb is Element of the Sorts of (S,X) . x
(OSNat_Hom ((S,X),(S,X),x)) . tb is Element of OSClass ((S,X),x)
OSClass ((S,X),tb) is Element of OSClass ((S,X),x)
Class ((CompClass ((S,X),(CComp x))),tb) is Element of bool K541(S, the Sorts of (S,X),(CComp x))
bool K541(S, the Sorts of (S,X),(CComp x)) is non empty set
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
t2 is Element of the carrier of (S,X)
root-tree t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree t2) is set
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),t1) is Element of OSClass ((S,X),(S,X,t1))
(S,X,t1) is Element of the carrier of S
OSClass ((S,X),(S,X,t1)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,t1)))))
CComp (S,X,t1) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,t1)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,t1))) is set
{ ( the Sorts of (S,X) . b<sub>1</sub>) where b<sub>1</sub> is Element of the carrier of S : b<sub>1</sub> in CComp (S,X,t1) } is set
union { ( the Sorts of (S,X) . b<sub>1</sub>) where b<sub>1</sub> is Element of the carrier of S : b<sub>1</sub> in CComp (S,X,t1) } is set
CompClass ((S,X),(CComp (S,X,t1))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,t1))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,t1))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t1))),K541(S, the Sorts of (S,X),(CComp (S,X,t1))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,t1))),K541(S, the Sorts of (S,X),(CComp (S,X,t1))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t1))),K541(S, the Sorts of (S,X),(CComp (S,X,t1))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,t1)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,t1)))
bool (Class (CompClass ((S,X),(CComp (S,X,t1))))) is non empty set
dom (OSNat_Hom ((S,X),(S,X),x)) is Element of bool ( the Sorts of (S,X) . x)
t1 is Element of the Sorts of (S,X) . x
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),t2) is Element of OSClass ((S,X),(S,X,t2))
(S,X,t2) is Element of the carrier of S
OSClass ((S,X),(S,X,t2)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,t2)))))
CComp (S,X,t2) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,t2)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,t2))) is set
{ ( the Sorts of (S,X) . b<sub>1</sub>) where b<sub>1</sub> is Element of the carrier of S : b<sub>1</sub> in CComp (S,X,t2) } is set
union { ( the Sorts of (S,X) . b<sub>1</sub>) where b<sub>1</sub> is Element of the carrier of S : b<sub>1</sub> in CComp (S,X,t2) } is set
CompClass ((S,X),(CComp (S,X,t2))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,t2))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,t2))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t2))),K541(S, the Sorts of (S,X),(CComp (S,X,t2))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,t2))),K541(S, the Sorts of (S,X),(CComp (S,X,t2))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t2))),K541(S, the Sorts of (S,X),(CComp (S,X,t2))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,t2)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,t2)))
bool (Class (CompClass ((S,X),(CComp (S,X,t2))))) is non empty set
OSClass ((S,X),t1) is Element of OSClass ((S,X),x)
Class ((CompClass ((S,X),(CComp x))),t1) is Element of bool K541(S, the Sorts of (S,X),(CComp x))
(OSNat_Hom ((S,X),(S,X),x)) . (root-tree t2) is set
s is Relation-like Function-like set
proj1 s is set
proj2 s is set
a is Relation-like (S,X,x) -defined (S,X,x) -valued Function-like V29((S,X,x),(S,X,x)) Element of bool [:(S,X,x),(S,X,x):]
b is Element of the carrier of (S,X)
root-tree b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree b) is set
a . (((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree b)) is set
y is Relation-like (S,X,x) -defined (S,X,x) -valued Function-like V29((S,X,x),(S,X,x)) Element of bool [:(S,X,x),(S,X,x):]
t is Relation-like (S,X,x) -defined (S,X,x) -valued Function-like V29((S,X,x),(S,X,x)) Element of bool [:(S,X,x),(S,X,x):]
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
{ (((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree b<sub>1</sub>)) where b<sub>1</sub> is Element of the carrier of (S,X) : ( b<sub>1</sub> in Terminals (S,X) & b<sub>1</sub> `2 = x ) } is set
dom t is Element of bool (S,X,x)
bool (S,X,x) is non empty set
R is set
y . R is set
t . R is set
i is Element of the carrier of (S,X)
root-tree i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree i) is set
i `2 is set
y . (((OSNat_Hom ((S,X),(S,X))) . x) . (root-tree i)) is set
dom y is Element of bool (S,X,x)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total (S,(S,X))
(S,X) is strict non-empty order-sorted monotone MSAlgebra over S
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
QuotOSAlg ((S,X),(S,X)) is strict non-empty order-sorted monotone MSAlgebra over S
OSClass (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
OSQuotCharact (S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((OSClass (S,X)) #), the ResultSort of S * (OSClass (S,X))
(OSClass (S,X)) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((OSClass (S,X)) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * (OSClass (S,X)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (OSClass (S,X)),(OSQuotCharact (S,X)) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total ManySortedSubset of the Sorts of (S,X)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
t is set
tx is Element of the carrier of S
(S,X,tx) is Relation-like (S,X,tx) -defined (S,X,tx) -valued Function-like V29((S,X,tx),(S,X,tx)) Element of bool [:(S,X,tx),(S,X,tx):]
(S,X,tx) is non empty Element of bool ( the Sorts of (S,X) . tx)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . tx is non empty set
bool ( the Sorts of (S,X) . tx) is non empty set
(S,X,tx) is non empty Element of bool ( the Sorts of (S,X) . tx)
the Sorts of (S,X) . tx is non empty set
bool ( the Sorts of (S,X) . tx) is non empty set
[:(S,X,tx),(S,X,tx):] is non empty Relation-like set
bool [:(S,X,tx),(S,X,tx):] is non empty set
P is Element of the carrier of S
(S,X,P) is Relation-like (S,X,P) -defined (S,X,P) -valued Function-like V29((S,X,P),(S,X,P)) Element of bool [:(S,X,P),(S,X,P):]
(S,X,P) is non empty Element of bool ( the Sorts of (S,X) . P)
the Sorts of (S,X) . P is non empty set
bool ( the Sorts of (S,X) . P) is non empty set
(S,X,P) is non empty Element of bool ( the Sorts of (S,X) . P)
the Sorts of (S,X) . P is non empty set
bool ( the Sorts of (S,X) . P) is non empty set
[:(S,X,P),(S,X,P):] is non empty Relation-like set
bool [:(S,X,P),(S,X,P):] is non empty set
t is Relation-like Function-like set
proj1 t is set
tx is non empty Relation-like the carrier of S -defined Function-like total set
dom tx is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
P is set
tx . P is set
O1 is Element of the carrier of S
tx . O1 is set
(S,X,O1) is Relation-like (S,X,O1) -defined (S,X,O1) -valued Function-like V29((S,X,O1),(S,X,O1)) Element of bool [:(S,X,O1),(S,X,O1):]
(S,X,O1) is non empty Element of bool ( the Sorts of (S,X) . O1)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . O1 is non empty set
bool ( the Sorts of (S,X) . O1) is non empty set
(S,X,O1) is non empty Element of bool ( the Sorts of (S,X) . O1)
the Sorts of (S,X) . O1 is non empty set
bool ( the Sorts of (S,X) . O1) is non empty set
[:(S,X,O1),(S,X,O1):] is non empty Relation-like set
bool [:(S,X,O1),(S,X,O1):] is non empty set
P is non empty Relation-like the carrier of S -defined Function-like total V32() V33() set
O1 is set
P . O1 is Relation-like Function-like set
(S,X) . O1 is set
(S,X) . O1 is set
[:((S,X) . O1),((S,X) . O1):] is Relation-like set
bool [:((S,X) . O1),((S,X) . O1):] is non empty set
R is Element of the carrier of S
(S,X) . R is set
(S,X,R) is non empty Element of bool ( the Sorts of (S,X) . R)
the Sorts of (S,X) . R is non empty set
bool ( the Sorts of (S,X) . R) is non empty set
(S,X,R) is Relation-like (S,X,R) -defined (S,X,R) -valued Function-like V29((S,X,R),(S,X,R)) Element of bool [:(S,X,R),(S,X,R):]
(S,X,R) is non empty Element of bool ( the Sorts of (S,X) . R)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . R is non empty set
bool ( the Sorts of (S,X) . R) is non empty set
[:(S,X,R),(S,X,R):] is non empty Relation-like set
bool [:(S,X,R),(S,X,R):] is non empty set
(S,X) . R is non empty set
O1 is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of (S,X),(S,X)
R is Element of the carrier of S
O1 . R is Relation-like (S,X) . R -defined (S,X) . R -valued Function-like V29((S,X) . R,(S,X) . R) Element of bool [:((S,X) . R),((S,X) . R):]
(S,X) . R is non empty set
(S,X) . R is set
[:((S,X) . R),((S,X) . R):] is Relation-like set
bool [:((S,X) . R),((S,X) . R):] is non empty set
(S,X,R) is Relation-like (S,X,R) -defined (S,X,R) -valued Function-like V29((S,X,R),(S,X,R)) Element of bool [:(S,X,R),(S,X,R):]
(S,X,R) is non empty Element of bool ( the Sorts of (S,X) . R)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . R is non empty set
bool ( the Sorts of (S,X) . R) is non empty set
(S,X,R) is non empty Element of bool ( the Sorts of (S,X) . R)
the Sorts of (S,X) . R is non empty set
bool ( the Sorts of (S,X) . R) is non empty set
[:(S,X,R),(S,X,R):] is non empty Relation-like set
bool [:(S,X,R),(S,X,R):] is non empty set
x is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of (S,X),(S,X)
y is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of (S,X),(S,X)
t is set
x . t is Relation-like Function-like set
y . t is Relation-like Function-like set
tx is Element of the carrier of S
x . tx is Relation-like (S,X) . tx -defined (S,X) . tx -valued Function-like V29((S,X) . tx,(S,X) . tx) Element of bool [:((S,X) . tx),((S,X) . tx):]
(S,X) . tx is non empty set
(S,X) . tx is set
[:((S,X) . tx),((S,X) . tx):] is Relation-like set
bool [:((S,X) . tx),((S,X) . tx):] is non empty set
(S,X,tx) is Relation-like (S,X,tx) -defined (S,X,tx) -valued Function-like V29((S,X,tx),(S,X,tx)) Element of bool [:(S,X,tx),(S,X,tx):]
(S,X,tx) is non empty Element of bool ( the Sorts of (S,X) . tx)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) . tx is non empty set
bool ( the Sorts of (S,X) . tx) is non empty set
(S,X,tx) is non empty Element of bool ( the Sorts of (S,X) . tx)
the Sorts of (S,X) . tx is non empty set
bool ( the Sorts of (S,X) . tx) is non empty set
[:(S,X,tx),(S,X,tx):] is non empty Relation-like set
bool [:(S,X,tx),(S,X,tx):] is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted monotone MSAlgebra over S
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
QuotOSAlg ((S,X),(S,X)) is strict non-empty order-sorted monotone MSAlgebra over S
OSClass (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
OSQuotCharact (S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((OSClass (S,X)) #), the ResultSort of S * (OSClass (S,X))
(OSClass (S,X)) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((OSClass (S,X)) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * (OSClass (S,X)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (OSClass (S,X)),(OSQuotCharact (S,X)) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total (S,(S,X))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
P is non-empty order-sorted monotone MSAlgebra over S
the Sorts of P is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
O1 is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of (S,X), the Sorts of P
OSNat_Hom ((S,X),(S,X)) is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of the Sorts of (S,X), the Sorts of (QuotOSAlg ((S,X),(S,X)))
the Sorts of (QuotOSAlg ((S,X),(S,X))) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total ManySortedSubset of the Sorts of (S,X)
b is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of the Sorts of (S,X), the Sorts of (S,X)
b || (S,X) is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of (S,X), the Sorts of (S,X)
tb is Element of the carrier of S
(b || (S,X)) . tb is Relation-like (S,X) . tb -defined the Sorts of (S,X) . tb -valued Function-like V29((S,X) . tb, the Sorts of (S,X) . tb) Element of bool [:((S,X) . tb),( the Sorts of (S,X) . tb):]
(S,X) . tb is set
the Sorts of (S,X) . tb is non empty set
[:((S,X) . tb),( the Sorts of (S,X) . tb):] is Relation-like set
bool [:((S,X) . tb),( the Sorts of (S,X) . tb):] is non empty set
the Sorts of (S,X) . tb is non empty set
b . tb is Relation-like the Sorts of (S,X) . tb -defined the Sorts of (S,X) . tb -valued Function-like V29( the Sorts of (S,X) . tb, the Sorts of (S,X) . tb) Element of bool [:( the Sorts of (S,X) . tb),( the Sorts of (S,X) . tb):]
[:( the Sorts of (S,X) . tb),( the Sorts of (S,X) . tb):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . tb),( the Sorts of (S,X) . tb):] is non empty set
(b . tb) | ((S,X) . tb) is Relation-like (S,X) . tb -defined the Sorts of (S,X) . tb -defined the Sorts of (S,X) . tb -valued Function-like Element of bool [:( the Sorts of (S,X) . tb),( the Sorts of (S,X) . tb):]
(S,X,tb) is non empty Element of bool ( the Sorts of (S,X) . tb)
bool ( the Sorts of (S,X) . tb) is non empty set
(b . tb) | (S,X,tb) is Relation-like the Sorts of (S,X) . tb -defined (S,X,tb) -defined the Sorts of (S,X) . tb -defined the Sorts of (S,X) . tb -valued Function-like Element of bool [:( the Sorts of (S,X) . tb),( the Sorts of (S,X) . tb):]
dom (b . tb) is Element of bool ( the Sorts of (S,X) . tb)
proj2 (b . tb) is set
dom ((b || (S,X)) . tb) is Element of bool ((S,X) . tb)
bool ((S,X) . tb) is non empty set
(S,X) . tb is non empty set
t1 is set
(S,X,tb) is non empty Element of bool ( the Sorts of (S,X) . tb)
bool ( the Sorts of (S,X) . tb) is non empty set
X . tb is non empty set
(OSNat_Hom ((S,X),(S,X))) . tb is Relation-like the Sorts of (S,X) . tb -defined the Sorts of (QuotOSAlg ((S,X),(S,X))) . tb -valued Function-like V29( the Sorts of (S,X) . tb, the Sorts of (QuotOSAlg ((S,X),(S,X))) . tb) Element of bool [:( the Sorts of (S,X) . tb),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . tb):]
the Sorts of (QuotOSAlg ((S,X),(S,X))) . tb is non empty set
[:( the Sorts of (S,X) . tb),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . tb):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . tb),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . tb):] is non empty set
t2 is set
[t2,tb] is V26() set
{t2,tb} is non empty set
{t2} is non empty set
{{t2,tb},{t2}} is non empty set
root-tree [t2,tb] is Relation-like Function-like DecoratedTree-like set
((OSNat_Hom ((S,X),(S,X))) . tb) . (root-tree [t2,tb]) is set
t1 is Relation-like Function-like DecoratedTree-like set
((b || (S,X)) . tb) . t1 is set
t2 is set
((b || (S,X)) . tb) . t2 is set
X . tb is non empty set
t1 is set
[t1,tb] is V26() set
{t1,tb} is non empty set
{t1} is non empty set
{{t1,tb},{t1}} is non empty set
root-tree [t1,tb] is Relation-like Function-like DecoratedTree-like set
(OSNat_Hom ((S,X),(S,X))) . tb is Relation-like the Sorts of (S,X) . tb -defined the Sorts of (QuotOSAlg ((S,X),(S,X))) . tb -valued Function-like V29( the Sorts of (S,X) . tb, the Sorts of (QuotOSAlg ((S,X),(S,X))) . tb) Element of bool [:( the Sorts of (S,X) . tb),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . tb):]
the Sorts of (QuotOSAlg ((S,X),(S,X))) . tb is non empty set
[:( the Sorts of (S,X) . tb),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . tb):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . tb),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . tb):] is non empty set
((OSNat_Hom ((S,X),(S,X))) . tb) . (root-tree [t1,tb]) is set
(S,X,tb) is non empty Element of bool ( the Sorts of (S,X) . tb)
bool ( the Sorts of (S,X) . tb) is non empty set
proj2 ((b || (S,X)) . tb) is set
[:(S,X,tb),((S,X) . tb):] is non empty Relation-like set
bool [:(S,X,tb),((S,X) . tb):] is non empty set
[:((S,X) . tb),((S,X) . tb):] is Relation-like set
bool [:((S,X) . tb),((S,X) . tb):] is non empty set
tb is set
(b || (S,X)) . tb is Relation-like Function-like set
(S,X) . tb is set
(S,X) . tb is set
[:((S,X) . tb),((S,X) . tb):] is Relation-like set
bool [:((S,X) . tb),((S,X) . tb):] is non empty set
tb is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of (S,X),(S,X)
O1 ** tb is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of (S,X), the Sorts of P
t1 is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of the Sorts of (S,X), the Sorts of P
t1 || (S,X) is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of (S,X), the Sorts of P
OSCng t1 is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like OrderSortedRelation of (S,X)
OSHomQuot (t1,(S,X)) is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of the Sorts of (QuotOSAlg ((S,X),(S,X))), the Sorts of P
t1 is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of the Sorts of (S,X), the Sorts of P
t1 || (S,X) is non empty Relation-like the carrier of S -defined Function-like total V32() V33() ManySortedFunction of (S,X), the Sorts of P
t2 is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
t2 is Element of the carrier of S
the Sorts of (S,X) . t2 is non empty set
the Sorts of P . t2 is non empty set
[:( the Sorts of (S,X) . t2),( the Sorts of P . t2):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . t2),( the Sorts of P . t2):] is non empty set
t1 . t2 is Relation-like the Sorts of (S,X) . t2 -defined the Sorts of P . t2 -valued Function-like V29( the Sorts of (S,X) . t2, the Sorts of P . t2) Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of P . t2):]
O1 . t2 is Relation-like (S,X) . t2 -defined the Sorts of P . t2 -valued Function-like V29((S,X) . t2, the Sorts of P . t2) Element of bool [:((S,X) . t2),( the Sorts of P . t2):]
(S,X) . t2 is non empty set
[:((S,X) . t2),( the Sorts of P . t2):] is non empty Relation-like set
bool [:((S,X) . t2),( the Sorts of P . t2):] is non empty set
(S,X,t2) is non empty Element of bool ( the Sorts of (S,X) . t2)
bool ( the Sorts of (S,X) . t2) is non empty set
the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2 is non empty set
OSHomQuot (t1,(S,X),t2) is Relation-like the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2 -defined the Sorts of P . t2 -valued Function-like V29( the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2, the Sorts of P . t2) Element of bool [:( the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2),( the Sorts of P . t2):]
[:( the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2),( the Sorts of P . t2):] is non empty Relation-like set
bool [:( the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2),( the Sorts of P . t2):] is non empty set
dom (OSHomQuot (t1,(S,X),t2)) is Element of bool ( the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2)
bool ( the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2) is non empty set
(OSHomQuot (t1,(S,X),t2)) | ((S,X) . t2) is Relation-like (S,X) . t2 -defined the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2 -defined the Sorts of P . t2 -valued Function-like Element of bool [:( the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2),( the Sorts of P . t2):]
dom ((OSHomQuot (t1,(S,X),t2)) | ((S,X) . t2)) is Element of bool ((S,X) . t2)
bool ((S,X) . t2) is non empty set
proj2 ((OSHomQuot (t1,(S,X),t2)) | ((S,X) . t2)) is set
(S,X) . t2 is set
tb . t2 is Relation-like (S,X) . t2 -defined (S,X) . t2 -valued Function-like V29((S,X) . t2,(S,X) . t2) Element of bool [:((S,X) . t2),((S,X) . t2):]
[:((S,X) . t2),((S,X) . t2):] is Relation-like set
bool [:((S,X) . t2),((S,X) . t2):] is non empty set
dom (tb . t2) is Element of bool ((S,X) . t2)
bool ((S,X) . t2) is non empty set
(S,X,t2) is non empty Element of bool ( the Sorts of (S,X) . t2)
the Sorts of (S,X) . t2 is non empty set
bool ( the Sorts of (S,X) . t2) is non empty set
t1 . t2 is Relation-like the Sorts of (S,X) . t2 -defined the Sorts of P . t2 -valued Function-like V29( the Sorts of (S,X) . t2, the Sorts of P . t2) Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of P . t2):]
[:( the Sorts of (S,X) . t2),( the Sorts of P . t2):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . t2),( the Sorts of P . t2):] is non empty set
(t1 . t2) | ((S,X) . t2) is Relation-like (S,X) . t2 -defined the Sorts of (S,X) . t2 -defined the Sorts of P . t2 -valued Function-like Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of P . t2):]
(O1 ** tb) . t2 is Relation-like (S,X) . t2 -defined the Sorts of P . t2 -valued Function-like V29((S,X) . t2, the Sorts of P . t2) Element of bool [:((S,X) . t2),( the Sorts of P . t2):]
[:((S,X) . t2),( the Sorts of P . t2):] is Relation-like set
bool [:((S,X) . t2),( the Sorts of P . t2):] is non empty set
(O1 . t2) * (tb . t2) is Relation-like (S,X) . t2 -defined the Sorts of P . t2 -valued Function-like Element of bool [:((S,X) . t2),( the Sorts of P . t2):]
s3 is set
X . t2 is non empty set
(OSNat_Hom ((S,X),(S,X))) . t2 is Relation-like the Sorts of (S,X) . t2 -defined the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2 -valued Function-like V29( the Sorts of (S,X) . t2, the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2) Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2):]
[:( the Sorts of (S,X) . t2),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . t2),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2):] is non empty set
o1 is set
[o1,t2] is V26() set
{o1,t2} is non empty set
{o1} is non empty set
{{o1,t2},{o1}} is non empty set
root-tree [o1,t2] is Relation-like Function-like DecoratedTree-like set
((OSNat_Hom ((S,X),(S,X))) . t2) . (root-tree [o1,t2]) is set
ts3 is Element of the Sorts of (S,X) . t2
OSClass ((S,X),ts3) is Element of OSClass ((S,X),t2)
OSClass ((S,X),t2) is non empty Element of bool (Class (CompClass ((S,X),(CComp t2))))
CComp t2 is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),t2) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp t2)) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp t2 } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp t2 } is set
CompClass ((S,X),(CComp t2)) is Relation-like K541(S, the Sorts of (S,X),(CComp t2)) -defined K541(S, the Sorts of (S,X),(CComp t2)) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp t2)),K541(S, the Sorts of (S,X),(CComp t2)):]
[:K541(S, the Sorts of (S,X),(CComp t2)),K541(S, the Sorts of (S,X),(CComp t2)):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp t2)),K541(S, the Sorts of (S,X),(CComp t2)):] is non empty set
Class (CompClass ((S,X),(CComp t2))) is a_partition of K541(S, the Sorts of (S,X),(CComp t2))
bool (Class (CompClass ((S,X),(CComp t2)))) is non empty set
Class ((CompClass ((S,X),(CComp t2))),ts3) is Element of bool K541(S, the Sorts of (S,X),(CComp t2))
bool K541(S, the Sorts of (S,X),(CComp t2)) is non empty set
OSNat_Hom ((S,X),(S,X),t2) is Relation-like the Sorts of (S,X) . t2 -defined OSClass ((S,X),t2) -valued Function-like V29( the Sorts of (S,X) . t2, OSClass ((S,X),t2)) Element of bool [:( the Sorts of (S,X) . t2),(OSClass ((S,X),t2)):]
[:( the Sorts of (S,X) . t2),(OSClass ((S,X),t2)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . t2),(OSClass ((S,X),t2)):] is non empty set
(OSNat_Hom ((S,X),(S,X),t2)) . ts3 is Element of OSClass ((S,X),t2)
(t1 . t2) . ts3 is Element of the Sorts of P . t2
((t1 . t2) | ((S,X) . t2)) . ts3 is set
(OSHomQuot (t1,(S,X),t2)) . (OSClass ((S,X),ts3)) is set
(tb . t2) . ts3 is set
((OSNat_Hom ((S,X),(S,X))) . t2) | (S,X,t2) is Relation-like (S,X,t2) -defined the Sorts of (S,X) . t2 -defined the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2 -valued Function-like Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2):]
(((OSNat_Hom ((S,X),(S,X))) . t2) | (S,X,t2)) . ts3 is set
((OSNat_Hom ((S,X),(S,X))) . t2) . ts3 is Element of the Sorts of (QuotOSAlg ((S,X),(S,X))) . t2
(O1 . t2) . s3 is set
((OSHomQuot (t1,(S,X),t2)) | ((S,X) . t2)) . s3 is set
t2 is Relation-like (S,X) . t2 -defined the Sorts of P . t2 -valued Function-like V29((S,X) . t2, the Sorts of P . t2) Element of bool [:((S,X) . t2),( the Sorts of P . t2):]
s3 is Relation-like the Sorts of (S,X) . t2 -defined the Sorts of P . t2 -valued Function-like V29( the Sorts of (S,X) . t2, the Sorts of P . t2) Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of P . t2):]
s3 | ((S,X) . t2) is Relation-like the Sorts of (S,X) . t2 -defined (S,X) . t2 -defined the Sorts of (S,X) . t2 -defined the Sorts of P . t2 -valued Function-like Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of P . t2):]
t2 is set
the Sorts of (S,X) . t2 is set
the Sorts of P . t2 is set
[:( the Sorts of (S,X) . t2),( the Sorts of P . t2):] is Relation-like set
bool [:( the Sorts of (S,X) . t2),( the Sorts of P . t2):] is non empty set
t2 is Relation-like the Sorts of (S,X) . t2 -defined the Sorts of P . t2 -valued Function-like V29( the Sorts of (S,X) . t2, the Sorts of P . t2) Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of P . t2):]
t1 . t2 is Relation-like Function-like set
O1 . t2 is Relation-like Function-like set
(S,X) . t2 is set
t2 | ((S,X) . t2) is Relation-like the Sorts of (S,X) . t2 -defined (S,X) . t2 -defined the Sorts of (S,X) . t2 -defined the Sorts of P . t2 -valued Function-like Element of bool [:( the Sorts of (S,X) . t2),( the Sorts of P . t2):]
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted monotone MSAlgebra over S
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
QuotOSAlg ((S,X),(S,X)) is strict non-empty order-sorted monotone MSAlgebra over S
OSClass (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
OSQuotCharact (S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((OSClass (S,X)) #), the ResultSort of S * (OSClass (S,X))
(OSClass (S,X)) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((OSClass (S,X)) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * (OSClass (S,X)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (OSClass (S,X)),(OSQuotCharact (S,X)) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total (S,(S,X))
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable locally_directed OverloadedRSSign
the non-empty order-sorted MSAlgebra over S is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
the Sorts of the non-empty order-sorted MSAlgebra over S is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
x is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,x) is strict non-empty order-sorted monotone MSAlgebra over S
(S,x) is strict non-empty order-sorted MSAlgebra over S
(S,x) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,x) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,x) #), the ResultSort of S * (S,x)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,x) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,x) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,x) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,x),(S,x) #) is strict MSAlgebra over S
(S,x) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,x)
QuotOSAlg ((S,x),(S,x)) is strict non-empty order-sorted monotone MSAlgebra over S
OSClass (S,x) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
OSQuotCharact (S,x) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((OSClass (S,x)) #), the ResultSort of S * (OSClass (S,x))
(OSClass (S,x)) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((OSClass (S,x)) #) is non empty Relation-like the carrier' of S -defined Function-like total set
the ResultSort of S * (OSClass (S,x)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (OSClass (S,x)),(OSQuotCharact (S,x)) #) is strict MSAlgebra over S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable monotone regular locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)),(TS (S,X)):] is non empty Relation-like set
bool [:(TS (S,X)),(TS (S,X)):] is non empty set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
t is Relation-like TS (S,X) -defined TS (S,X) -valued Function-like V29( TS (S,X), TS (S,X)) V32() V33() Element of bool [:(TS (S,X)),(TS (S,X)):]
tx is Element of the carrier of (S,X)
root-tree tx is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
t . (root-tree tx) is Relation-like Function-like set
(S,X,tx) is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
tx is Element of the carrier of (S,X)
(S,X,tx) is monotone regular Element of the carrier' of S
P is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots P is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
tx -tree P is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
t . (tx -tree P) is Relation-like Function-like set
t * P is Relation-like K32() -defined TS (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding Element of (TS (S,X)) *
(TS (S,X)) * is non empty functional FinSequence-membered M10( TS (S,X))
(S,X,(S,X,tx),(t * P)) is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
O1 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
(S,X,(S,X,tx),O1) is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
In ((S,X,(S,X,tx),O1),(TS (S,X))) is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
t is Relation-like TS (S,X) -defined TS (S,X) -valued Function-like V29( TS (S,X), TS (S,X)) V32() V33() Element of bool [:(TS (S,X)),(TS (S,X)):]
tx is Relation-like TS (S,X) -defined TS (S,X) -valued Function-like V29( TS (S,X), TS (S,X)) V32() V33() Element of bool [:(TS (S,X)),(TS (S,X)):]
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable monotone regular locally_directed OverloadedRSSign
the carrier of S is non empty set
the carrier' of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is Relation-like TS (S,X) -defined TS (S,X) -valued Function-like V29( TS (S,X), TS (S,X)) V32() V33() Element of bool [:(TS (S,X)),(TS (S,X)):]
[:(TS (S,X)),(TS (S,X)):] is non empty Relation-like set
bool [:(TS (S,X)),(TS (S,X)):] is non empty set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
x is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . x is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),x) is Element of OSClass ((S,X),(S,X,x))
(S,X,x) is Element of the carrier of S
OSClass ((S,X),(S,X,x)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,x)))))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
CComp (S,X,x) is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),(S,X,x)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,x))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,x) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,x) } is set
CompClass ((S,X),(CComp (S,X,x))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,x))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,x))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,x))),K541(S, the Sorts of (S,X),(CComp (S,X,x))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,x))),K541(S, the Sorts of (S,X),(CComp (S,X,x))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,x))),K541(S, the Sorts of (S,X),(CComp (S,X,x))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,x)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,x)))
bool (Class (CompClass ((S,X),(CComp (S,X,x))))) is non empty set
(S,X,((S,X) . x)) is Element of the carrier of S
(S,X) is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
i is Element of the carrier of (S,X)
s is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots s is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
proj2 s is set
i -tree s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
b is monotone regular Element of the carrier' of S
[b, the carrier of S] is V26() set
{b, the carrier of S} is non empty set
{b} is non empty set
{{b, the carrier of S},{b}} is non empty set
Args (b,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (b,(S,X)) is Relation-like Args (b,(S,X)) -defined Result (b,(S,X)) -valued Function-like V29( Args (b,(S,X)), Result (b,(S,X))) Element of bool [:(Args (b,(S,X))),(Result (b,(S,X))):]
Result (b,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (b,(S,X))),(Result (b,(S,X))):] is non empty Relation-like set
bool [:(Args (b,(S,X))),(Result (b,(S,X))):] is non empty set
(Den (b,(S,X))) . s is set
the_result_sort_of b is Element of the carrier of S
(S,X) * s is Relation-like K32() -defined TS (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding Element of (TS (S,X)) *
(TS (S,X)) * is non empty functional FinSequence-membered M10( TS (S,X))
(S,X,((S,X) * s)) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the_arity_of b is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
LBound (b,(S,X,((S,X) * s))) is monotone regular Element of the carrier' of S
dom s is Element of bool K32()
dom (the_arity_of b) is Element of bool K32()
dom ((S,X) * s) is Element of bool K32()
dom (S,X,((S,X) * s)) is Element of bool K32()
(S,X,i) is monotone regular Element of the carrier' of S
(S,X) . (i -tree s) is Relation-like Function-like set
(S,X,b,((S,X) * s)) is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . a is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
t2 is monotone regular Element of the carrier' of S
(S,X,t2) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
the_arity_of t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
t2 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots t2 is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
(S,X,t2) -tree t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) * t2 is Relation-like K32() -defined TS (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding Element of (TS (S,X)) *
(S,X,((S,X) * t2)) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
roots ((S,X) * t2) is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
LBound (t2,(S,X,((S,X) * t2))) is monotone regular Element of the carrier' of S
(S,X,(LBound (t2,(S,X,((S,X) * t2))))) is Element of NonTerminals (S,X)
[(LBound (t2,(S,X,((S,X) * t2)))), the carrier of S] is V26() set
{(LBound (t2,(S,X,((S,X) * t2)))), the carrier of S} is non empty set
{(LBound (t2,(S,X,((S,X) * t2))))} is non empty set
{{(LBound (t2,(S,X,((S,X) * t2)))), the carrier of S},{(LBound (t2,(S,X,((S,X) * t2))))}} is non empty set
(S,X,(LBound (t2,(S,X,((S,X) * t2))))) -tree ((S,X) * t2) is Relation-like Function-like DecoratedTree-like set
len (S,X,((S,X) * s)) is V4() V5() V6() V10() Element of K32()
len (the_arity_of b) is V4() V5() V6() V10() Element of K32()
o3 is set
(S,X,((S,X) * s)) . o3 is set
(the_arity_of b) . o3 is set
k is V4() V5() V6() V10() set
s . k is Relation-like Function-like set
tk1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(the_arity_of b) /. k is Element of the carrier of S
((S,X) * s) . k is Relation-like Function-like set
(S,X) . tk1 is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
the Sorts of (S,X) . ((the_arity_of b) /. k) is non empty set
(S,X,tk1) is Element of the carrier of S
tk3 is Element of the carrier of S
tak is Element of the carrier of S
(S,X,((S,X) * s)) . k is set
tk2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,tk2) is Element of the carrier of S
rt is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . rt is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),rt) is Element of OSClass ((S,X),(S,X,rt))
(S,X,rt) is Element of the carrier of S
OSClass ((S,X),(S,X,rt)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,rt)))))
CComp (S,X,rt) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,rt)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,rt))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,rt) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,rt) } is set
CompClass ((S,X),(CComp (S,X,rt))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,rt))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,rt))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,rt))),K541(S, the Sorts of (S,X),(CComp (S,X,rt))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,rt))),K541(S, the Sorts of (S,X),(CComp (S,X,rt))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,rt))),K541(S, the Sorts of (S,X),(CComp (S,X,rt))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,rt)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,rt)))
bool (Class (CompClass ((S,X),(CComp (S,X,rt))))) is non empty set
(S,X,((S,X) . rt)) is Element of the carrier of S
the_arity_of (LBound (t2,(S,X,((S,X) * t2)))) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
Args ((LBound (t2,(S,X,((S,X) * t2)))),(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Args (t2,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
t2 is Element of the carrier of S
X . t2 is non empty set
t2 is set
[t2,t2] is V26() set
{t2,t2} is non empty set
{t2} is non empty set
{{t2,t2},{t2}} is non empty set
root-tree [t2,t2] is Relation-like Function-like DecoratedTree-like set
a . {} is set
(S,X) . a is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
(S,X) * s is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like Element of (bool [:(TS (S,X)), the carrier of S:]) *
(bool [:(TS (S,X)), the carrier of S:]) * is non empty functional FinSequence-membered M10( bool [:(TS (S,X)), the carrier of S:])
(S,X,i,((S,X) * s)) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
dom ((S,X) * s) is Element of bool K32()
{ [((Den (b₁,(S,X))) . b₂),b₃] where b₁ is Element of the carrier' of S, b₂ is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (b₁,(S,X)), b₃ is Element of the carrier of S : ( ex b₄ being Element of the carrier' of S st
( i = [b₄, the carrier of S] & b₄ ~= b₁ & len (the_arity_of b₄) = len (the_arity_of b₁) & the_result_sort_of b₄ <= b₃ & the_result_sort_of b₁ <= b₃ ) & ex b₄ being Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S * st
( dom b₄ = dom ((S,X) * s) & ( for b₅ being V4() V5() V6() V10() set holds
( not b₅ in dom ((S,X) * s) or [(b₂ . b₅),(b₄ /. b₅)] in ((S,X) * s) . b₅ ) ) ) ) } is set
(S,X,(S,X),a) is Element of OSClass ((S,X),(S,X,a))
(S,X,a) is Element of the carrier of S
OSClass ((S,X),(S,X,a)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,a)))))
CComp (S,X,a) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,a)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,a))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,a) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,a) } is set
CompClass ((S,X),(CComp (S,X,a))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,a))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,a))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,a))),K541(S, the Sorts of (S,X),(CComp (S,X,a))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,a))),K541(S, the Sorts of (S,X),(CComp (S,X,a))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,a))),K541(S, the Sorts of (S,X),(CComp (S,X,a))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,a)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,a)))
bool (Class (CompClass ((S,X),(CComp (S,X,a))))) is non empty set
(S,X,((S,X) . a)) is Element of the carrier of S
the Sorts of (S,X) . (S,X,a) is non empty set
(S,X,b) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
(S,X,(LBound (b,(S,X,((S,X) * s))))) is Element of NonTerminals (S,X)
[(LBound (b,(S,X,((S,X) * s)))), the carrier of S] is V26() set
{(LBound (b,(S,X,((S,X) * s)))), the carrier of S} is non empty set
{(LBound (b,(S,X,((S,X) * s))))} is non empty set
{{(LBound (b,(S,X,((S,X) * s)))), the carrier of S},{(LBound (b,(S,X,((S,X) * s))))}} is non empty set
roots ((S,X) * s) is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
(S,X,(LBound (b,(S,X,((S,X) * s))))) -tree ((S,X) * s) is Relation-like Function-like DecoratedTree-like set
t2 is monotone regular Element of the carrier' of S
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
Args (t2,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Den (t2,(S,X)) is Relation-like Args (t2,(S,X)) -defined Result (t2,(S,X)) -valued Function-like V29( Args (t2,(S,X)), Result (t2,(S,X))) Element of bool [:(Args (t2,(S,X))),(Result (t2,(S,X))):]
Result (t2,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (t2,(S,X))),(Result (t2,(S,X))):] is non empty Relation-like set
bool [:(Args (t2,(S,X))),(Result (t2,(S,X))):] is non empty set
(Den (t2,(S,X))) . ((S,X) * s) is set
the_result_sort_of t2 is Element of the carrier of S
Args ((LBound (b,(S,X,((S,X) * s)))),(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Result ((LBound (b,(S,X,((S,X) * s)))),(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den ((LBound (b,(S,X,((S,X) * s)))),(S,X)) is Relation-like Args ((LBound (b,(S,X,((S,X) * s)))),(S,X)) -defined Result ((LBound (b,(S,X,((S,X) * s)))),(S,X)) -valued Function-like V29( Args ((LBound (b,(S,X,((S,X) * s)))),(S,X)), Result ((LBound (b,(S,X,((S,X) * s)))),(S,X))) Element of bool [:(Args ((LBound (b,(S,X,((S,X) * s)))),(S,X))),(Result ((LBound (b,(S,X,((S,X) * s)))),(S,X))):]
[:(Args ((LBound (b,(S,X,((S,X) * s)))),(S,X))),(Result ((LBound (b,(S,X,((S,X) * s)))),(S,X))):] is non empty Relation-like set
bool [:(Args ((LBound (b,(S,X,((S,X) * s)))),(S,X))),(Result ((LBound (b,(S,X,((S,X) * s)))),(S,X))):] is non empty set
s3 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args ((LBound (b,(S,X,((S,X) * s)))),(S,X))
(Den ((LBound (b,(S,X,((S,X) * s)))),(S,X))) . s3 is Element of Result ((LBound (b,(S,X,((S,X) * s)))),(S,X))
the_arity_of (LBound (b,(S,X,((S,X) * s)))) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of (LBound (b,(S,X,((S,X) * s))))) is V4() V5() V6() V10() Element of K32()
len (the_arity_of b) is V4() V5() V6() V10() Element of K32()
t2 is Element of the Sorts of (S,X) . (S,X,a)
OSClass ((S,X),t2) is Element of OSClass ((S,X),(S,X,a))
Class ((CompClass ((S,X),(CComp (S,X,a)))),t2) is Element of bool K541(S, the Sorts of (S,X),(CComp (S,X,a)))
bool K541(S, the Sorts of (S,X),(CComp (S,X,a))) is non empty set
proj1 ((S,X) . a) is set
the_result_sort_of (LBound (b,(S,X,((S,X) * s)))) is Element of the carrier of S
o1 is set
((S,X) * s) . o1 is Relation-like Function-like set
((S,X) * s) . o1 is set
s . o1 is Relation-like Function-like set
(S,X) . (s . o1) is set
ts3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . (s . o1) is Relation-like Function-like set
(S,X,ts3) is Element of the carrier of S
the Sorts of (S,X) . (S,X,ts3) is non empty set
(S,X,(S,X),ts3) is Element of OSClass ((S,X),(S,X,ts3))
OSClass ((S,X),(S,X,ts3)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,ts3)))))
CComp (S,X,ts3) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,ts3)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,ts3))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,ts3) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,ts3) } is set
CompClass ((S,X),(CComp (S,X,ts3))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,ts3))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,ts3))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,ts3))),K541(S, the Sorts of (S,X),(CComp (S,X,ts3))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,ts3))),K541(S, the Sorts of (S,X),(CComp (S,X,ts3))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,ts3))),K541(S, the Sorts of (S,X),(CComp (S,X,ts3))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,ts3)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,ts3)))
bool (Class (CompClass ((S,X),(CComp (S,X,ts3))))) is non empty set
o3 is Element of the Sorts of (S,X) . (S,X,ts3)
OSClass ((S,X),o3) is Element of OSClass ((S,X),(S,X,ts3))
Class ((CompClass ((S,X),(CComp (S,X,ts3)))),o3) is Element of bool K541(S, the Sorts of (S,X),(CComp (S,X,ts3)))
bool K541(S, the Sorts of (S,X),(CComp (S,X,ts3))) is non empty set
proj1 (((S,X) * s) . o1) is set
k is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . k is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),k) is Element of OSClass ((S,X),(S,X,k))
(S,X,k) is Element of the carrier of S
OSClass ((S,X),(S,X,k)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,k)))))
CComp (S,X,k) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,k)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,k))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,k) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,k) } is set
CompClass ((S,X),(CComp (S,X,k))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,k))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,k))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,k))),K541(S, the Sorts of (S,X),(CComp (S,X,k))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,k))),K541(S, the Sorts of (S,X),(CComp (S,X,k))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,k))),K541(S, the Sorts of (S,X),(CComp (S,X,k))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,k)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,k)))
bool (Class (CompClass ((S,X),(CComp (S,X,k))))) is non empty set
(S,X,((S,X) . k)) is Element of the carrier of S
k is set
[(((S,X) * s) . o1),k] is V26() set
{(((S,X) * s) . o1),k} is non empty set
{(((S,X) * s) . o1)} is non empty functional set
{{(((S,X) * s) . o1),k},{(((S,X) * s) . o1)}} is non empty set
o1 is Relation-like Function-like set
proj1 o1 is set
proj2 o1 is set
o3 is V4() V5() V6() V10() set
Seg o3 is V34() V41(o3) Element of bool K32()
ts3 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
o3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of S
k is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
tk1 is V4() V5() V6() V10() set
s3 . tk1 is set
k /. tk1 is Element of the carrier of S
[(s3 . tk1),(k /. tk1)] is V26() set
{(s3 . tk1),(k /. tk1)} is non empty set
{(s3 . tk1)} is non empty set
{{(s3 . tk1),(k /. tk1)},{(s3 . tk1)}} is non empty set
((S,X) * s) . tk1 is set
k . tk1 is set
[((Den ((LBound (b,(S,X,((S,X) * s)))),(S,X))) . s3),(the_result_sort_of b)] is V26() set
{((Den ((LBound (b,(S,X,((S,X) * s)))),(S,X))) . s3),(the_result_sort_of b)} is non empty set
{((Den ((LBound (b,(S,X,((S,X) * s)))),(S,X))) . s3)} is non empty set
{{((Den ((LBound (b,(S,X,((S,X) * s)))),(S,X))) . s3),(the_result_sort_of b)},{((Den ((LBound (b,(S,X,((S,X) * s)))),(S,X))) . s3)}} is non empty set
ts3 is set
o1 is Element of the carrier of S
X . o1 is non empty set
[ts3,o1] is V26() set
{ts3,o1} is non empty set
{ts3} is non empty set
{{ts3,o1},{ts3}} is non empty set
root-tree [ts3,o1] is Relation-like Function-like DecoratedTree-like set
o3 is monotone regular Element of the carrier' of S
(S,X,o3) is Element of NonTerminals (S,X)
[o3, the carrier of S] is V26() set
{o3, the carrier of S} is non empty set
{o3} is non empty set
{{o3, the carrier of S},{o3}} is non empty set
k is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots k is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
(S,X,o3) -tree k is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) * k is Relation-like K32() -defined TS (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding Element of (TS (S,X)) *
(S,X,((S,X) * k)) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the_arity_of o3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
roots ((S,X) * k) is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
LBound (o3,(S,X,((S,X) * k))) is monotone regular Element of the carrier' of S
(S,X,(LBound (o3,(S,X,((S,X) * k))))) is Element of NonTerminals (S,X)
[(LBound (o3,(S,X,((S,X) * k)))), the carrier of S] is V26() set
{(LBound (o3,(S,X,((S,X) * k)))), the carrier of S} is non empty set
{(LBound (o3,(S,X,((S,X) * k))))} is non empty set
{{(LBound (o3,(S,X,((S,X) * k)))), the carrier of S},{(LBound (o3,(S,X,((S,X) * k))))}} is non empty set
(S,X,(LBound (o3,(S,X,((S,X) * k))))) -tree ((S,X) * k) is Relation-like Function-like DecoratedTree-like set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
i is Element of the carrier of (S,X)
root-tree i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . s is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),s) is Element of OSClass ((S,X),(S,X,s))
(S,X,s) is Element of the carrier of S
OSClass ((S,X),(S,X,s)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,s)))))
CComp (S,X,s) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,s)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,s))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,s) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,s) } is set
CompClass ((S,X),(CComp (S,X,s))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,s))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,s))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,s))),K541(S, the Sorts of (S,X),(CComp (S,X,s))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,s))),K541(S, the Sorts of (S,X),(CComp (S,X,s))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,s))),K541(S, the Sorts of (S,X),(CComp (S,X,s))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,s)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,s)))
bool (Class (CompClass ((S,X),(CComp (S,X,s))))) is non empty set
(S,X,((S,X) . s)) is Element of the carrier of S
(S,X) . (root-tree i) is Relation-like Function-like set
(S,X,i) is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
b is set
a is Element of the carrier of S
X . a is non empty set
[b,a] is V26() set
{b,a} is non empty set
{b} is non empty set
{{b,a},{b}} is non empty set
root-tree [b,a] is Relation-like Function-like DecoratedTree-like set
a is monotone regular Element of the carrier' of S
(S,X,a) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
[a, the carrier of S] is V26() set
{a, the carrier of S} is non empty set
{a} is non empty set
{{a, the carrier of S},{a}} is non empty set
b is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots b is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
(S,X,a) -tree b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
s . {} is set
(S,X) * b is Relation-like K32() -defined TS (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding Element of (TS (S,X)) *
(TS (S,X)) * is non empty functional FinSequence-membered M10( TS (S,X))
(S,X,((S,X) * b)) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the_arity_of a is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
roots ((S,X) * b) is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
LBound (a,(S,X,((S,X) * b))) is monotone regular Element of the carrier' of S
(S,X,(LBound (a,(S,X,((S,X) * b))))) is Element of NonTerminals (S,X)
[(LBound (a,(S,X,((S,X) * b)))), the carrier of S] is V26() set
{(LBound (a,(S,X,((S,X) * b)))), the carrier of S} is non empty set
{(LBound (a,(S,X,((S,X) * b))))} is non empty set
{{(LBound (a,(S,X,((S,X) * b)))), the carrier of S},{(LBound (a,(S,X,((S,X) * b))))}} is non empty set
(S,X,(LBound (a,(S,X,((S,X) * b))))) -tree ((S,X) * b) is Relation-like Function-like DecoratedTree-like set
tb is set
ta is Element of the carrier of S
X . ta is non empty set
[tb,ta] is V26() set
{tb,ta} is non empty set
{tb} is non empty set
{{tb,ta},{tb}} is non empty set
s is set
i is Element of the carrier of S
X . i is non empty set
[s,i] is V26() set
{s,i} is non empty set
{s} is non empty set
{{s,i},{s}} is non empty set
root-tree [s,i] is Relation-like Function-like DecoratedTree-like set
a is monotone regular Element of the carrier' of S
(S,X,a) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
[a, the carrier of S] is V26() set
{a, the carrier of S} is non empty set
{a} is non empty set
{{a, the carrier of S},{a}} is non empty set
b is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots b is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
(S,X,a) -tree b is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) * b is Relation-like K32() -defined TS (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding Element of (TS (S,X)) *
(TS (S,X)) * is non empty functional FinSequence-membered M10( TS (S,X))
(S,X,((S,X) * b)) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the_arity_of a is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
roots ((S,X) * b) is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
LBound (a,(S,X,((S,X) * b))) is monotone regular Element of the carrier' of S
(S,X,(LBound (a,(S,X,((S,X) * b))))) is Element of NonTerminals (S,X)
[(LBound (a,(S,X,((S,X) * b)))), the carrier of S] is V26() set
{(LBound (a,(S,X,((S,X) * b)))), the carrier of S} is non empty set
{(LBound (a,(S,X,((S,X) * b))))} is non empty set
{{(LBound (a,(S,X,((S,X) * b)))), the carrier of S},{(LBound (a,(S,X,((S,X) * b))))}} is non empty set
(S,X,(LBound (a,(S,X,((S,X) * b))))) -tree ((S,X) * b) is Relation-like Function-like DecoratedTree-like set
ta is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . ta is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),ta) is Element of OSClass ((S,X),(S,X,ta))
(S,X,ta) is Element of the carrier of S
OSClass ((S,X),(S,X,ta)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,ta)))))
CComp (S,X,ta) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,ta)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,ta))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,ta) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,ta) } is set
CompClass ((S,X),(CComp (S,X,ta))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,ta))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,ta))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,ta))),K541(S, the Sorts of (S,X),(CComp (S,X,ta))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,ta))),K541(S, the Sorts of (S,X),(CComp (S,X,ta))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,ta))),K541(S, the Sorts of (S,X),(CComp (S,X,ta))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,ta)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,ta)))
bool (Class (CompClass ((S,X),(CComp (S,X,ta))))) is non empty set
(S,X,((S,X) . ta)) is Element of the carrier of S
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable monotone regular locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is Relation-like TS (S,X) -defined TS (S,X) -valued Function-like V29( TS (S,X), TS (S,X)) V32() V33() Element of bool [:(TS (S,X)),(TS (S,X)):]
[:(TS (S,X)),(TS (S,X)):] is non empty Relation-like set
bool [:(TS (S,X)),(TS (S,X)):] is non empty set
x is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),x) is Element of OSClass ((S,X),(S,X,x))
(S,X,x) is Element of the carrier of S
OSClass ((S,X),(S,X,x)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,x)))))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
CComp (S,X,x) is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),(S,X,x)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,x))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,x) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,x) } is set
CompClass ((S,X),(CComp (S,X,x))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,x))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,x))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,x))),K541(S, the Sorts of (S,X),(CComp (S,X,x))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,x))),K541(S, the Sorts of (S,X),(CComp (S,X,x))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,x))),K541(S, the Sorts of (S,X),(CComp (S,X,x))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,x)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,x)))
bool (Class (CompClass ((S,X),(CComp (S,X,x))))) is non empty set
(S,X) . x is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X) is Relation-like TS (S,X) -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V29( TS (S,X), bool [:(TS (S,X)), the carrier of S:]) Element of bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):]
[:(TS (S,X)), the carrier of S:] is non empty Relation-like set
bool [:(TS (S,X)), the carrier of S:] is non empty set
[:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty Relation-like set
bool [:(TS (S,X)),(bool [:(TS (S,X)), the carrier of S:]):] is non empty set
i is Element of the carrier of (S,X)
s is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots s is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
proj2 s is set
i -tree s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . a is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
(S,X) * s is Relation-like K32() -defined bool [:(TS (S,X)), the carrier of S:] -valued Function-like V34() FinSequence-like FinSubsequence-like Element of (bool [:(TS (S,X)), the carrier of S:]) *
(bool [:(TS (S,X)), the carrier of S:]) * is non empty functional FinSequence-membered M10( bool [:(TS (S,X)), the carrier of S:])
(S,X,i,((S,X) * s)) is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
dom ((S,X) * s) is Element of bool K32()
{ [((Den (b₁,(S,X))) . b₂),b₃] where b₁ is Element of the carrier' of S, b₂ is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (b₁,(S,X)), b₃ is Element of the carrier of S : ( ex b₄ being Element of the carrier' of S st
( i = [b₄, the carrier of S] & b₄ ~= b₁ & len (the_arity_of b₄) = len (the_arity_of b₁) & the_result_sort_of b₄ <= b₃ & the_result_sort_of b₁ <= b₃ ) & ex b₄ being Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S * st
( dom b₄ = dom ((S,X) * s) & ( for b₅ being V4() V5() V6() V10() set holds
( not b₅ in dom ((S,X) * s) or [(b₂ . b₅),(b₄ /. b₅)] in ((S,X) * s) . b₅ ) ) ) ) } is set
b is monotone regular Element of the carrier' of S
[b, the carrier of S] is V26() set
{b, the carrier of S} is non empty set
{b} is non empty set
{{b, the carrier of S},{b}} is non empty set
Args (b,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (b,(S,X)) is Relation-like Args (b,(S,X)) -defined Result (b,(S,X)) -valued Function-like V29( Args (b,(S,X)), Result (b,(S,X))) Element of bool [:(Args (b,(S,X))),(Result (b,(S,X))):]
Result (b,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (b,(S,X))),(Result (b,(S,X))):] is non empty Relation-like set
bool [:(Args (b,(S,X))),(Result (b,(S,X))):] is non empty set
(Den (b,(S,X))) . s is set
the_result_sort_of b is Element of the carrier of S
(S,X,b) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
(S,X,b) -tree s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X) * s is Relation-like K32() -defined TS (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding Element of (TS (S,X)) *
(TS (S,X)) * is non empty functional FinSequence-membered M10( TS (S,X))
(S,X,((S,X) * s)) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
the_arity_of b is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom s is Element of bool K32()
dom (the_arity_of b) is Element of bool K32()
(S,X,a) is Element of the carrier of S
the Sorts of (S,X) . (S,X,a) is non empty set
(S,X,(S,X),a) is Element of OSClass ((S,X),(S,X,a))
OSClass ((S,X),(S,X,a)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,a)))))
CComp (S,X,a) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,a)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,a))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,a) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,a) } is set
CompClass ((S,X),(CComp (S,X,a))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,a))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,a))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,a))),K541(S, the Sorts of (S,X),(CComp (S,X,a))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,a))),K541(S, the Sorts of (S,X),(CComp (S,X,a))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,a))),K541(S, the Sorts of (S,X),(CComp (S,X,a))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,a)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,a)))
bool (Class (CompClass ((S,X),(CComp (S,X,a))))) is non empty set
(S,X) . a is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
t1 is Element of the Sorts of (S,X) . (S,X,a)
OSClass ((S,X),t1) is Element of OSClass ((S,X),(S,X,a))
Class ((CompClass ((S,X),(CComp (S,X,a)))),t1) is Element of bool K541(S, the Sorts of (S,X),(CComp (S,X,a)))
bool K541(S, the Sorts of (S,X),(CComp (S,X,a))) is non empty set
proj1 ((S,X) . a) is set
dom ((S,X) * s) is Element of bool K32()
LBound (b,(S,X,((S,X) * s))) is monotone regular Element of the carrier' of S
(S,X,(LBound (b,(S,X,((S,X) * s))))) is Element of NonTerminals (S,X)
[(LBound (b,(S,X,((S,X) * s)))), the carrier of S] is V26() set
{(LBound (b,(S,X,((S,X) * s)))), the carrier of S} is non empty set
{(LBound (b,(S,X,((S,X) * s))))} is non empty set
{{(LBound (b,(S,X,((S,X) * s)))), the carrier of S},{(LBound (b,(S,X,((S,X) * s))))}} is non empty set
(S,X,(LBound (b,(S,X,((S,X) * s))))) -tree ((S,X) * s) is Relation-like Function-like DecoratedTree-like set
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . t2 is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
t1 is set
[t2,t1] is V26() set
{t2,t1} is non empty set
{t2} is non empty functional set
{{t2,t1},{t2}} is non empty set
t2 is monotone regular Element of the carrier' of S
Args (t2,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Result (t2,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den (t2,(S,X)) is Relation-like Args (t2,(S,X)) -defined Result (t2,(S,X)) -valued Function-like V29( Args (t2,(S,X)), Result (t2,(S,X))) Element of bool [:(Args (t2,(S,X))),(Result (t2,(S,X))):]
[:(Args (t2,(S,X))),(Result (t2,(S,X))):] is non empty Relation-like set
bool [:(Args (t2,(S,X))),(Result (t2,(S,X))):] is non empty set
t2 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (t2,(S,X))
(Den (t2,(S,X))) . t2 is Element of Result (t2,(S,X))
s3 is Element of the carrier of S
[((Den (t2,(S,X))) . t2),s3] is V26() set
{((Den (t2,(S,X))) . t2),s3} is non empty set
{((Den (t2,(S,X))) . t2)} is non empty set
{{((Den (t2,(S,X))) . t2),s3},{((Den (t2,(S,X))) . t2)}} is non empty set
the_arity_of t2 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of t2) is V4() V5() V6() V10() Element of K32()
the_result_sort_of t2 is Element of the carrier of S
o1 is monotone regular Element of the carrier' of S
[o1, the carrier of S] is V26() set
{o1, the carrier of S} is non empty set
{o1} is non empty set
{{o1, the carrier of S},{o1}} is non empty set
the_arity_of o1 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of o1) is V4() V5() V6() V10() Element of K32()
the_result_sort_of o1 is Element of the carrier of S
o1 is monotone regular Element of the carrier' of S
[o1, the carrier of S] is V26() set
{o1, the carrier of S} is non empty set
{o1} is non empty set
{{o1, the carrier of S},{o1}} is non empty set
the_arity_of o1 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
len (the_arity_of o1) is V4() V5() V6() V10() Element of K32()
the_result_sort_of o1 is Element of the carrier of S
dom (the_arity_of t2) is Element of bool K32()
ts3 is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
dom ts3 is Element of bool K32()
(S,X) * ts3 is Relation-like K32() -defined TS (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding Element of (TS (S,X)) *
dom ((S,X) * ts3) is Element of bool K32()
proj2 ts3 is set
o3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom o3 is Element of bool K32()
o3 is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
dom o3 is Element of bool K32()
k is V4() V5() V6() V10() set
((S,X) * ts3) . k is Relation-like Function-like set
((S,X) * s) . k is Relation-like Function-like set
ts3 . k is Relation-like Function-like set
s . k is Relation-like Function-like set
tk1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,tk1) is Element of the carrier of S
the Sorts of (S,X) . (S,X,tk1) is non empty set
tk2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),tk2) is Element of OSClass ((S,X),(S,X,tk2))
(S,X,tk2) is Element of the carrier of S
OSClass ((S,X),(S,X,tk2)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,tk2)))))
CComp (S,X,tk2) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,tk2)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,tk2))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,tk2) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,tk2) } is set
CompClass ((S,X),(CComp (S,X,tk2))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,tk2))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,tk2))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,tk2))),K541(S, the Sorts of (S,X),(CComp (S,X,tk2))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,tk2))),K541(S, the Sorts of (S,X),(CComp (S,X,tk2))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,tk2))),K541(S, the Sorts of (S,X),(CComp (S,X,tk2))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,tk2)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,tk2)))
bool (Class (CompClass ((S,X),(CComp (S,X,tk2))))) is non empty set
(S,X) . tk2 is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
tk3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
o3 /. k is Element of the carrier of S
[tk3,(o3 /. k)] is V26() set
{tk3,(o3 /. k)} is non empty set
{tk3} is non empty functional set
{{tk3,(o3 /. k)},{tk3}} is non empty set
((S,X) * s) . k is set
(S,X) . tk1 is Relation-like TS (S,X) -defined the carrier of S -valued Element of bool [:(TS (S,X)), the carrier of S:]
(S,X,(S,X),tk1) is Element of OSClass ((S,X),(S,X,tk1))
OSClass ((S,X),(S,X,tk1)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,tk1)))))
CComp (S,X,tk1) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,tk1)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,tk1))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,tk1) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,tk1) } is set
CompClass ((S,X),(CComp (S,X,tk1))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,tk1))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,tk1))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,tk1))),K541(S, the Sorts of (S,X),(CComp (S,X,tk1))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,tk1))),K541(S, the Sorts of (S,X),(CComp (S,X,tk1))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,tk1))),K541(S, the Sorts of (S,X),(CComp (S,X,tk1))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,tk1)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,tk1)))
bool (Class (CompClass ((S,X),(CComp (S,X,tk1))))) is non empty set
tak is Element of the Sorts of (S,X) . (S,X,tk1)
OSClass ((S,X),tak) is Element of OSClass ((S,X),(S,X,tk1))
Class ((CompClass ((S,X),(CComp (S,X,tk1)))),tak) is Element of bool K541(S, the Sorts of (S,X),(CComp (S,X,tk1)))
bool K541(S, the Sorts of (S,X),(CComp (S,X,tk1))) is non empty set
proj1 ((S,X) . tk1) is set
(S,X) . tk3 is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . tk1 is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X,t2) is Element of NonTerminals (S,X)
[t2, the carrier of S] is V26() set
{t2, the carrier of S} is non empty set
{t2} is non empty set
{{t2, the carrier of S},{t2}} is non empty set
roots t2 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
(S,X,t2) -tree ts3 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
o3 is monotone regular Element of the carrier' of S
[o3, the carrier of S] is V26() set
{o3, the carrier of S} is non empty set
{o3} is non empty set
{{o3, the carrier of S},{o3}} is non empty set
Args (o3,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Den (o3,(S,X)) is Relation-like Args (o3,(S,X)) -defined Result (o3,(S,X)) -valued Function-like V29( Args (o3,(S,X)), Result (o3,(S,X))) Element of bool [:(Args (o3,(S,X))),(Result (o3,(S,X))):]
Result (o3,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (o3,(S,X))),(Result (o3,(S,X))):] is non empty Relation-like set
bool [:(Args (o3,(S,X))),(Result (o3,(S,X))):] is non empty set
(Den (o3,(S,X))) . ts3 is set
the_result_sort_of o3 is Element of the carrier of S
o3 is monotone regular Element of the carrier' of S
[o3, the carrier of S] is V26() set
{o3, the carrier of S} is non empty set
{o3} is non empty set
{{o3, the carrier of S},{o3}} is non empty set
Args (o3,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Den (o3,(S,X)) is Relation-like Args (o3,(S,X)) -defined Result (o3,(S,X)) -valued Function-like V29( Args (o3,(S,X)), Result (o3,(S,X))) Element of bool [:(Args (o3,(S,X))),(Result (o3,(S,X))):]
Result (o3,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (o3,(S,X))),(Result (o3,(S,X))):] is non empty Relation-like set
bool [:(Args (o3,(S,X))),(Result (o3,(S,X))):] is non empty set
(Den (o3,(S,X))) . ts3 is set
(S,X,((S,X) * ts3)) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
LBound (t2,(S,X,((S,X) * ts3))) is monotone regular Element of the carrier' of S
(S,X,(LBound (t2,(S,X,((S,X) * ts3))))) is Element of NonTerminals (S,X)
[(LBound (t2,(S,X,((S,X) * ts3)))), the carrier of S] is V26() set
{(LBound (t2,(S,X,((S,X) * ts3)))), the carrier of S} is non empty set
{(LBound (t2,(S,X,((S,X) * ts3))))} is non empty set
{{(LBound (t2,(S,X,((S,X) * ts3)))), the carrier of S},{(LBound (t2,(S,X,((S,X) * ts3))))}} is non empty set
(S,X,(LBound (t2,(S,X,((S,X) * ts3))))) -tree ((S,X) * ts3) is Relation-like Function-like DecoratedTree-like set
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
i is Element of the carrier of (S,X)
root-tree i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),s) is Element of OSClass ((S,X),(S,X,s))
(S,X,s) is Element of the carrier of S
OSClass ((S,X),(S,X,s)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,s)))))
CComp (S,X,s) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,s)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,s))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,s) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,s) } is set
CompClass ((S,X),(CComp (S,X,s))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,s))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,s))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,s))),K541(S, the Sorts of (S,X),(CComp (S,X,s))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,s))),K541(S, the Sorts of (S,X),(CComp (S,X,s))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,s))),K541(S, the Sorts of (S,X),(CComp (S,X,s))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,s)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,s)))
bool (Class (CompClass ((S,X),(CComp (S,X,s))))) is non empty set
(S,X) . s is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . a is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
ta is set
b is Element of the carrier of S
X . b is non empty set
[ta,b] is V26() set
{ta,b} is non empty set
{ta} is non empty set
{{ta,b},{ta}} is non empty set
i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . i is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
s is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),s) is Element of OSClass ((S,X),(S,X,s))
(S,X,s) is Element of the carrier of S
OSClass ((S,X),(S,X,s)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,s)))))
CComp (S,X,s) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,s)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,s))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,s) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,s) } is set
CompClass ((S,X),(CComp (S,X,s))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,s))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,s))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,s))),K541(S, the Sorts of (S,X),(CComp (S,X,s))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,s))),K541(S, the Sorts of (S,X),(CComp (S,X,s))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,s))),K541(S, the Sorts of (S,X),(CComp (S,X,s))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,s)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,s)))
bool (Class (CompClass ((S,X),(CComp (S,X,s))))) is non empty set
(S,X) . s is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable monotone regular locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is Relation-like TS (S,X) -defined TS (S,X) -valued Function-like V29( TS (S,X), TS (S,X)) V32() V33() Element of bool [:(TS (S,X)),(TS (S,X)):]
[:(TS (S,X)),(TS (S,X)):] is non empty Relation-like set
bool [:(TS (S,X)),(TS (S,X)):] is non empty set
y is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
x is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),x) is Element of OSClass ((S,X),(S,X,x))
(S,X,x) is Element of the carrier of S
OSClass ((S,X),(S,X,x)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,x)))))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
CComp (S,X,x) is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),(S,X,x)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,x))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,x) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,x) } is set
CompClass ((S,X),(CComp (S,X,x))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,x))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,x))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,x))),K541(S, the Sorts of (S,X),(CComp (S,X,x))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,x))),K541(S, the Sorts of (S,X),(CComp (S,X,x))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,x))),K541(S, the Sorts of (S,X),(CComp (S,X,x))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,x)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,x)))
bool (Class (CompClass ((S,X),(CComp (S,X,x))))) is non empty set
(S,X) . y is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . x is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X,(S,X),y) is Element of OSClass ((S,X),(S,X,y))
(S,X,y) is Element of the carrier of S
OSClass ((S,X),(S,X,y)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,y)))))
CComp (S,X,y) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,y)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,y))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,y) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,y) } is set
CompClass ((S,X),(CComp (S,X,y))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,y))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,y))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,y))),K541(S, the Sorts of (S,X),(CComp (S,X,y))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,y)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,y)))
bool (Class (CompClass ((S,X),(CComp (S,X,y))))) is non empty set
(S,X,(S,X),((S,X) . y)) is Element of OSClass ((S,X),(S,X,((S,X) . y)))
(S,X,((S,X) . y)) is Element of the carrier of S
OSClass ((S,X),(S,X,((S,X) . y))) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,((S,X) . y))))))
CComp (S,X,((S,X) . y)) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,((S,X) . y))) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . y)))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,((S,X) . y)) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,((S,X) . y)) } is set
CompClass ((S,X),(CComp (S,X,((S,X) . y)))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . y)))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . y)))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . y)))),K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . y)))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . y)))),K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . y)))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . y)))),K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . y)))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,((S,X) . y))))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . y))))
bool (Class (CompClass ((S,X),(CComp (S,X,((S,X) . y)))))) is non empty set
(S,X,(S,X),((S,X) . x)) is Element of OSClass ((S,X),(S,X,((S,X) . x)))
(S,X,((S,X) . x)) is Element of the carrier of S
OSClass ((S,X),(S,X,((S,X) . x))) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,((S,X) . x))))))
CComp (S,X,((S,X) . x)) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,((S,X) . x))) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . x)))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,((S,X) . x)) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,((S,X) . x)) } is set
CompClass ((S,X),(CComp (S,X,((S,X) . x)))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . x)))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . x)))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . x)))),K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . x)))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . x)))),K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . x)))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . x)))),K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . x)))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,((S,X) . x))))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,((S,X) . x))))
bool (Class (CompClass ((S,X),(CComp (S,X,((S,X) . x)))))) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable monotone regular locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is Relation-like TS (S,X) -defined TS (S,X) -valued Function-like V29( TS (S,X), TS (S,X)) V32() V33() Element of bool [:(TS (S,X)),(TS (S,X)):]
[:(TS (S,X)),(TS (S,X)):] is non empty Relation-like set
bool [:(TS (S,X)),(TS (S,X)):] is non empty set
x is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . x is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . ((S,X) . x) is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X,(S,X),x) is Element of OSClass ((S,X),(S,X,x))
(S,X,x) is Element of the carrier of S
OSClass ((S,X),(S,X,x)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,x)))))
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
CComp (S,X,x) is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),(S,X,x)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,x))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,x) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,x) } is set
CompClass ((S,X),(CComp (S,X,x))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,x))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,x))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,x))),K541(S, the Sorts of (S,X),(CComp (S,X,x))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,x))),K541(S, the Sorts of (S,X),(CComp (S,X,x))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,x))),K541(S, the Sorts of (S,X),(CComp (S,X,x))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,x)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,x)))
bool (Class (CompClass ((S,X),(CComp (S,X,x))))) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable monotone regular locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is Relation-like TS (S,X) -defined TS (S,X) -valued Function-like V29( TS (S,X), TS (S,X)) V32() V33() Element of bool [:(TS (S,X)),(TS (S,X)):]
[:(TS (S,X)),(TS (S,X)):] is non empty Relation-like set
bool [:(TS (S,X)),(TS (S,X)):] is non empty set
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
P is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
O1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . O1 is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
[O1,((S,X) . O1)] is V26() set
{O1,((S,X) . O1)} is non empty functional set
{O1} is non empty functional set
{{O1,((S,X) . O1)},{O1}} is non empty set
(S,X,O1) is Element of the carrier of S
P . (S,X,O1) is Relation-like the Sorts of (S,X) . (S,X,O1) -defined the Sorts of (S,X) . (S,X,O1) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (S,X,O1)),( the Sorts of (S,X) . (S,X,O1)):]
the Sorts of (S,X) . (S,X,O1) is non empty set
[:( the Sorts of (S,X) . (S,X,O1)),( the Sorts of (S,X) . (S,X,O1)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (S,X,O1)),( the Sorts of (S,X) . (S,X,O1)):] is non empty set
R is Element of the carrier of (S,X)
i is Relation-like K32() -defined FinTrees the carrier of (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding FinSequence of TS (S,X)
roots i is Relation-like K32() -defined the carrier of (S,X) -valued Function-like V34() FinSequence-like FinSubsequence-like FinSequence of the carrier of (S,X)
proj2 i is set
R -tree i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
s is monotone regular Element of the carrier' of S
[s, the carrier of S] is V26() set
{s, the carrier of S} is non empty set
{s} is non empty set
{{s, the carrier of S},{s}} is non empty set
Args (s,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
the Sorts of (S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
proj2 ( the Sorts of (S,X) #) is non empty set
Den (s,(S,X)) is Relation-like Args (s,(S,X)) -defined Result (s,(S,X)) -valued Function-like V29( Args (s,(S,X)), Result (s,(S,X))) Element of bool [:(Args (s,(S,X))),(Result (s,(S,X))):]
Result (s,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
proj2 the Sorts of (S,X) is non empty V205() set
[:(Args (s,(S,X))),(Result (s,(S,X))):] is non empty Relation-like set
bool [:(Args (s,(S,X))),(Result (s,(S,X))):] is non empty set
(Den (s,(S,X))) . i is set
the_result_sort_of s is Element of the carrier of S
(S,X) * i is Relation-like K32() -defined TS (S,X) -valued Function-like V32() V33() V34() FinSequence-like FinSubsequence-like DTree-yielding Element of (TS (S,X)) *
(TS (S,X)) * is non empty functional FinSequence-membered M10( TS (S,X))
dom ((S,X) * i) is Element of bool K32()
dom i is Element of bool K32()
the_arity_of s is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
(S,X,((S,X) * i)) is Relation-like K32() -defined the carrier of S -valued Function-like V34() FinSequence-like FinSubsequence-like Element of the carrier of S *
LBound (s,(S,X,((S,X) * i))) is monotone regular Element of the carrier' of S
a is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,s) is Element of NonTerminals (S,X)
NonTerminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
(S,X,s) -tree i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
(S,X,(LBound (s,(S,X,((S,X) * i))))) is Element of NonTerminals (S,X)
[(LBound (s,(S,X,((S,X) * i)))), the carrier of S] is V26() set
{(LBound (s,(S,X,((S,X) * i)))), the carrier of S} is non empty set
{(LBound (s,(S,X,((S,X) * i))))} is non empty set
{{(LBound (s,(S,X,((S,X) * i)))), the carrier of S},{(LBound (s,(S,X,((S,X) * i))))}} is non empty set
roots ((S,X) * i) is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like set
Args ((LBound (s,(S,X,((S,X) * i)))),(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
dom (the_arity_of s) is Element of bool K32()
t2 is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args ((LBound (s,(S,X,((S,X) * i)))),(S,X))
dom t2 is Element of bool K32()
b is Relation-like K32() -defined Function-like V34() FinSequence-like FinSubsequence-like Element of Args (s,(S,X))
t1 is V4() V5() V6() V10() set
t2 . t1 is set
b . t1 is set
[(t2 . t1),(b . t1)] is V26() set
{(t2 . t1),(b . t1)} is non empty set
{(t2 . t1)} is non empty set
{{(t2 . t1),(b . t1)},{(t2 . t1)}} is non empty set
(the_arity_of s) /. t1 is Element of the carrier of S
P . ((the_arity_of s) /. t1) is Relation-like the Sorts of (S,X) . ((the_arity_of s) /. t1) -defined the Sorts of (S,X) . ((the_arity_of s) /. t1) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . ((the_arity_of s) /. t1)),( the Sorts of (S,X) . ((the_arity_of s) /. t1)):]
the Sorts of (S,X) . ((the_arity_of s) /. t1) is non empty set
[:( the Sorts of (S,X) . ((the_arity_of s) /. t1)),( the Sorts of (S,X) . ((the_arity_of s) /. t1)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . ((the_arity_of s) /. t1)),( the Sorts of (S,X) . ((the_arity_of s) /. t1)):] is non empty set
i . t1 is Relation-like Function-like set
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . t2 is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
[t2,((S,X) . t2)] is V26() set
{t2,((S,X) . t2)} is non empty functional set
{t2} is non empty functional set
{{t2,((S,X) . t2)},{t2}} is non empty set
(S,X,t2) is Element of the carrier of S
P . (S,X,t2) is Relation-like the Sorts of (S,X) . (S,X,t2) -defined the Sorts of (S,X) . (S,X,t2) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (S,X,t2)),( the Sorts of (S,X) . (S,X,t2)):]
the Sorts of (S,X) . (S,X,t2) is non empty set
[:( the Sorts of (S,X) . (S,X,t2)),( the Sorts of (S,X) . (S,X,t2)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (S,X,t2)),( the Sorts of (S,X) . (S,X,t2)):] is non empty set
field (P . (S,X,t2)) is set
[((S,X) . t2),t2] is V26() set
{((S,X) . t2),t2} is non empty functional set
{((S,X) . t2)} is non empty functional set
{{((S,X) . t2),t2},{((S,X) . t2)}} is non empty set
Result ((LBound (s,(S,X,((S,X) * i)))),(S,X)) is non empty Element of proj2 the Sorts of (S,X)
Den ((LBound (s,(S,X,((S,X) * i)))),(S,X)) is Relation-like Args ((LBound (s,(S,X,((S,X) * i)))),(S,X)) -defined Result ((LBound (s,(S,X,((S,X) * i)))),(S,X)) -valued Function-like V29( Args ((LBound (s,(S,X,((S,X) * i)))),(S,X)), Result ((LBound (s,(S,X,((S,X) * i)))),(S,X))) Element of bool [:(Args ((LBound (s,(S,X,((S,X) * i)))),(S,X))),(Result ((LBound (s,(S,X,((S,X) * i)))),(S,X))):]
[:(Args ((LBound (s,(S,X,((S,X) * i)))),(S,X))),(Result ((LBound (s,(S,X,((S,X) * i)))),(S,X))):] is non empty Relation-like set
bool [:(Args ((LBound (s,(S,X,((S,X) * i)))),(S,X))),(Result ((LBound (s,(S,X,((S,X) * i)))),(S,X))):] is non empty set
(Den ((LBound (s,(S,X,((S,X) * i)))),(S,X))) . t2 is Element of Result ((LBound (s,(S,X,((S,X) * i)))),(S,X))
(Den (s,(S,X))) . b is Element of Result (s,(S,X))
[((Den ((LBound (s,(S,X,((S,X) * i)))),(S,X))) . t2),((Den (s,(S,X))) . b)] is V26() set
{((Den ((LBound (s,(S,X,((S,X) * i)))),(S,X))) . t2),((Den (s,(S,X))) . b)} is non empty set
{((Den ((LBound (s,(S,X,((S,X) * i)))),(S,X))) . t2)} is non empty set
{{((Den ((LBound (s,(S,X,((S,X) * i)))),(S,X))) . t2),((Den (s,(S,X))) . b)},{((Den ((LBound (s,(S,X,((S,X) * i)))),(S,X))) . t2)}} is non empty set
P . (the_result_sort_of s) is Relation-like the Sorts of (S,X) . (the_result_sort_of s) -defined the Sorts of (S,X) . (the_result_sort_of s) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (the_result_sort_of s)),( the Sorts of (S,X) . (the_result_sort_of s)):]
the Sorts of (S,X) . (the_result_sort_of s) is non empty set
[:( the Sorts of (S,X) . (the_result_sort_of s)),( the Sorts of (S,X) . (the_result_sort_of s)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (the_result_sort_of s)),( the Sorts of (S,X) . (the_result_sort_of s)):] is non empty set
(S,X,a) is Element of the carrier of S
(S,X) . a is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
[a,((S,X) . a)] is V26() set
{a,((S,X) . a)} is non empty functional set
{a} is non empty functional set
{{a,((S,X) . a)},{a}} is non empty set
P . (S,X,a) is Relation-like the Sorts of (S,X) . (S,X,a) -defined the Sorts of (S,X) . (S,X,a) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (S,X,a)),( the Sorts of (S,X) . (S,X,a)):]
the Sorts of (S,X) . (S,X,a) is non empty set
[:( the Sorts of (S,X) . (S,X,a)),( the Sorts of (S,X) . (S,X,a)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (S,X,a)),( the Sorts of (S,X) . (S,X,a)):] is non empty set
field (P . (the_result_sort_of s)) is set
[((Den (s,(S,X))) . b),((Den ((LBound (s,(S,X,((S,X) * i)))),(S,X))) . t2)] is V26() set
{((Den (s,(S,X))) . b),((Den ((LBound (s,(S,X,((S,X) * i)))),(S,X))) . t2)} is non empty set
{((Den (s,(S,X))) . b)} is non empty set
{{((Den (s,(S,X))) . b),((Den ((LBound (s,(S,X,((S,X) * i)))),(S,X))) . t2)},{((Den (s,(S,X))) . b)}} is non empty set
(S,X,(LBound (s,(S,X,((S,X) * i))))) -tree ((S,X) * i) is Relation-like Function-like DecoratedTree-like set
t1 is monotone regular Element of the carrier' of S
[t1, the carrier of S] is V26() set
{t1, the carrier of S} is non empty set
{t1} is non empty set
{{t1, the carrier of S},{t1}} is non empty set
Args (t1,(S,X)) is non empty functional Element of proj2 ( the Sorts of (S,X) #)
Den (t1,(S,X)) is Relation-like Args (t1,(S,X)) -defined Result (t1,(S,X)) -valued Function-like V29( Args (t1,(S,X)), Result (t1,(S,X))) Element of bool [:(Args (t1,(S,X))),(Result (t1,(S,X))):]
Result (t1,(S,X)) is non empty Element of proj2 the Sorts of (S,X)
[:(Args (t1,(S,X))),(Result (t1,(S,X))):] is non empty Relation-like set
bool [:(Args (t1,(S,X))),(Result (t1,(S,X))):] is non empty set
(Den (t1,(S,X))) . ((S,X) * i) is set
the_result_sort_of t1 is Element of the carrier of S
Terminals (S,X) is non empty Element of bool the carrier of (S,X)
bool the carrier of (S,X) is non empty set
R is Element of the carrier of (S,X)
root-tree R is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of FinTrees the carrier of (S,X)
a is set
s is Element of the carrier of S
X . s is non empty set
[a,s] is V26() set
{a,s} is non empty set
{a} is non empty set
{{a,s},{a}} is non empty set
i is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . i is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
[i,((S,X) . i)] is V26() set
{i,((S,X) . i)} is non empty functional set
{i} is non empty functional set
{{i,((S,X) . i)},{i}} is non empty set
(S,X,i) is Element of the carrier of S
P . (S,X,i) is Relation-like the Sorts of (S,X) . (S,X,i) -defined the Sorts of (S,X) . (S,X,i) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (S,X,i)),( the Sorts of (S,X) . (S,X,i)):]
the Sorts of (S,X) . (S,X,i) is non empty set
[:( the Sorts of (S,X) . (S,X,i)),( the Sorts of (S,X) . (S,X,i)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (S,X,i)),( the Sorts of (S,X) . (S,X,i)):] is non empty set
field (P . (S,X,i)) is set
a is set
s is Element of the carrier of S
X . s is non empty set
[a,s] is V26() set
{a,s} is non empty set
{a} is non empty set
{{a,s},{a}} is non empty set
R is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . R is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
[R,((S,X) . R)] is V26() set
{R,((S,X) . R)} is non empty functional set
{R} is non empty functional set
{{R,((S,X) . R)},{R}} is non empty set
(S,X,R) is Element of the carrier of S
P . (S,X,R) is Relation-like the Sorts of (S,X) . (S,X,R) -defined the Sorts of (S,X) . (S,X,R) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (S,X,R)),( the Sorts of (S,X) . (S,X,R)):]
the Sorts of (S,X) . (S,X,R) is non empty set
[:( the Sorts of (S,X) . (S,X,R)),( the Sorts of (S,X) . (S,X,R)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (S,X,R)),( the Sorts of (S,X) . (S,X,R)):] is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable monotone regular locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
the Sorts of (S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
(S,X) is Relation-like TS (S,X) -defined TS (S,X) -valued Function-like V29( TS (S,X), TS (S,X)) V32() V33() Element of bool [:(TS (S,X)),(TS (S,X)):]
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)),(TS (S,X)):] is non empty Relation-like set
bool [:(TS (S,X)),(TS (S,X)):] is non empty set
R is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
i is set
(S,X) . i is set
R . i is set
s is Element of the carrier of S
(S,X) . s is Relation-like the Sorts of (S,X) . s -defined the Sorts of (S,X) . s -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):]
the Sorts of (S,X) . s is non empty set
[:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):] is non empty set
R . s is Relation-like the Sorts of (S,X) . s -defined the Sorts of (S,X) . s -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . s),( the Sorts of (S,X) . s):]
field (R . s) is set
a is set
b is set
[a,b] is V26() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Sorts of (S,X) . i is set
ta is Element of the Sorts of (S,X) . s
OSClass ((S,X),ta) is Element of OSClass ((S,X),s)
OSClass ((S,X),s) is non empty Element of bool (Class (CompClass ((S,X),(CComp s))))
CComp s is non empty Element of K539(S)
bool the carrier of S is non empty set
K539(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Path_Rel S is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (Path_Rel S) is a_partition of the carrier of S
Class ((Path_Rel S),s) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp s)) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp s } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp s } is set
CompClass ((S,X),(CComp s)) is Relation-like K541(S, the Sorts of (S,X),(CComp s)) -defined K541(S, the Sorts of (S,X),(CComp s)) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp s)),K541(S, the Sorts of (S,X),(CComp s)):]
[:K541(S, the Sorts of (S,X),(CComp s)),K541(S, the Sorts of (S,X),(CComp s)):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp s)),K541(S, the Sorts of (S,X),(CComp s)):] is non empty set
Class (CompClass ((S,X),(CComp s))) is a_partition of K541(S, the Sorts of (S,X),(CComp s))
bool (Class (CompClass ((S,X),(CComp s)))) is non empty set
Class ((CompClass ((S,X),(CComp s))),ta) is Element of bool K541(S, the Sorts of (S,X),(CComp s))
bool K541(S, the Sorts of (S,X),(CComp s)) is non empty set
tb is Element of the Sorts of (S,X) . s
OSClass ((S,X),tb) is Element of OSClass ((S,X),s)
Class ((CompClass ((S,X),(CComp s))),tb) is Element of bool K541(S, the Sorts of (S,X),(CComp s))
dom the Sorts of (S,X) is non empty Element of bool the carrier of S
Union the Sorts of (S,X) is non empty set
t1 is Element of Union the Sorts of (S,X)
t2 is Element of Union the Sorts of (S,X)
t2 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X,t2) is Element of the carrier of S
the Sorts of (S,X) . (S,X,t2) is non empty set
(S,X) . t2 is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X,((S,X) . t2)) is Element of the carrier of S
the Sorts of (S,X) . (S,X,((S,X) . t2)) is non empty set
O1 is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
O1 . (S,X,((S,X) . t2)) is set
O1 . (S,X,t2) is set
[t2,((S,X) . t2)] is V26() set
{t2,((S,X) . t2)} is non empty functional set
{t2} is non empty functional set
{{t2,((S,X) . t2)},{t2}} is non empty set
R . (S,X,t2) is Relation-like the Sorts of (S,X) . (S,X,t2) -defined the Sorts of (S,X) . (S,X,t2) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (S,X,t2)),( the Sorts of (S,X) . (S,X,t2)):]
[:( the Sorts of (S,X) . (S,X,t2)),( the Sorts of (S,X) . (S,X,t2)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (S,X,t2)),( the Sorts of (S,X) . (S,X,t2)):] is non empty set
[((S,X) . t2),t2] is V26() set
{((S,X) . t2),t2} is non empty functional set
{((S,X) . t2)} is non empty functional set
{{((S,X) . t2),t2},{((S,X) . t2)}} is non empty set
t1 is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . t1 is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X,((S,X) . t1)) is Element of the carrier of S
(S,X,t1) is Element of the carrier of S
O1 . (S,X,((S,X) . t1)) is set
O1 . (S,X,t1) is set
the Sorts of (S,X) . (S,X,((S,X) . t1)) is non empty set
[t1,((S,X) . t1)] is V26() set
{t1,((S,X) . t1)} is non empty functional set
{t1} is non empty functional set
{{t1,((S,X) . t1)},{t1}} is non empty set
R . (S,X,t1) is Relation-like the Sorts of (S,X) . (S,X,t1) -defined the Sorts of (S,X) . (S,X,t1) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of (S,X) . (S,X,t1)),( the Sorts of (S,X) . (S,X,t1)):]
the Sorts of (S,X) . (S,X,t1) is non empty set
[:( the Sorts of (S,X) . (S,X,t1)),( the Sorts of (S,X) . (S,X,t1)):] is non empty Relation-like set
bool [:( the Sorts of (S,X) . (S,X,t1)),( the Sorts of (S,X) . (S,X,t1)):] is non empty set
(S,X,(S,X),t2) is Element of OSClass ((S,X),(S,X,t2))
OSClass ((S,X),(S,X,t2)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,t2)))))
CComp (S,X,t2) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,t2)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,t2))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,t2) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,t2) } is set
CompClass ((S,X),(CComp (S,X,t2))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,t2))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,t2))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t2))),K541(S, the Sorts of (S,X),(CComp (S,X,t2))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,t2))),K541(S, the Sorts of (S,X),(CComp (S,X,t2))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t2))),K541(S, the Sorts of (S,X),(CComp (S,X,t2))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,t2)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,t2)))
bool (Class (CompClass ((S,X),(CComp (S,X,t2))))) is non empty set
(S,X,(S,X),t1) is Element of OSClass ((S,X),(S,X,t1))
OSClass ((S,X),(S,X,t1)) is non empty Element of bool (Class (CompClass ((S,X),(CComp (S,X,t1)))))
CComp (S,X,t1) is non empty Element of K539(S)
Class ((Path_Rel S),(S,X,t1)) is Element of bool the carrier of S
K541(S, the Sorts of (S,X),(CComp (S,X,t1))) is set
{ ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,t1) } is set
union { ( the Sorts of (S,X) . b₁) where b₁ is Element of the carrier of S : b₁ in CComp (S,X,t1) } is set
CompClass ((S,X),(CComp (S,X,t1))) is Relation-like K541(S, the Sorts of (S,X),(CComp (S,X,t1))) -defined K541(S, the Sorts of (S,X),(CComp (S,X,t1))) -valued total reflexive symmetric transitive Element of bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t1))),K541(S, the Sorts of (S,X),(CComp (S,X,t1))):]
[:K541(S, the Sorts of (S,X),(CComp (S,X,t1))),K541(S, the Sorts of (S,X),(CComp (S,X,t1))):] is Relation-like set
bool [:K541(S, the Sorts of (S,X),(CComp (S,X,t1))),K541(S, the Sorts of (S,X),(CComp (S,X,t1))):] is non empty set
Class (CompClass ((S,X),(CComp (S,X,t1)))) is a_partition of K541(S, the Sorts of (S,X),(CComp (S,X,t1)))
bool (Class (CompClass ((S,X),(CComp (S,X,t1))))) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable monotone regular locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
(S,X) is strict non-empty order-sorted MSAlgebra over S
(S,X) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,X) is non empty Relation-like the carrier' of S -defined Function-like total V32() V33() ManySortedFunction of the Arity of S * ((S,X) #), the ResultSort of S * (S,X)
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 V29( the carrier' of S, the carrier of S * ) V32() V33() Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,X) # is non empty Relation-like the carrier of S * -defined Function-like total set
the Arity of S * ((S,X) #) is non empty 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 V29( 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 non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,X) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,X),(S,X) #) is strict MSAlgebra over S
(S,X) is non empty Relation-like the carrier of S -defined Function-like total V33() MSEquivalence-like MSCongruence-like monotone OrderSortedRelation of (S,X)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable monotone regular locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
bool (FinTrees the carrier of (S,X)) is non empty set
(S,X) is Relation-like TS (S,X) -defined TS (S,X) -valued Function-like V29( TS (S,X), TS (S,X)) V32() V33() Element of bool [:(TS (S,X)),(TS (S,X)):]
[:(TS (S,X)),(TS (S,X)):] is non empty Relation-like set
bool [:(TS (S,X)),(TS (S,X)):] is non empty set
the Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . the Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X) is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . ((S,X) . the Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)) is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable monotone regular locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is Relation-like TS (S,X) -defined TS (S,X) -valued Function-like V29( TS (S,X), TS (S,X)) V32() V33() Element of bool [:(TS (S,X)),(TS (S,X)):]
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
the carrier of (S,X) is non empty set
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
[:(TS (S,X)),(TS (S,X)):] is non empty Relation-like set
bool [:(TS (S,X)),(TS (S,X)):] is non empty set
proj2 (S,X) is set
bool (TS (S,X)) is non empty set
S is non empty non void V60() reflexive transitive antisymmetric order-sorted discernable monotone regular locally_directed OverloadedRSSign
the carrier of S is non empty set
X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,X) is non empty strict with_terminals with_nonterminals with_useful_nonterminals DTConstrStr
the carrier' of S is non empty set
{ the carrier of S} is non empty set
[: the carrier' of S,{ the carrier of S}:] is non empty Relation-like set
coprod X is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
Union (coprod X) is non empty set
[: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) is non empty set
(S,X) is Relation-like [: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)) -defined ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * -valued Element of bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):]
([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) * is non empty functional FinSequence-membered M10([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X)))
[:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty Relation-like set
bool [:([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))) *):] is non empty set
DTConstrStr(# ([: the carrier' of S,{ the carrier of S}:] \/ (Union (coprod X))),(S,X) #) is non empty strict DTConstrStr
the carrier of (S,X) is non empty set
(S,X) is functional constituted-DTrees Element of bool (TS (S,X))
TS (S,X) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (S,X))
FinTrees the carrier of (S,X) is non empty functional constituted-DTrees DTree-set of the carrier of (S,X)
bool (FinTrees the carrier of (S,X)) is non empty set
bool (TS (S,X)) is non empty set
(S,X) is Relation-like TS (S,X) -defined TS (S,X) -valued Function-like V29( TS (S,X), TS (S,X)) V32() V33() Element of bool [:(TS (S,X)),(TS (S,X)):]
[:(TS (S,X)),(TS (S,X)):] is non empty Relation-like set
bool [:(TS (S,X)),(TS (S,X)):] is non empty set
proj2 (S,X) is set
x is set
y is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like (S,X)
(S,X) . y is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
dom (S,X) is functional constituted-DTrees Element of bool (TS (S,X))
y is set
(S,X) . y is Relation-like Function-like set
t is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . t is Relation-like Function-like DecoratedTree-like Element of TS (S,X)
tx is Relation-like the carrier of (S,X) -valued Function-like DecoratedTree-like Element of TS (S,X)
(S,X) . tx is Relation-like Function-like DecoratedTree-like Element of TS (S,X)