:: ABCMIZ_A semantic presentation

REAL is set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal Element of bool REAL
bool REAL is non empty set
omega is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal set
bool omega is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
{} is empty trivial Relation-like non-empty empty-yielding NAT -defined non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative set
the empty trivial Relation-like non-empty empty-yielding NAT -defined non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative set is empty trivial Relation-like non-empty empty-yielding NAT -defined non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative set
1 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative Element of NAT
{{},1} is non empty finite V32() non with_pair set
Trees is non empty constituted-Trees set
bool Trees is non empty set
COMPLEX is set
FinTrees is non empty constituted-Trees constituted-FinTrees Element of bool Trees
K422() is non empty V137() L15()
the carrier of K422() is non empty set
FinTrees the carrier of K422() is non empty functional constituted-DTrees DTree-set of the carrier of K422()
K421(K422()) is functional constituted-DTrees Element of bool (FinTrees the carrier of K422())
bool (FinTrees the carrier of K422()) is non empty set
[:K421(K422()),NAT:] is Relation-like set
bool [:K421(K422()),NAT:] is non empty set
[:NAT,K421(K422()):] is Relation-like set
bool [:NAT,K421(K422()):] is non empty set
K488() is set
2 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative Element of NAT
2 -tuples_on K488() is FinSequenceSet of K488()
[:(2 -tuples_on K488()),K488():] is Relation-like set
bool [:(2 -tuples_on K488()),K488():] is non empty set
3 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative Element of NAT
3 -tuples_on K488() is FinSequenceSet of K488()
[:(3 -tuples_on K488()),K488():] is Relation-like set
bool [:(3 -tuples_on K488()),K488():] is non empty set
K524() is Relation-like 2 -tuples_on K488() -defined K488() -valued Function-like V25(2 -tuples_on K488(),K488()) Element of bool [:(2 -tuples_on K488()),K488():]
Vars is non empty set
bool Vars is non empty set
[:Vars,NAT:] is non empty non trivial Relation-like non finite set
bool [:Vars,NAT:] is non empty non trivial non finite set
QuasiLoci is non empty FinSequenceSet of Vars
a_Type is set
0 is empty trivial Relation-like non-empty empty-yielding NAT -defined non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative Element of NAT
an_Adj is set
a_Term is set
{a_Type,an_Adj,a_Term} is non empty finite set
[:QuasiLoci,NAT:] is non empty non trivial Relation-like non finite set
VarPoset is non empty V261() V263() V264() V265() L25()
the carrier of VarPoset is non empty set
RAT is set
INT is set
<*> NAT is empty trivial proper Relation-like non-empty empty-yielding NAT -defined NAT -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative FinSequence of NAT
[:NAT,NAT:] is non empty non trivial Relation-like non finite set
Seg 1 is non empty trivial finite 1 -element Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT : ( 1 <= b₁ & b₁ <= 1 ) } is set
{1} is non empty trivial finite V32() 1 -element non with_pair set
Seg 2 is non empty finite 2 -element Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT : ( 1 <= b₁ & b₁ <= 2 ) } is set
{1,2} is non empty finite V32() non with_pair set
K179(0) is non empty V39() set
{0} is non empty trivial functional finite V32() 1 -element non with_pair Element of bool NAT
{0,1,2} is non empty finite non with_pair Element of bool NAT
{ [(varcl b₁),b₂] where b₁ is Element of bool Vars, b₂ is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT : b₁ is finite } is set
K829(Vars) is empty trivial Relation-like non-empty empty-yielding NAT -defined Vars -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative Element of Vars *
Vars * is non empty functional FinSequence-membered FinSequenceSet of Vars
* is set
non_op is set
{*,non_op} is non empty finite set
<*an_Adj,a_Type*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like set
<*an_Adj*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,an_Adj] is non empty pair set
{1,an_Adj} is non empty finite set
{{1,an_Adj},{1}} is non empty finite V32() set
{[1,an_Adj]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*a_Type*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,a_Type] is non empty pair set
{1,a_Type} is non empty finite set
{{1,a_Type},{1}} is non empty finite V32() set
{[1,a_Type]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*an_Adj*> ^ <*a_Type*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like set
K747(1,1) is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative Element of NAT
{a_Term} is non empty trivial finite 1 -element set
{a_Term} * is non empty functional FinSequence-membered FinSequenceSet of {a_Term}
Constructors is non empty set
Modes is non empty set
{a_Type} is non empty trivial finite 1 -element set
[:{a_Type},[:QuasiLoci,NAT:]:] is non empty non trivial Relation-like non finite set
Attrs is non empty set
{an_Adj} is non empty trivial finite 1 -element set
[:{an_Adj},[:QuasiLoci,NAT:]:] is non empty non trivial Relation-like non finite set
Modes \/ Attrs is non empty set
Funcs is non empty set
[:{a_Term},[:QuasiLoci,NAT:]:] is non empty non trivial Relation-like non finite set
(Modes \/ Attrs) \/ Funcs is non empty set
MaxConstrSign is non empty non void V68() strict V146() constructor initialized with_an_operation_for_each_sort ManySortedSign
{*,non_op} \/ Constructors is non empty set
MC is non empty pair set
MC `1 is set
MC `2 is set
[(MC `1),(MC `2)] is non empty pair set
{(MC `1),(MC `2)} is non empty finite set
{(MC `1)} is non empty trivial finite 1 -element set
{{(MC `1),(MC `2)},{(MC `1)}} is non empty finite V32() set
F₁() is non empty finite set
card F₁() is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
the Element of F₁() is Element of F₁()
(card F₁()) + 1 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
d is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
f is set
the set is set
x is set
d is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len d is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
d . 1 is set
dom d is finite Element of bool NAT
d . 0 is set
f is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
d . f is set
f + 1 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
d . (f + 1) is set
0 + 1 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
proj2 d is finite set
f is set
x is set
d . x is set
f is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
x is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
d . x is set
d . f is set
f + 1 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
T is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
(f + 1) + T is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
(f + 1) + 0 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
d . ((f + 1) + 0) is set
p is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
(f + 1) + p is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
d . ((f + 1) + p) is set
p + 1 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
(f + 1) + (p + 1) is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
d . ((f + 1) + (p + 1)) is set
((f + 1) + p) + 1 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
f + p is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
1 + (f + p) is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
Seg ((card F₁()) + 1) is non empty finite (card F₁()) + 1 -element Element of bool NAT
{ b₁ where b₁ is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT : ( 1 <= b₁ & b₁ <= (card F₁()) + 1 ) } is set
card (Seg ((card F₁()) + 1)) is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
card (proj2 d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
f is set
x is set
d . f is set
d . x is set
T is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
p is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
d . T is set
F₁() is finite set
bool F₁() is non empty finite V32() set
MC is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
l is finite Element of bool F₁()
card l is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
d is set
f is finite Element of bool F₁()
card f is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
card F₁() is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
[#] F₁() is non proper finite Element of bool F₁()
MC is finite Element of bool F₁()
card MC is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
F₁() is finite set
MC is Relation-like NAT -defined Function-like one-to-one finite FinSequence-like FinSubsequence-like set
proj2 MC is finite set
dom MC is finite Element of bool NAT
l is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
d is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
MC . l is set
MC . d is set
bool F₁() is non empty finite V32() set
MC is finite Element of bool F₁()
l is Relation-like NAT -defined Function-like one-to-one finite FinSequence-like FinSubsequence-like set
proj2 l is finite set
dom l is finite Element of bool NAT
l is non empty finite set
d is set
f is set
d is set
f is set
x is set
d is set
{d} is non empty trivial finite 1 -element set
MC \ {d} is finite Element of bool F₁()
x is Relation-like NAT -defined Function-like one-to-one finite FinSequence-like FinSubsequence-like set
proj2 x is finite set
dom x is finite Element of bool NAT
<*d*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,d] is non empty pair set
{1,d} is non empty finite set
{{1,d},{1}} is non empty finite V32() set
{[1,d]} is non empty trivial Relation-like Function-like constant finite 1 -element set
proj2 <*d*> is non empty trivial finite 1 -element set
<*d*> ^ x is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len <*d*> is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
T is Relation-like NAT -defined Function-like one-to-one finite FinSequence-like FinSubsequence-like set
proj2 T is finite set
dom T is finite Element of bool NAT
(proj2 <*d*>) \/ (proj2 x) is non empty finite set
{d} \/ (MC \ {d}) is non empty finite set
p is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
T . p is set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
T . o is set
dom <*d*> is non empty trivial finite 1 -element Element of bool NAT
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
1 + o is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
1 + o is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
1 + o is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
1 + o is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
1 + o is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
1 + o is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
x . o is set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
1 + o is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
q is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
1 + q is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
1 + o is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
q is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
1 + q is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
x . o is set
x . q is set
MC is Element of Vars
vars MC is finite Element of bool Vars
varcl (vars MC) is set
l is Element of bool Vars
varcl l is set
d is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[(varcl l),d] is non empty pair set
{(varcl l),d} is non empty finite set
{(varcl l)} is non empty trivial finite 1 -element set
{{(varcl l),d},{(varcl l)}} is non empty finite V32() set
MC is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
the carrier' of MC is non empty set
QuasiTerms MC is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (MC,(MSVars MC))))
bool (Union the Sorts of (Free (MC,(MSVars MC)))) is non empty set
a_Term MC is Element of the carrier of MC
the Sorts of (Free (MC,(MSVars MC))) . (a_Term MC) is set
an_Adj MC is Element of the carrier of MC
non_op MC is OperSymbol of an_Adj MC
a_Type MC is Element of the carrier of MC
ast MC is OperSymbol of a_Type MC
d is Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
f is Element of Vars
f -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
[f,a_Term] is non empty pair set
{f,a_Term} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,a_Term},{f}} is non empty finite V32() set
root-tree [f,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
T is Relation-like NAT -defined Union the Sorts of (Free (MC,(MSVars MC))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of QuasiTerms MC
len T is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
x is constructor Element of the carrier' of MC
the_arity_of x is Relation-like NAT -defined the carrier of MC -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
K122( the carrier' of MC,( the carrier of MC *), the Arity of MC,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
len (the_arity_of x) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
x -trm T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MC,(MSVars MC)))
p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, an_Adj MC
(non_op MC) term p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MC,(MSVars MC)))
o is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, an_Adj MC
o is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, a_Type MC
(ast MC) term (o,o) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MC,(MSVars MC)))
MC is non empty non void V68() V146() constructor ManySortedSign
the carrier' of MC is non empty set
l is Element of the carrier' of MC
the carrier' of MaxConstrSign is non empty set
MC is Element of the carrier' of MaxConstrSign
MC `1 is set
the_result_sort_of MC is Element of the carrier of MaxConstrSign
the carrier of MaxConstrSign is non empty set
the ResultSort of MaxConstrSign is Relation-like the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign -valued Function-like V25( the carrier' of MaxConstrSign, the carrier of MaxConstrSign) Element of bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:]
[: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:] is non empty Relation-like set
bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:] is non empty set
K122( the carrier' of MaxConstrSign, the carrier of MaxConstrSign, the ResultSort of MaxConstrSign,MC) is Element of the carrier of MaxConstrSign
MC `2 is set
(MC `2) `1 is set
card ((MC `2) `1) is epsilon-transitive epsilon-connected ordinal cardinal set
the_arity_of MC is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
the carrier of MaxConstrSign * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MaxConstrSign
the Arity of MaxConstrSign is Relation-like the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign * -valued Function-like V25( the carrier' of MaxConstrSign, the carrier of MaxConstrSign * ) Function-yielding V54() Element of bool [: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):]
[: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):] is non empty Relation-like set
bool [: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):] is non empty set
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,MC) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
len (the_arity_of MC) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
the ResultSort of MaxConstrSign . MC is set
the Arity of MaxConstrSign . MC is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
card ( the Arity of MaxConstrSign . MC) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
the carrier' of MC is non empty set
l is constructor Element of the carrier' of MC
l `2 is set
(l `2) `1 is set
d is Element of Constructors
loci_of d is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
d `2 is Element of [:QuasiLoci,NAT:]
(d `2) `1 is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
MC is non empty non void V68() V146() constructor ManySortedSign
l is V146() Subsignature of MC
MC is non empty non void V68() V146() constructor initialized ManySortedSign
l is non empty non void V68() V146() constructor Subsignature of MC
MC is non empty non void V68() V146() constructor () ManySortedSign
l is non empty non void V68() V146() constructor Subsignature of MC
the carrier' of l is non empty set
d is Element of the carrier' of l
d `1 is set
the_result_sort_of d is Element of the carrier of l
the carrier of l is non empty set
the ResultSort of l is Relation-like the carrier' of l -defined the carrier of l -valued Function-like V25( the carrier' of l, the carrier of l) Element of bool [: the carrier' of l, the carrier of l:]
[: the carrier' of l, the carrier of l:] is non empty Relation-like set
bool [: the carrier' of l, the carrier of l:] is non empty set
K122( the carrier' of l, the carrier of l, the ResultSort of l,d) is Element of the carrier of l
d `2 is set
(d `2) `1 is set
card ((d `2) `1) is epsilon-transitive epsilon-connected ordinal cardinal set
the_arity_of d is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
the carrier' of MC is non empty set
f is Element of the carrier' of MC
the carrier of MC is non empty set
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
the Arity of MC | the carrier' of l is Relation-like the carrier' of l -defined the carrier' of MC -defined the carrier of MC * -valued Function-like Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
the ResultSort of MC | the carrier' of l is Relation-like the carrier' of l -defined the carrier' of MC -defined the carrier of MC -valued Function-like Element of bool [: the carrier' of MC, the carrier of MC:]
the_result_sort_of f is Element of the carrier of MC
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,f) is Element of the carrier of MC
the_arity_of f is Relation-like NAT -defined the carrier of MC -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
K122( the carrier' of MC,( the carrier of MC *), the Arity of MC,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
MC is non empty non void V68() V146() constructor () ManySortedSign
the carrier' of MC is non empty set
l is non empty non void V68() V146() constructor () ManySortedSign
the carrier' of l is non empty set
the carrier of MC is non empty set
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
ManySortedSign(# the carrier of MC, the carrier' of MC, the Arity of MC, the ResultSort of MC #) is non empty V68() strict V146() ManySortedSign
the carrier of l is non empty set
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
the ResultSort of l is Relation-like the carrier' of l -defined the carrier of l -valued Function-like V25( the carrier' of l, the carrier of l) Element of bool [: the carrier' of l, the carrier of l:]
[: the carrier' of l, the carrier of l:] is non empty Relation-like set
bool [: the carrier' of l, the carrier of l:] is non empty set
ManySortedSign(# the carrier of l, the carrier' of l, the Arity of l, the ResultSort of l #) is non empty V68() strict V146() ManySortedSign
d is Element of the carrier' of MC
the Arity of MC . d is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the Arity of l . d is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f is Element of the carrier' of l
d `2 is set
(d `2) `1 is set
card ((d `2) `1) is epsilon-transitive epsilon-connected ordinal cardinal set
the_arity_of d is Relation-like NAT -defined the carrier of MC -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
K122( the carrier' of MC,( the carrier of MC *), the Arity of MC,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
len (the_arity_of d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
the_arity_of f is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of f) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
(len (the_arity_of d)) |-> a_Term is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(len (the_arity_of f)) |-> a_Term is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the Arity of MC . d is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
the Arity of l . d is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f is Element of the carrier' of l
d is Element of the carrier' of MC
the ResultSort of MC . d is set
the ResultSort of l . d is set
f is Element of the carrier' of l
the_result_sort_of d is Element of the carrier of MC
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,d) is Element of the carrier of MC
d `1 is set
the_result_sort_of f is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,f) is Element of the carrier of l
the ResultSort of MC . d is set
the ResultSort of l . d is set
f is Element of the carrier' of l
MC is non empty non void V68() V146() constructor ManySortedSign
the carrier' of MaxConstrSign is non empty set
the Arity of MaxConstrSign is Relation-like the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign * -valued Function-like V25( the carrier' of MaxConstrSign, the carrier of MaxConstrSign * ) Function-yielding V54() Element of bool [: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):]
the carrier of MaxConstrSign is non empty set
the carrier of MaxConstrSign * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MaxConstrSign
[: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):] is non empty Relation-like set
bool [: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):] is non empty set
dom the Arity of MaxConstrSign is Element of bool the carrier' of MaxConstrSign
bool the carrier' of MaxConstrSign is non empty set
the ResultSort of MaxConstrSign is Relation-like the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign -valued Function-like V25( the carrier' of MaxConstrSign, the carrier of MaxConstrSign) Element of bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:]
[: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:] is non empty Relation-like set
bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:] is non empty set
dom the ResultSort of MaxConstrSign is Element of bool the carrier' of MaxConstrSign
the carrier' of MC is non empty set
the carrier of MC is non empty set
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
l is set
d is set
[l,d] is non empty pair set
{l,d} is non empty finite set
{l} is non empty trivial finite 1 -element set
{{l,d},{l}} is non empty finite V32() set
f is Element of the carrier' of MC
the Arity of MC . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x is Element of the carrier' of MaxConstrSign
the Arity of MaxConstrSign . x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x is Element of the carrier' of MaxConstrSign
f `2 is set
(f `2) `1 is set
card ((f `2) `1) is epsilon-transitive epsilon-connected ordinal cardinal set
the_arity_of f is Relation-like NAT -defined the carrier of MC -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
K122( the carrier' of MC,( the carrier of MC *), the Arity of MC,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
len (the_arity_of f) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
card d is epsilon-transitive epsilon-connected ordinal cardinal set
the Arity of MaxConstrSign . x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
card ( the Arity of MaxConstrSign . x) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
l is set
d is set
[l,d] is non empty pair set
{l,d} is non empty finite set
{l} is non empty trivial finite 1 -element set
{{l,d},{l}} is non empty finite V32() set
f is Element of the carrier' of MC
the ResultSort of MC . f is set
x is Element of the carrier' of MaxConstrSign
the ResultSort of MaxConstrSign . x is set
x is Element of the carrier' of MaxConstrSign
f `1 is set
the_result_sort_of f is Element of the carrier of MC
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,f) is Element of the carrier of MC
the_result_sort_of x is Element of the carrier of MaxConstrSign
K122( the carrier' of MaxConstrSign, the carrier of MaxConstrSign, the ResultSort of MaxConstrSign,x) is Element of the carrier of MaxConstrSign
the ResultSort of MaxConstrSign . x is set
x is Element of the carrier' of MaxConstrSign
the carrier' of MC is non empty set
l is Element of the carrier' of MC
l `1 is set
the_result_sort_of l is Element of the carrier of MC
the carrier of MC is non empty set
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,l) is Element of the carrier of MC
l `2 is set
(l `2) `1 is set
card ((l `2) `1) is epsilon-transitive epsilon-connected ordinal cardinal set
the_arity_of l is Relation-like NAT -defined the carrier of MC -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
K122( the carrier' of MC,( the carrier of MC *), the Arity of MC,l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
len (the_arity_of l) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
d is Element of the carrier' of MaxConstrSign
the ResultSort of MaxConstrSign . d is set
the ResultSort of MaxConstrSign | the carrier' of MC is Relation-like the carrier' of MaxConstrSign -defined the carrier' of MC -defined the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign -valued Function-like Element of bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:]
( the ResultSort of MaxConstrSign | the carrier' of MC) . l is set
the ResultSort of MC . l is set
the Arity of MaxConstrSign . d is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
card ( the Arity of MaxConstrSign . d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
the Arity of MaxConstrSign | the carrier' of MC is Relation-like the carrier' of MaxConstrSign -defined the carrier' of MC -defined the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign * -valued Function-like Function-yielding V54() Element of bool [: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):]
( the Arity of MaxConstrSign | the carrier' of MC) . l is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
card (( the Arity of MaxConstrSign | the carrier' of MC) . l) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
the Arity of MC . l is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
card ( the Arity of MC . l) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
MC is non empty non void V68() V146() constructor initialized ManySortedSign
a_Term MC is Element of the carrier of MC
the carrier of MC is non empty set
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the Element of Vars is Element of Vars
the Element of Vars -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
[ the Element of Vars ,a_Term] is non empty pair set
{ the Element of Vars ,a_Term} is non empty finite set
{ the Element of Vars } is non empty trivial finite 1 -element set
{{ the Element of Vars ,a_Term},{ the Element of Vars }} is non empty finite V32() set
root-tree [ the Element of Vars ,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
MC is Element of Vars
l is Element of bool Vars
varcl l is set
d is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[(varcl l),d] is non empty pair set
{(varcl l),d} is non empty finite set
{(varcl l)} is non empty trivial finite 1 -element set
{{(varcl l),d},{(varcl l)}} is non empty finite V32() set
MC is non empty pair Element of Vars
vars MC is finite Element of bool Vars
MC `1 is finite set
d is Element of bool Vars
varcl d is set
f is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[(varcl d),f] is non empty pair set
{(varcl d),f} is non empty finite set
{(varcl d)} is non empty trivial finite 1 -element set
{{(varcl d),f},{(varcl d)}} is non empty finite V32() set
l is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
the epsilon-transitive epsilon-connected ordinal Element of l is epsilon-transitive epsilon-connected ordinal Element of l
T is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
MC is set
l is non empty pair Element of Vars
d is Element of bool Vars
varcl d is set
f is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[(varcl d),f] is non empty pair set
{(varcl d),f} is non empty finite set
{(varcl d)} is non empty trivial finite 1 -element set
{{(varcl d),f},{(varcl d)}} is non empty finite V32() set
l `2 is set
x is set
T is set
[x,T] is non empty pair set
{x,T} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,T},{x}} is non empty finite V32() set
MC is non empty pair Element of Vars
l is non empty pair Element of Vars
MC is non empty non void V68() V146() constructor () ManySortedSign
the carrier' of MC is non empty set
l is set
d is non empty pair Element of Vars
f is Element of the carrier' of MC
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
the carrier' of MC is non empty set
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is set
the carrier of MC --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined bool NAT -valued Function-like constant total total V25( the carrier of MC, bool NAT) with_missing_variables Element of bool [: the carrier of MC,(bool NAT):]
[: the carrier of MC,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of MC,(bool NAT):] is non empty non trivial non finite set
(MSVars MC) \/ ( the carrier of MC --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined Function-like total total with_missing_variables set
DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is L15()
{ the carrier of MC} is non empty trivial finite 1 -element set
[: the carrier' of MC,{ the carrier of MC}:] is non empty Relation-like set
coprod ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like Function-like set
Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like set
[: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Relation-like set
REL ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) -defined ([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * -valued Element of bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):]
([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))
[:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty set
G15(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(REL ((MSVars MC) \/ ( the carrier of MC --> {0})))) is V137() L15()
the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is set
FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
x is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
x . {} is set
T is Element of the carrier of MC
((MSVars MC) \/ ( the carrier of MC --> {0})) . T is non empty set
p is Element of ((MSVars MC) \/ ( the carrier of MC --> {0})) . T
[p,T] is non empty pair Element of [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:]
[:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:] is non empty Relation-like set
{p,T} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p,T},{p}} is non empty finite V32() set
T is Element of the carrier of MC
((MSVars MC) \/ ( the carrier of MC --> {0})) . T is non empty set
p is Element of ((MSVars MC) \/ ( the carrier of MC --> {0})) . T
[p,T] is non empty pair Element of [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:]
[:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:] is non empty Relation-like set
{p,T} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p,T},{p}} is non empty finite V32() set
dom the Sorts of (Free (MC,(MSVars MC))) is non empty Element of bool the carrier of MC
bool the carrier of MC is non empty set
o is set
the Sorts of (Free (MC,(MSVars MC))) . o is set
o is Element of the carrier of MC
root-tree [p,T] is non empty Relation-like [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:] -valued Function-like DecoratedTree-like Element of FinTrees [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:]
FinTrees [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:] is non empty functional constituted-DTrees DTree-set of [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:]
the_sort_of x is Element of the carrier of MC
MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is MSAlgebra over MC
FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier of MC -defined Function-like total set
FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier' of MC -defined Function-like total ManySortedFunction of the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #), the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})))
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
(FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) # is non empty Relation-like the carrier of MC * -defined Function-like total set
the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is Relation-like the carrier' of MC -defined Function-like set
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like the carrier' of MC -defined Function-like set
MSAlgebra(# (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))),(FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is strict MSAlgebra over MC
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total set
the Sorts of (Free (MC,(MSVars MC))) . o is set
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) . o is set
FreeSort (((MSVars MC) \/ ( the carrier of MC --> {0})),o) is functional constituted-DTrees Element of bool K421((DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
K421((DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
bool K421((DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
((MSVars MC) \/ ( the carrier of MC --> {0})) . o is non empty set
{ b₁ where b₁ is Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),K421((DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))) : ( ex b₂ being set st
( b₂ in ((MSVars MC) \/ ( the carrier of MC --> {0})) . o & b₁ = root-tree [b₂,o] ) or ex b₂ being Element of the carrier' of MC st
( [b₂, the carrier of MC] = b₁ . {} & the_result_sort_of b₂ = o ) ) } is set
(MSVars MC) . o is set
q is non empty pair Element of Vars
q -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
a_Term MC is Element of the carrier of MC
[q,a_Term] is non empty pair set
{q,a_Term} is non empty finite set
{q} is non empty trivial Relation-like finite 1 -element set
{{q,a_Term},{q}} is non empty finite V32() set
root-tree [q,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
x is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
x . {} is set
T is set
p is set
[T,p] is non empty pair set
{T,p} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T,p},{T}} is non empty finite V32() set
o is Element of the carrier' of MC
x is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
x . {} is set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is set
the carrier' of MC is non empty set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
a_Term MC is Element of the carrier of MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
f is Element of the carrier' of MC
[f, the carrier of MC] is non empty pair set
{f, the carrier of MC} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f, the carrier of MC},{f}} is non empty finite V32() set
MC is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
the carrier' of MC is non empty set
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is set
d is Element of the carrier' of MC
[d, the carrier of MC] is non empty pair set
{d, the carrier of MC} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MC},{d}} is non empty finite V32() set
the_result_sort_of d is Element of the carrier of MC
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,d) is Element of the carrier of MC
the carrier of MC --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined bool NAT -valued Function-like constant total total V25( the carrier of MC, bool NAT) with_missing_variables Element of bool [: the carrier of MC,(bool NAT):]
[: the carrier of MC,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of MC,(bool NAT):] is non empty non trivial non finite set
(MSVars MC) \/ ( the carrier of MC --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined Function-like total total with_missing_variables set
DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is L15()
{ the carrier of MC} is non empty trivial finite 1 -element set
[: the carrier' of MC,{ the carrier of MC}:] is non empty Relation-like set
coprod ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like Function-like set
Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like set
[: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Relation-like set
REL ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) -defined ([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * -valued Element of bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):]
([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))
[:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty set
G15(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(REL ((MSVars MC) \/ ( the carrier of MC --> {0})))) is V137() L15()
the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is set
FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
T is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
variables_in T is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of (MSVars MC) \/ ( the carrier of MC --> {0})
MC variables_in T is non empty Relation-like the carrier of MC -defined Function-like total set
the_sort_of T is Element of the carrier of MC
{ b₁ where b₁ is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0}))) : ( the_sort_of b₁ = the_sort_of T & variables_in b₁ c= MSVars MC ) } is set
MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is MSAlgebra over MC
FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier of MC -defined Function-like total set
FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier' of MC -defined Function-like total ManySortedFunction of the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #), the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})))
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
(FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) # is non empty Relation-like the carrier of MC * -defined Function-like total set
the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is Relation-like the carrier' of MC -defined Function-like set
the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like the carrier' of MC -defined Function-like set
MSAlgebra(# (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))),(FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is strict MSAlgebra over MC
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total set
(MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0})))) . (the_sort_of T) is set
the Sorts of (Free (MC,(MSVars MC))) . (the_sort_of T) is set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
a_Type MC is Element of the carrier of MC
an_Adj MC is Element of the carrier of MC
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is non empty pair set
(l . {}) `1 is set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
a_Term MC is Element of the carrier of MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
a_Term MC is Element of the carrier of MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
the carrier' of MC is non empty set
d is Element of the carrier' of MC
[d, the carrier of MC] is non empty pair set
{d, the carrier of MC} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MC},{d}} is non empty finite V32() set
d is Element of the carrier' of MC
[d, the carrier of MC] is non empty pair set
{d, the carrier of MC} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MC},{d}} is non empty finite V32() set
the carrier of MC --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined bool NAT -valued Function-like constant total total V25( the carrier of MC, bool NAT) with_missing_variables Element of bool [: the carrier of MC,(bool NAT):]
[: the carrier of MC,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of MC,(bool NAT):] is non empty non trivial non finite set
(MSVars MC) \/ ( the carrier of MC --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined Function-like total total with_missing_variables set
DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is L15()
{ the carrier of MC} is non empty trivial finite 1 -element set
[: the carrier' of MC,{ the carrier of MC}:] is non empty Relation-like set
coprod ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like Function-like set
Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like set
[: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Relation-like set
REL ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) -defined ([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * -valued Element of bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):]
([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))
[:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty set
G15(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(REL ((MSVars MC) \/ ( the carrier of MC --> {0})))) is V137() L15()
the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is set
FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
T is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
variables_in T is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of (MSVars MC) \/ ( the carrier of MC --> {0})
MC variables_in T is non empty Relation-like the carrier of MC -defined Function-like total set
the_sort_of T is Element of the carrier of MC
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0}))) : ( the_sort_of b<sub>1</sub> = the_sort_of T & variables_in b<sub>1</sub> c= MSVars MC ) } is set
MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is MSAlgebra over MC
FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier of MC -defined Function-like total set
FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier' of MC -defined Function-like total ManySortedFunction of the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #), the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})))
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
(FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) # is non empty Relation-like the carrier of MC * -defined Function-like total set
the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is Relation-like the carrier' of MC -defined Function-like set
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like the carrier' of MC -defined Function-like set
MSAlgebra(# (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))),(FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is strict MSAlgebra over MC
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total set
(MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0})))) . (the_sort_of T) is set
the Sorts of (Free (MC,(MSVars MC))) . (the_sort_of T) is set
non_op MC is OperSymbol of an_Adj MC
the_result_sort_of (non_op MC) is Element of the carrier of MC
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,(non_op MC)) is Element of the carrier of MC
ast MC is OperSymbol of a_Type MC
the_result_sort_of (ast MC) is Element of the carrier of MC
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,(ast MC)) is Element of the carrier of MC
the_result_sort_of d is Element of the carrier of MC
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,d) is Element of the carrier of MC
the carrier' of MC is non empty set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
a_Term MC is Element of the carrier of MC
the carrier' of MC is non empty set
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is non empty pair set
(l . {}) `1 is set
(l . {}) `2 is set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
d is Element of the carrier' of MC
[d, the carrier of MC] is non empty pair set
{d, the carrier of MC} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MC},{d}} is non empty finite V32() set
d is Element of the carrier' of MC
[d, the carrier of MC] is non empty pair set
{d, the carrier of MC} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MC},{d}} is non empty finite V32() set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is non empty pair set
(l . {}) `1 is set
((l . {}) `1) `1 is set
the Sorts of (Free (MC,(MSVars MC))) . (((l . {}) `1) `1) is set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
a_Term MC is Element of the carrier of MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
a_Term MC is Element of the carrier of MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
the carrier' of MC is non empty set
d is Element of the carrier' of MC
[d, the carrier of MC] is non empty pair set
{d, the carrier of MC} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MC},{d}} is non empty finite V32() set
d is Element of the carrier' of MC
[d, the carrier of MC] is non empty pair set
{d, the carrier of MC} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MC},{d}} is non empty finite V32() set
the carrier of MC --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined bool NAT -valued Function-like constant total total V25( the carrier of MC, bool NAT) with_missing_variables Element of bool [: the carrier of MC,(bool NAT):]
[: the carrier of MC,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of MC,(bool NAT):] is non empty non trivial non finite set
(MSVars MC) \/ ( the carrier of MC --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined Function-like total total with_missing_variables set
DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is L15()
{ the carrier of MC} is non empty trivial finite 1 -element set
[: the carrier' of MC,{ the carrier of MC}:] is non empty Relation-like set
coprod ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like Function-like set
Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like set
[: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Relation-like set
REL ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) -defined ([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * -valued Element of bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):]
([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))
[:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty set
G15(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(REL ((MSVars MC) \/ ( the carrier of MC --> {0})))) is V137() L15()
the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is set
FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
x is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
the_sort_of x is Element of the carrier of MC
the_result_sort_of d is Element of the carrier of MC
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,d) is Element of the carrier of MC
d `1 is set
variables_in x is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of (MSVars MC) \/ ( the carrier of MC --> {0})
MC variables_in x is non empty Relation-like the carrier of MC -defined Function-like total set
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0}))) : ( the_sort_of b<sub>1</sub> = the_sort_of x & variables_in b<sub>1</sub> c= MSVars MC ) } is set
MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is MSAlgebra over MC
FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier of MC -defined Function-like total set
FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier' of MC -defined Function-like total ManySortedFunction of the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #), the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})))
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
(FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) # is non empty Relation-like the carrier of MC * -defined Function-like total set
the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is Relation-like the carrier' of MC -defined Function-like set
the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like the carrier' of MC -defined Function-like set
MSAlgebra(# (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))),(FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is strict MSAlgebra over MC
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total set
(MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0})))) . (the_sort_of x) is set
the carrier' of MC is non empty set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
the carrier' of MC is non empty set
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is non empty pair set
(l . {}) `1 is set
ast MC is OperSymbol of a_Type MC
a_Type MC is Element of the carrier of MC
non_op MC is OperSymbol of an_Adj MC
an_Adj MC is Element of the carrier of MC
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is non empty pair set
(l . {}) `1 is set
the carrier of MC --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined bool NAT -valued Function-like constant total total V25( the carrier of MC, bool NAT) with_missing_variables Element of bool [: the carrier of MC,(bool NAT):]
[: the carrier of MC,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of MC,(bool NAT):] is non empty non trivial non finite set
(MSVars MC) \/ ( the carrier of MC --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined Function-like total total with_missing_variables set
DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is L15()
the carrier' of MC is non empty set
{ the carrier of MC} is non empty trivial finite 1 -element set
[: the carrier' of MC,{ the carrier of MC}:] is non empty Relation-like set
coprod ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like Function-like set
Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like set
[: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Relation-like set
REL ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) -defined ([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * -valued Element of bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):]
([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))
[:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty set
G15(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(REL ((MSVars MC) \/ ( the carrier of MC --> {0})))) is V137() L15()
the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is set
FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
x is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
x . {} is set
(x . {}) `1 is set
x is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
x . {} is set
T is Element of the carrier of MC
((MSVars MC) \/ ( the carrier of MC --> {0})) . T is non empty set
p is Element of ((MSVars MC) \/ ( the carrier of MC --> {0})) . T
[p,T] is non empty pair Element of [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:]
[:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:] is non empty Relation-like set
{p,T} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p,T},{p}} is non empty finite V32() set
T is Element of the carrier of MC
((MSVars MC) \/ ( the carrier of MC --> {0})) . T is non empty set
p is Element of ((MSVars MC) \/ ( the carrier of MC --> {0})) . T
[p,T] is non empty pair Element of [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:]
[:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:] is non empty Relation-like set
{p,T} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p,T},{p}} is non empty finite V32() set
root-tree [p,T] is non empty Relation-like [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:] -valued Function-like DecoratedTree-like Element of FinTrees [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:]
FinTrees [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:] is non empty functional constituted-DTrees DTree-set of [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:]
o is non empty pair Element of Vars
o -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
a_Term MC is Element of the carrier of MC
[o,a_Term] is non empty pair set
{o,a_Term} is non empty finite set
{o} is non empty trivial Relation-like finite 1 -element set
{{o,a_Term},{o}} is non empty finite V32() set
root-tree [o,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
( the carrier of MC --> {0}) . T is non empty set
(MSVars MC) . T is set
((MSVars MC) . T) \/ {0} is non empty set
{} \/ {0} is non empty finite V32() non with_pair set
x is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
x . {} is set
[*,3] is non empty pair set
{*,3} is non empty finite set
{*} is non empty trivial finite 1 -element set
{{*,3},{*}} is non empty finite V32() set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
an_Adj MC is Element of the carrier of MC
a_Type MC is Element of the carrier of MC
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is non empty pair set
(l . {}) `1 is set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
a_Term MC is Element of the carrier of MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
the carrier' of MC is non empty set
d is Element of the carrier' of MC
[d, the carrier of MC] is non empty pair set
{d, the carrier of MC} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MC},{d}} is non empty finite V32() set
the carrier of MC --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined bool NAT -valued Function-like constant total total V25( the carrier of MC, bool NAT) with_missing_variables Element of bool [: the carrier of MC,(bool NAT):]
[: the carrier of MC,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of MC,(bool NAT):] is non empty non trivial non finite set
(MSVars MC) \/ ( the carrier of MC --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined Function-like total total with_missing_variables set
DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is L15()
{ the carrier of MC} is non empty trivial finite 1 -element set
[: the carrier' of MC,{ the carrier of MC}:] is non empty Relation-like set
coprod ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like Function-like set
Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like set
[: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Relation-like set
REL ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) -defined ([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * -valued Element of bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):]
([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))
[:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty set
G15(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(REL ((MSVars MC) \/ ( the carrier of MC --> {0})))) is V137() L15()
the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is set
FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
Sym (d,((MSVars MC) \/ ( the carrier of MC --> {0}))) is Element of K424((DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
K424((DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Element of bool the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
bool the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty set
x is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
T is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() ArgumentSeq of Sym (d,((MSVars MC) \/ ( the carrier of MC --> {0})))
[d, the carrier of MC] -tree T is non empty Relation-like Function-like DecoratedTree-like set
[d, the carrier of MC] `1 is set
ast MC is OperSymbol of a_Type MC
the_arity_of (ast MC) is Relation-like NAT -defined the carrier of MC -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
K122( the carrier' of MC,( the carrier of MC *), the Arity of MC,(ast MC)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
<*(an_Adj MC),(a_Type MC)*> is non empty Relation-like NAT -defined the carrier of MC -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of MC
<*(an_Adj MC)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(an_Adj MC)] is non empty pair set
{1,(an_Adj MC)} is non empty finite set
{{1,(an_Adj MC)},{1}} is non empty finite V32() set
{[1,(an_Adj MC)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(a_Type MC)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(a_Type MC)] is non empty pair set
{1,(a_Type MC)} is non empty finite set
{{1,(a_Type MC)},{1}} is non empty finite V32() set
{[1,(a_Type MC)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(an_Adj MC)*> ^ <*(a_Type MC)*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like set
len T is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
the_arity_of d is Relation-like NAT -defined the carrier of MC -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
K122( the carrier' of MC,( the carrier of MC *), the Arity of MC,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
len (the_arity_of d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
dom T is finite Element of bool NAT
T . 1 is Relation-like Function-like set
T . 2 is Relation-like Function-like set
doms T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Tree-yielding set
len (doms T) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
(doms T) . 1 is set
p is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
proj1 p is non empty finite V39() set
(doms T) . 2 is set
o is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
proj1 o is non empty finite V39() set
0 + 1 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
1 + 1 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
<*0*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like nonpair-yielding FinSequence of NAT
[1,0] is non empty pair set
{1,0} is non empty finite V32() non with_pair set
{{1,0},{1}} is non empty finite V32() set
{[1,0]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*0*> ^ (<*> NAT) is non empty Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
<*1*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like nonpair-yielding FinSequence of NAT
[1,1] is non empty pair set
{1,1} is non empty finite V32() non with_pair set
{{1,1},{1}} is non empty finite V32() set
{[1,1]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*1*> ^ (<*> NAT) is non empty Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
proj1 x is non empty finite V39() set
tree (doms T) is non empty V39() set
o is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like Element of proj1 x
x | o is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
q is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like Element of proj1 x
x | q is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
variables_in p is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of (MSVars MC) \/ ( the carrier of MC --> {0})
MC variables_in p is non empty Relation-like the carrier of MC -defined Function-like total set
variables_in x is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of (MSVars MC) \/ ( the carrier of MC --> {0})
MC variables_in x is non empty Relation-like the carrier of MC -defined Function-like total set
variables_in o is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of (MSVars MC) \/ ( the carrier of MC --> {0})
MC variables_in o is non empty Relation-like the carrier of MC -defined Function-like total set
the_sort_of p is Element of the carrier of MC
(the_arity_of d) . 1 is set
{ b₁ where b₁ is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0}))) : ( the_sort_of b₁ = an_Adj MC & variables_in b₁ c= MSVars MC ) } is set
MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is MSAlgebra over MC
FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier of MC -defined Function-like total set
FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier' of MC -defined Function-like total ManySortedFunction of the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #), the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})))
(FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) # is non empty Relation-like the carrier of MC * -defined Function-like total set
the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is Relation-like the carrier' of MC -defined Function-like set
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like the carrier' of MC -defined Function-like set
MSAlgebra(# (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))),(FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is strict MSAlgebra over MC
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total set
(MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0})))) . (an_Adj MC) is set
the Sorts of (Free (MC,(MSVars MC))) . (an_Adj MC) is set
the_sort_of o is Element of the carrier of MC
(the_arity_of d) . 2 is set
{ b₁ where b₁ is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0}))) : ( the_sort_of b₁ = a_Type MC & variables_in b₁ c= MSVars MC ) } is set
(MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0})))) . (a_Type MC) is set
the Sorts of (Free (MC,(MSVars MC))) . (a_Type MC) is set
B is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, an_Adj MC
T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, a_Type MC
[*,3] -tree (B,T) is non empty Relation-like Function-like DecoratedTree-like set
<*B,T*> is non empty Relation-like NAT -defined Union the Sorts of (Free (MC,(MSVars MC))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MC,(MSVars MC)))
<*B*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,B] is non empty pair set
{1,B} is non empty finite V32() non with_pair set
{{1,B},{1}} is non empty finite V32() set
{[1,B]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*T*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,T] is non empty pair set
{1,T} is non empty finite V32() non with_pair set
{{1,T},{1}} is non empty finite V32() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*B*> ^ <*T*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like DTree-yielding set
[non_op,3] is non empty pair set
{non_op,3} is non empty finite set
{non_op} is non empty trivial finite 1 -element set
{{non_op,3},{non_op}} is non empty finite V32() set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
an_Adj MC is Element of the carrier of MC
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is non empty pair set
(l . {}) `1 is set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
a_Term MC is Element of the carrier of MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
the carrier' of MC is non empty set
d is Element of the carrier' of MC
[d, the carrier of MC] is non empty pair set
{d, the carrier of MC} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MC},{d}} is non empty finite V32() set
the carrier of MC --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined bool NAT -valued Function-like constant total total V25( the carrier of MC, bool NAT) with_missing_variables Element of bool [: the carrier of MC,(bool NAT):]
[: the carrier of MC,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of MC,(bool NAT):] is non empty non trivial non finite set
(MSVars MC) \/ ( the carrier of MC --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined Function-like total total with_missing_variables set
DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is L15()
{ the carrier of MC} is non empty trivial finite 1 -element set
[: the carrier' of MC,{ the carrier of MC}:] is non empty Relation-like set
coprod ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like Function-like set
Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like set
[: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Relation-like set
REL ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) -defined ([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * -valued Element of bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):]
([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))
[:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty set
G15(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(REL ((MSVars MC) \/ ( the carrier of MC --> {0})))) is V137() L15()
the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is set
FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
Sym (d,((MSVars MC) \/ ( the carrier of MC --> {0}))) is Element of K424((DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
K424((DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Element of bool the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
bool the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty set
x is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
T is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() ArgumentSeq of Sym (d,((MSVars MC) \/ ( the carrier of MC --> {0})))
[d, the carrier of MC] -tree T is non empty Relation-like Function-like DecoratedTree-like set
[d, the carrier of MC] `1 is set
non_op MC is OperSymbol of an_Adj MC
the_arity_of (non_op MC) is Relation-like NAT -defined the carrier of MC -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
K122( the carrier' of MC,( the carrier of MC *), the Arity of MC,(non_op MC)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
<*(an_Adj MC)*> is non empty trivial Relation-like NAT -defined the carrier of MC -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of MC
[1,(an_Adj MC)] is non empty pair set
{1,(an_Adj MC)} is non empty finite set
{{1,(an_Adj MC)},{1}} is non empty finite V32() set
{[1,(an_Adj MC)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
len T is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
the_arity_of d is Relation-like NAT -defined the carrier of MC -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
K122( the carrier' of MC,( the carrier of MC *), the Arity of MC,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MC *
len (the_arity_of d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
dom T is finite Element of bool NAT
T . 1 is Relation-like Function-like set
doms T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Tree-yielding set
len (doms T) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
(doms T) . 1 is set
p is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
proj1 p is non empty finite V39() set
0 + 1 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
<*0*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like nonpair-yielding FinSequence of NAT
[1,0] is non empty pair set
{1,0} is non empty finite V32() non with_pair set
{{1,0},{1}} is non empty finite V32() set
{[1,0]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*0*> ^ (<*> NAT) is non empty Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
proj1 x is non empty finite V39() set
tree (doms T) is non empty V39() set
o is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like Element of proj1 x
x | o is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
variables_in p is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of (MSVars MC) \/ ( the carrier of MC --> {0})
MC variables_in p is non empty Relation-like the carrier of MC -defined Function-like total set
variables_in x is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of (MSVars MC) \/ ( the carrier of MC --> {0})
MC variables_in x is non empty Relation-like the carrier of MC -defined Function-like total set
the_sort_of p is Element of the carrier of MC
(the_arity_of d) . 1 is set
{ b₁ where b₁ is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0}))) : ( the_sort_of b₁ = an_Adj MC & variables_in b₁ c= MSVars MC ) } is set
MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is MSAlgebra over MC
FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier of MC -defined Function-like total set
FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier' of MC -defined Function-like total ManySortedFunction of the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #), the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})))
(FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) # is non empty Relation-like the carrier of MC * -defined Function-like total set
the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is Relation-like the carrier' of MC -defined Function-like set
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like the carrier' of MC -defined Function-like set
MSAlgebra(# (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))),(FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is strict MSAlgebra over MC
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total set
(MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0})))) . (an_Adj MC) is set
the Sorts of (Free (MC,(MSVars MC))) . (an_Adj MC) is set
o is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, an_Adj MC
[non_op,3] -tree o is non empty Relation-like Function-like DecoratedTree-like set
<*o*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (MC,(MSVars MC))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MC,(MSVars MC)))
[1,o] is non empty pair set
{1,o} is non empty finite V32() non with_pair set
{{1,o},{1}} is non empty finite V32() set
{[1,o]} is non empty trivial Relation-like Function-like constant finite 1 -element set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
the carrier' of MC is non empty set
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is non empty pair set
(l . {}) `1 is set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
a_Term MC is Element of the carrier of MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
a_Term MC is Element of the carrier of MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
d is Element of the carrier' of MC
[d, the carrier of MC] is non empty pair set
{d, the carrier of MC} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MC},{d}} is non empty finite V32() set
d is Element of the carrier' of MC
[d, the carrier of MC] is non empty pair set
{d, the carrier of MC} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MC},{d}} is non empty finite V32() set
the_result_sort_of d is Element of the carrier of MC
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,d) is Element of the carrier of MC
d `1 is set
(l . {}) `2 is set
the carrier of MC --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined bool NAT -valued Function-like constant total total V25( the carrier of MC, bool NAT) with_missing_variables Element of bool [: the carrier of MC,(bool NAT):]
[: the carrier of MC,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of MC,(bool NAT):] is non empty non trivial non finite set
(MSVars MC) \/ ( the carrier of MC --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined Function-like total total with_missing_variables set
DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is L15()
{ the carrier of MC} is non empty trivial finite 1 -element set
[: the carrier' of MC,{ the carrier of MC}:] is non empty Relation-like set
coprod ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like Function-like set
Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like set
[: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Relation-like set
REL ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) -defined ([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * -valued Element of bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):]
([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))
[:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty set
G15(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(REL ((MSVars MC) \/ ( the carrier of MC --> {0})))) is V137() L15()
the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is set
FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
T is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
variables_in T is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of (MSVars MC) \/ ( the carrier of MC --> {0})
MC variables_in T is non empty Relation-like the carrier of MC -defined Function-like total set
the_sort_of T is Element of the carrier of MC
the Sorts of (Free (MC,(MSVars MC))) . (the_result_sort_of d) is set
MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is MSAlgebra over MC
FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier of MC -defined Function-like total set
FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier' of MC -defined Function-like total ManySortedFunction of the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #), the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})))
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
(FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) # is non empty Relation-like the carrier of MC * -defined Function-like total set
the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is Relation-like the carrier' of MC -defined Function-like set
the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like the carrier' of MC -defined Function-like set
MSAlgebra(# (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))),(FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is strict MSAlgebra over MC
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total set
(MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0})))) . (the_result_sort_of d) is set
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0}))) : ( the_sort_of b<sub>1</sub> = the_result_sort_of d & variables_in b<sub>1</sub> c= MSVars MC ) } is set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
a_Term MC is Element of the carrier of MC
the carrier of MC is non empty set
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined bool NAT -valued Function-like constant total total V25( the carrier of MC, bool NAT) with_missing_variables Element of bool [: the carrier of MC,(bool NAT):]
[: the carrier of MC,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of MC,(bool NAT):] is non empty non trivial non finite set
(MSVars MC) \/ ( the carrier of MC --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined Function-like total total with_missing_variables set
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, a_Term MC
f . {} is non empty pair set
(f . {}) `1 is set
((f . {}) `1) `1 is set
MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is MSAlgebra over MC
FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier of MC -defined Function-like total set
FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier' of MC -defined Function-like total ManySortedFunction of the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #), the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})))
the carrier' of MC is non empty set
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
(FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) # is non empty Relation-like the carrier of MC * -defined Function-like total set
the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is Relation-like the carrier' of MC -defined Function-like set
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like the carrier' of MC -defined Function-like set
MSAlgebra(# (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))),(FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is strict MSAlgebra over MC
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
(MC -Terms ((MSVars MC),((MSVars MC) \/ ( the carrier of MC --> {0})))) . (a_Term MC) is set
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) . (a_Term MC) is set
(FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) . (a_Term MC) is set
FreeSort (((MSVars MC) \/ ( the carrier of MC --> {0})),(a_Term MC)) is functional constituted-DTrees Element of bool K421((DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is L15()
{ the carrier of MC} is non empty trivial finite 1 -element set
[: the carrier' of MC,{ the carrier of MC}:] is non empty Relation-like set
coprod ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like Function-like set
Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like set
[: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Relation-like set
REL ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) -defined ([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * -valued Element of bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):]
([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))
[:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty set
G15(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(REL ((MSVars MC) \/ ( the carrier of MC --> {0})))) is V137() L15()
K421((DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is set
FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
bool K421((DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
((MSVars MC) \/ ( the carrier of MC --> {0})) . (a_Term MC) is non empty set
{ b₁ where b₁ is Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),K421((DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))) : ( ex b₂ being set st
( b₂ in ((MSVars MC) \/ ( the carrier of MC --> {0})) . (a_Term MC) & b₁ = root-tree [b₂,(a_Term MC)] ) or ex b₂ being Element of the carrier' of MC st
( [b₂, the carrier of MC] = b₁ . {} & the_result_sort_of b₂ = a_Term MC ) ) } is set
(MSVars MC) . a_Term is set
MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
x is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
x . {} is set
T is Element of the carrier of MC
((MSVars MC) \/ ( the carrier of MC --> {0})) . T is non empty set
p is Element of ((MSVars MC) \/ ( the carrier of MC --> {0})) . T
[p,T] is non empty pair Element of [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:]
[:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:] is non empty Relation-like set
{p,T} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p,T},{p}} is non empty finite V32() set
T is Element of the carrier of MC
((MSVars MC) \/ ( the carrier of MC --> {0})) . T is non empty set
p is Element of ((MSVars MC) \/ ( the carrier of MC --> {0})) . T
[p,T] is non empty pair Element of [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:]
[:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:] is non empty Relation-like set
{p,T} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p,T},{p}} is non empty finite V32() set
root-tree [p,T] is non empty Relation-like [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:] -valued Function-like DecoratedTree-like Element of FinTrees [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:]
FinTrees [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:] is non empty functional constituted-DTrees DTree-set of [:(((MSVars MC) \/ ( the carrier of MC --> {0})) . T), the carrier of MC:]
the_sort_of x is Element of the carrier of MC
o is non empty pair Element of Vars
o -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
[o,a_Term] is non empty pair set
{o,a_Term} is non empty finite set
{o} is non empty trivial Relation-like finite 1 -element set
{{o,a_Term},{o}} is non empty finite V32() set
root-tree [o,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
vars o is finite Element of bool Vars
x is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
x . {} is set
T is set
p is set
[T,p] is non empty pair set
{T,p} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T,p},{T}} is non empty finite V32() set
o is Element of the carrier' of MC
the_result_sort_of o is Element of the carrier of MC
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,o) is Element of the carrier of MC
the_sort_of x is Element of the carrier of MC
ast MC is OperSymbol of a_Type MC
a_Type MC is Element of the carrier of MC
non_op MC is OperSymbol of an_Adj MC
an_Adj MC is Element of the carrier of MC
o `1 is set
(x . {}) `1 is set
((x . {}) `1) `1 is set
o is non empty pair Element of Vars
o -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
[o,a_Term] is non empty pair set
{o,a_Term} is non empty finite set
{o} is non empty trivial Relation-like finite 1 -element set
{{o,a_Term},{o}} is non empty finite V32() set
root-tree [o,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
x is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
x . {} is set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
a_Term MC is Element of the carrier of MC
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is non empty pair set
(l . {}) `1 is set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
a_Term MC is Element of the carrier of MC
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
l . {} is non empty pair set
(l . {}) `1 is set
((l . {}) `1) `1 is set
d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, a_Term MC
d is non empty pair Element of Vars
d -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
[d,a_Term] is non empty pair set
{d,a_Term} is non empty finite set
{d} is non empty trivial Relation-like finite 1 -element set
{{d,a_Term},{d}} is non empty finite V32() set
root-tree [d,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
the carrier' of MC is non empty set
d is Element of the carrier' of MC
the_result_sort_of d is Element of the carrier of MC
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,d) is Element of the carrier of MC
d `1 is set
f is non empty pair Element of Vars
f -term MC is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MC, a_Term MC
[f,a_Term] is non empty pair set
{f,a_Term} is non empty finite set
{f} is non empty trivial Relation-like finite 1 -element set
{{f,a_Term},{f}} is non empty finite V32() set
root-tree [f,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
an_Adj MC is Element of the carrier of MC
the carrier of MC --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined bool NAT -valued Function-like constant total total V25( the carrier of MC, bool NAT) with_missing_variables Element of bool [: the carrier of MC,(bool NAT):]
[: the carrier of MC,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of MC,(bool NAT):] is non empty non trivial non finite set
(MSVars MC) \/ ( the carrier of MC --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined Function-like total total with_missing_variables set
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
f . {} is non empty pair set
(f . {}) `1 is set
((f . {}) `1) `1 is set
FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is MSAlgebra over MC
FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier of MC -defined Function-like total set
FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier' of MC -defined Function-like total ManySortedFunction of the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #), the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})))
the carrier' of MC is non empty set
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
(FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) # is non empty Relation-like the carrier of MC * -defined Function-like total set
the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is Relation-like the carrier' of MC -defined Function-like set
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like the carrier' of MC -defined Function-like set
MSAlgebra(# (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))),(FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is strict MSAlgebra over MC
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total set
Reverse ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier of MC -defined Function-like total Function-yielding V54() ManySortedFunction of FreeGen ((MSVars MC) \/ ( the carrier of MC --> {0})),(MSVars MC) \/ ( the carrier of MC --> {0})
FreeGen ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined Function-like total with_missing_variables GeneratorSet of FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))
(Reverse ((MSVars MC) \/ ( the carrier of MC --> {0}))) "" (MSVars MC) is non empty Relation-like the carrier of MC -defined Function-like total set
x is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
GenMSAlg x is strict MSSubAlgebra of FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))
the Sorts of (Free (MC,(MSVars MC))) . (an_Adj MC) is set
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) . (an_Adj MC) is set
(f . {}) `2 is set
a_Term MC is Element of the carrier of MC
(f . {}) `2 is set
DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is L15()
{ the carrier of MC} is non empty trivial finite 1 -element set
[: the carrier' of MC,{ the carrier of MC}:] is non empty Relation-like set
coprod ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like Function-like set
Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like set
[: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Relation-like set
REL ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) -defined ([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * -valued Element of bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):]
([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))
[:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty set
G15(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(REL ((MSVars MC) \/ ( the carrier of MC --> {0})))) is V137() L15()
the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is set
FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
T is Element of the carrier' of MC
T `1 is set
the_result_sort_of T is Element of the carrier of MC
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,T) is Element of the carrier of MC
[T,((f . {}) `2)] is non empty pair set
{T,((f . {}) `2)} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T,((f . {}) `2)},{T}} is non empty finite V32() set
p is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
the_sort_of p is Element of the carrier of MC
o is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, an_Adj MC
non_op MC is OperSymbol of an_Adj MC
o is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, an_Adj MC
(non_op MC) term o is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MC,(MSVars MC)))
[non_op, the carrier of MC] is non empty pair set
{non_op, the carrier of MC} is non empty finite set
{{non_op, the carrier of MC},{non_op}} is non empty finite V32() set
<*o*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (MC,(MSVars MC))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MC,(MSVars MC)))
[1,o] is non empty pair set
{1,o} is non empty finite V32() non with_pair set
{{1,o},{1}} is non empty finite V32() set
{[1,o]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[non_op, the carrier of MC] -tree <*o*> is non empty Relation-like Function-like DecoratedTree-like set
o . {} is non empty pair set
(o . {}) `1 is set
a_Type MC is Element of the carrier of MC
T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, an_Adj MC
p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, a_Type MC
[*,3] -tree (T,p) is non empty Relation-like Function-like DecoratedTree-like set
<*T,p*> is non empty Relation-like NAT -defined Union the Sorts of (Free (MC,(MSVars MC))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MC,(MSVars MC)))
<*T*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,T] is non empty pair set
{1,T} is non empty finite V32() non with_pair set
{{1,T},{1}} is non empty finite V32() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*p*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,p] is non empty pair set
{1,p} is non empty finite V32() non with_pair set
{{1,p},{1}} is non empty finite V32() set
{[1,p]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*T*> ^ <*p*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like DTree-yielding set
[*,3] -tree <*T,p*> is non empty Relation-like Function-like DecoratedTree-like set
T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, an_Adj MC
[non_op,3] -tree T is non empty Relation-like Function-like DecoratedTree-like set
<*T*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (MC,(MSVars MC))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MC,(MSVars MC)))
[1,T] is non empty pair set
{1,T} is non empty finite V32() non with_pair set
{{1,T},{1}} is non empty finite V32() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[non_op,3] -tree <*T*> is non empty Relation-like Function-like DecoratedTree-like set
[non_op, the carrier of MC] is non empty pair set
{non_op, the carrier of MC} is non empty finite set
{{non_op, the carrier of MC},{non_op}} is non empty finite V32() set
[non_op, the carrier of MC] -tree <*T*> is non empty Relation-like Function-like DecoratedTree-like set
non_op MC is OperSymbol of an_Adj MC
(non_op MC) term T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MC,(MSVars MC)))
(f . {}) `2 is set
a_Term MC is Element of the carrier of MC
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
an_Adj MC is Element of the carrier of MC
the carrier of MC is non empty set
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(MC) expression of MC, an_Adj MC
l . {} is non empty pair set
(l . {}) `1 is set
non_op MC is OperSymbol of an_Adj MC
d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, an_Adj MC
(non_op MC) term d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MC,(MSVars MC)))
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
[non_op, the carrier of MC] is non empty pair set
{non_op, the carrier of MC} is non empty finite set
{{non_op, the carrier of MC},{non_op}} is non empty finite V32() set
<*d*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (MC,(MSVars MC))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MC,(MSVars MC)))
[1,d] is non empty pair set
{1,d} is non empty finite V32() non with_pair set
{{1,d},{1}} is non empty finite V32() set
{[1,d]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[non_op, the carrier of MC] -tree <*d*> is non empty Relation-like Function-like DecoratedTree-like set
MC is non empty non void V68() V146() constructor initialized () ManySortedSign
MSVars MC is non empty Relation-like non empty-yielding the carrier of MC -defined Function-like total with_missing_variables set
the carrier of MC is non empty set
Free (MC,(MSVars MC)) is strict non-empty non empty MSAlgebra over MC
the Sorts of (Free (MC,(MSVars MC))) is non empty Relation-like the carrier of MC -defined Function-like total set
Union the Sorts of (Free (MC,(MSVars MC))) is non empty set
a_Type MC is Element of the carrier of MC
the carrier of MC --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined bool NAT -valued Function-like constant total total V25( the carrier of MC, bool NAT) with_missing_variables Element of bool [: the carrier of MC,(bool NAT):]
[: the carrier of MC,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of MC,(bool NAT):] is non empty non trivial non finite set
(MSVars MC) \/ ( the carrier of MC --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined the carrier of MC -defined Function-like total total with_missing_variables set
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MC,(MSVars MC)))
f . {} is non empty pair set
(f . {}) `1 is set
((f . {}) `1) `1 is set
FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is MSAlgebra over MC
FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier of MC -defined Function-like total set
FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier' of MC -defined Function-like total ManySortedFunction of the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #), the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0})))
the carrier' of MC is non empty set
the Arity of MC is Relation-like the carrier' of MC -defined the carrier of MC * -valued Function-like V25( the carrier' of MC, the carrier of MC * ) Function-yielding V54() Element of bool [: the carrier' of MC,( the carrier of MC *):]
the carrier of MC * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MC
[: the carrier' of MC,( the carrier of MC *):] is non empty Relation-like set
bool [: the carrier' of MC,( the carrier of MC *):] is non empty set
(FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) # is non empty Relation-like the carrier of MC * -defined Function-like total set
the Arity of MC * ((FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is Relation-like the carrier' of MC -defined Function-like set
the ResultSort of MC is Relation-like the carrier' of MC -defined the carrier of MC -valued Function-like V25( the carrier' of MC, the carrier of MC) Element of bool [: the carrier' of MC, the carrier of MC:]
[: the carrier' of MC, the carrier of MC:] is non empty Relation-like set
bool [: the carrier' of MC, the carrier of MC:] is non empty set
the ResultSort of MC * (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like the carrier' of MC -defined Function-like set
MSAlgebra(# (FreeSort ((MSVars MC) \/ ( the carrier of MC --> {0}))),(FreeOper ((MSVars MC) \/ ( the carrier of MC --> {0}))) #) is strict MSAlgebra over MC
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty Relation-like the carrier of MC -defined Function-like total set
Reverse ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like the carrier of MC -defined Function-like total Function-yielding V54() ManySortedFunction of FreeGen ((MSVars MC) \/ ( the carrier of MC --> {0})),(MSVars MC) \/ ( the carrier of MC --> {0})
FreeGen ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty Relation-like non-empty non empty-yielding the carrier of MC -defined Function-like total with_missing_variables GeneratorSet of FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))
(Reverse ((MSVars MC) \/ ( the carrier of MC --> {0}))) "" (MSVars MC) is non empty Relation-like the carrier of MC -defined Function-like total set
x is non empty Relation-like the carrier of MC -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
GenMSAlg x is strict MSSubAlgebra of FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))
the Sorts of (Free (MC,(MSVars MC))) . (a_Type MC) is set
the Sorts of (FreeMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) . (a_Type MC) is set
(f . {}) `2 is set
a_Term MC is Element of the carrier of MC
(f . {}) `2 is set
DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})) is L15()
{ the carrier of MC} is non empty trivial finite 1 -element set
[: the carrier' of MC,{ the carrier of MC}:] is non empty Relation-like set
coprod ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like Function-like set
Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))) is Relation-like set
[: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty Relation-like set
REL ((MSVars MC) \/ ( the carrier of MC --> {0})) is Relation-like [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0})))) -defined ([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * -valued Element of bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):]
([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))
[:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))) *):] is non empty set
G15(([: the carrier' of MC,{ the carrier of MC}:] \/ (Union (coprod ((MSVars MC) \/ ( the carrier of MC --> {0}))))),(REL ((MSVars MC) \/ ( the carrier of MC --> {0})))) is V137() L15()
the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is set
FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))
MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0})))) is non empty set
T is Element of the carrier' of MC
T `1 is set
the_result_sort_of T is Element of the carrier of MC
K122( the carrier' of MC, the carrier of MC, the ResultSort of MC,T) is Element of the carrier of MC
[T,((f . {}) `2)] is non empty pair set
{T,((f . {}) `2)} is non empty finite set
{T} is non empty trivial finite 1 -element set
{{T,((f . {}) `2)},{T}} is non empty finite V32() set
p is non empty Relation-like the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars MC) \/ ( the carrier of MC --> {0}))),MC -Terms ((MSVars MC) \/ ( the carrier of MC --> {0})))
the_sort_of p is Element of the carrier of MC
o is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, a_Type MC
an_Adj MC is Element of the carrier of MC
ast MC is OperSymbol of a_Type MC
o is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, an_Adj MC
q is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, a_Type MC
(ast MC) term (o,q) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MC,(MSVars MC)))
[*, the carrier of MC] is non empty pair set
{*, the carrier of MC} is non empty finite set
{{*, the carrier of MC},{*}} is non empty finite V32() set
<*o,q*> is non empty Relation-like NAT -defined Union the Sorts of (Free (MC,(MSVars MC))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MC,(MSVars MC)))
<*o*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,o] is non empty pair set
{1,o} is non empty finite V32() non with_pair set
{{1,o},{1}} is non empty finite V32() set
{[1,o]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*q*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,q] is non empty pair set
{1,q} is non empty finite V32() non with_pair set
{{1,q},{1}} is non empty finite V32() set
{[1,q]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*o*> ^ <*q*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like DTree-yielding set
[*, the carrier of MC] -tree <*o,q*> is non empty Relation-like Function-like DecoratedTree-like set
o . {} is non empty pair set
(o . {}) `1 is set
an_Adj MC is Element of the carrier of MC
T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, an_Adj MC
p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, a_Type MC
[*,3] -tree (T,p) is non empty Relation-like Function-like DecoratedTree-like set
<*T,p*> is non empty Relation-like NAT -defined Union the Sorts of (Free (MC,(MSVars MC))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MC,(MSVars MC)))
<*T*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,T] is non empty pair set
{1,T} is non empty finite V32() non with_pair set
{{1,T},{1}} is non empty finite V32() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*p*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,p] is non empty pair set
{1,p} is non empty finite V32() non with_pair set
{{1,p},{1}} is non empty finite V32() set
{[1,p]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*T*> ^ <*p*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like DTree-yielding set
[*,3] -tree <*T,p*> is non empty Relation-like Function-like DecoratedTree-like set
[*, the carrier of MC] is non empty pair set
{*, the carrier of MC} is non empty finite set
{{*, the carrier of MC},{*}} is non empty finite V32() set
[*, the carrier of MC] -tree <*T,p*> is non empty Relation-like Function-like DecoratedTree-like set
ast MC is OperSymbol of a_Type MC
(ast MC) term (T,p) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MC,(MSVars MC)))
an_Adj MC is Element of the carrier of MC
T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MC, an_Adj MC
[non_op,3] -tree T is non empty Relation-like Function-like DecoratedTree-like set
<*T*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (MC,(MSVars MC))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MC,(MSVars MC)))
[1,T] is non empty pair set
{1,T} is non empty finite V32() non with_pair set
{{1,T},{1}} is non empty finite V32() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[non_op,3] -tree <*T*> is non empty Relation-like Function-like DecoratedTree-like set
(f . {}) `2 is set
a_Term MC is Element of the carrier of MC
QuasiAdjs MaxConstrSign is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))))
MSVars MaxConstrSign is non empty Relation-like non empty-yielding the carrier of MaxConstrSign -defined Function-like total with_missing_variables set
the carrier of MaxConstrSign is non empty set
Free (MaxConstrSign,(MSVars MaxConstrSign)) is strict non-empty non empty MSAlgebra over MaxConstrSign
the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) is non empty Relation-like the carrier of MaxConstrSign -defined Function-like total with_missing_variables set
Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) is non empty set
bool (Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))) is non empty set
an_Adj MaxConstrSign is Element of the carrier of MaxConstrSign
{ b₁ where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ is V274( MaxConstrSign ) } is set
QuasiTerms MaxConstrSign is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))))
a_Term MaxConstrSign is Element of the carrier of MaxConstrSign
the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) . (a_Term MaxConstrSign) is set
QuasiTypes MaxConstrSign is non empty set
a_Type MaxConstrSign is Element of the carrier of MaxConstrSign
bool (QuasiAdjs MaxConstrSign) is non empty set
{ [b₂,b₁] where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MaxConstrSign , a_Type MaxConstrSign, b₂ is functional finite constituted-DTrees Element of bool (QuasiAdjs MaxConstrSign) : b₁ is pure } is set
() is Element of bool (Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))))
() is Element of bool (Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))))
() is set
bool Constructors is non empty set
[{},0] is non empty pair set
{{},0} is non empty functional finite V32() non with_pair set
{{}} is non empty trivial functional finite V32() 1 -element non with_pair set
{{{},0},{{}}} is non empty finite V32() set
[a_Type,[{},0]] is non empty pair set
{a_Type,[{},0]} is non empty finite set
{{a_Type,[{},0]},{a_Type}} is non empty finite V32() set
() is non empty Element of bool Constructors
() is Element of ()
kind_of () is Element of {a_Type,an_Adj,a_Term}
loci_of () is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
() `2 is Element of [:QuasiLoci,NAT:]
(() `2) `1 is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
index_of () is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
(() `2) `2 is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[:{a_Type,an_Adj,a_Term},[:QuasiLoci,NAT:]:] is non empty non trivial Relation-like non finite set
[:{a_Type},[:QuasiLoci,NAT:]:] \/ [:{an_Adj},[:QuasiLoci,NAT:]:] is non empty Relation-like set
() is non empty Element of bool Constructors
([:{a_Type},[:QuasiLoci,NAT:]:] \/ [:{an_Adj},[:QuasiLoci,NAT:]:]) \/ () is non empty set
{a_Type} \/ {an_Adj} is non empty finite set
[:({a_Type} \/ {an_Adj}),[:QuasiLoci,NAT:]:] is non empty non trivial Relation-like non finite set
[:({a_Type} \/ {an_Adj}),[:QuasiLoci,NAT:]:] \/ () is non empty set
{a_Type,an_Adj} is non empty finite set
[:{a_Type,an_Adj},[:QuasiLoci,NAT:]:] is non empty non trivial Relation-like non finite set
[:{a_Type,an_Adj},[:QuasiLoci,NAT:]:] \/ () is non empty set
{a_Type,an_Adj} \/ {a_Term} is non empty finite set
[:({a_Type,an_Adj} \/ {a_Term}),[:QuasiLoci,NAT:]:] is non empty non trivial Relation-like non finite set
l is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
d is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
rng d is finite Element of bool Vars
[(rng d),l] is non empty pair set
{(rng d),l} is non empty finite V32() set
{(rng d)} is non empty trivial finite V32() 1 -element set
{{(rng d),l},{(rng d)}} is non empty finite V32() set
<*[(rng d),l]*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,[(rng d),l]] is non empty pair set
{1,[(rng d),l]} is non empty finite set
{{1,[(rng d),l]},{1}} is non empty finite V32() set
{[1,[(rng d),l]]} is non empty trivial Relation-like Function-like constant finite 1 -element set
d ^ <*[(rng d),l]*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
varcl (rng d) is set
f is non empty pair Element of Vars
vars f is finite Element of bool Vars
l is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
<*> Vars is empty trivial proper Relation-like non-empty empty-yielding NAT -defined Vars -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative FinSequence of Vars
[:NAT,Vars:] is non empty non trivial Relation-like non finite set
len (<*> Vars) is empty trivial Relation-like non-empty empty-yielding NAT -defined non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative Element of NAT
d is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
d + 1 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
f is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
len f is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[:(bool Vars),NAT:] is non empty non trivial Relation-like non finite set
rng f is finite Element of bool Vars
[(rng f),1] is non empty pair Element of [:(bool Vars),NAT:]
{(rng f),1} is non empty finite V32() set
{(rng f)} is non empty trivial finite V32() 1 -element set
{{(rng f),1},{(rng f)}} is non empty finite V32() set
<*[(rng f),1]*> is non empty trivial Relation-like NAT -defined [:(bool Vars),NAT:] -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of [:(bool Vars),NAT:]
[1,[(rng f),1]] is non empty pair set
{1,[(rng f),1]} is non empty finite set
{{1,[(rng f),1]},{1}} is non empty finite V32() set
{[1,[(rng f),1]]} is non empty trivial Relation-like Function-like constant finite 1 -element set
f ^ <*[(rng f),1]*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
len x is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
l is finite Element of bool Vars
varcl l is set
d is finite Element of bool Vars
f is set
x is set
x `1 is set
f `1 is set
T is Element of bool Vars
varcl T is set
p is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[(varcl T),p] is non empty pair set
{(varcl T),p} is non empty finite set
{(varcl T)} is non empty trivial finite 1 -element set
{{(varcl T),p},{(varcl T)}} is non empty finite V32() set
o is Element of bool Vars
varcl o is set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[(varcl o),o] is non empty pair set
{(varcl o),o} is non empty finite set
{(varcl o)} is non empty trivial finite 1 -element set
{{(varcl o),o},{(varcl o)}} is non empty finite V32() set
f is set
x is set
T is set
x `1 is set
T `1 is set
p is Element of bool Vars
varcl p is set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[(varcl p),o] is non empty pair set
{(varcl p),o} is non empty finite set
{(varcl p)} is non empty trivial finite 1 -element set
{{(varcl p),o},{(varcl p)}} is non empty finite V32() set
o is Element of bool Vars
varcl o is set
q is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[(varcl o),q] is non empty pair set
{(varcl o),q} is non empty finite set
{(varcl o)} is non empty trivial finite 1 -element set
{{(varcl o),q},{(varcl o)}} is non empty finite V32() set
f is Relation-like NAT -defined Function-like one-to-one finite FinSequence-like FinSubsequence-like set
proj2 f is finite set
dom f is finite Element of bool NAT
T is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
x is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like FinSequence of Vars
dom x is finite Element of bool NAT
p is non empty pair Element of Vars
x . T is set
o is non empty pair Element of Vars
vars p is finite Element of bool Vars
o is Element of bool Vars
varcl o is set
q is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[(varcl o),q] is non empty pair set
{(varcl o),q} is non empty finite set
{(varcl o)} is non empty trivial finite 1 -element set
{{(varcl o),q},{(varcl o)}} is non empty finite V32() set
rng x is finite Element of bool Vars
B is set
x . B is set
T is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
c<sub>13</sub> is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
x . c<sub>13</sub> is set
T is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
rng T is finite Element of bool Vars
l is set
d is set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like DTree-yielding set
d -tree f is non empty Relation-like Function-like DecoratedTree-like set
x is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars x is non empty Relation-like non empty-yielding the carrier of x -defined Function-like total with_missing_variables set
the carrier of x is non empty set
Free (x,(MSVars x)) is strict non-empty non empty MSAlgebra over x
the Sorts of (Free (x,(MSVars x))) is non empty Relation-like the carrier of x -defined Function-like total set
Union the Sorts of (Free (x,(MSVars x))) is non empty set
proj2 f is finite set
p is set
dom f is finite Element of bool NAT
o is set
f . o is set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
f . o is set
len f is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
o -' 1 is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
(o -' 1) + 1 is non empty non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real positive non negative set
doms f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Tree-yielding set
len (doms f) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
(doms f) . o is set
q is non empty Relation-like Function-like DecoratedTree-like set
proj1 q is non empty V39() set
T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (x,(MSVars x)))
proj1 T is non empty finite V39() set
tree (doms f) is non empty V39() set
<*(o -' 1)*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like nonpair-yielding FinSequence of NAT
[1,(o -' 1)] is non empty pair set
{1,(o -' 1)} is non empty finite V32() non with_pair set
{{1,(o -' 1)},{1}} is non empty finite V32() set
{[1,(o -' 1)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(o -' 1)*> ^ (<*> NAT) is non empty Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
B is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like Element of proj1 T
T | B is non empty Relation-like Function-like DecoratedTree-like set
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
Subtrees d is set
proj2 d is non empty finite set
proj1 (proj2 d) is set
the carrier' of l is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is constructor Element of the carrier' of l : verum } is set
(proj1 (proj2 d)) /\ { b<sub>1</sub> where b<sub>1</sub> is constructor Element of the carrier' of l : verum } is set
d . {} is set
(d . {}) `1 is set
f is set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like DTree-yielding set
f -tree x is non empty Relation-like Function-like DecoratedTree-like set
f is Relation-like NAT -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of Union the Sorts of (Free (l,(MSVars l)))
(d . {}) -tree f is non empty Relation-like Function-like DecoratedTree-like set
x is Relation-like NAT -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of Union the Sorts of (Free (l,(MSVars l)))
(d . {}) -tree x is non empty Relation-like Function-like DecoratedTree-like set
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
Subtrees d is set
d is non empty non void V68() V146() constructor initialized ManySortedSign
l is non empty pair Element of Vars
l -term d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of d, a_Term d
MSVars d is non empty Relation-like non empty-yielding the carrier of d -defined Function-like total with_missing_variables set
the carrier of d is non empty set
a_Term d is Element of the carrier of d
[l,a_Term] is non empty pair set
{l,a_Term} is non empty finite set
{l} is non empty trivial Relation-like finite 1 -element set
{{l,a_Term},{l}} is non empty finite V32() set
root-tree [l,a_Term] is non empty Relation-like Function-like DecoratedTree-like set
(d,(l -term d)) is set
l is non empty non void V68() V146() constructor initialized ManySortedSign
the carrier' of l is non empty set
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
d is constructor Element of the carrier' of l
the_arity_of d is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
f is Relation-like NAT -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of QuasiTerms l
len f is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
d -trm f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (l,(MSVars l)))
(l,(d -trm f)) is set
[d, the carrier of l] is non empty pair set
{d, the carrier of l} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of l},{d}} is non empty finite V32() set
[d, the carrier of l] -tree f is non empty Relation-like Function-like DecoratedTree-like set
(d -trm f) . {} is set
[d, the carrier of l] `1 is set
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
the carrier' of l is non empty set
d is Element of the carrier' of l
the_result_sort_of d is Element of the carrier of l
the ResultSort of l is Relation-like the carrier' of l -defined the carrier of l -valued Function-like V25( the carrier' of l, the carrier of l) Element of bool [: the carrier' of l, the carrier of l:]
[: the carrier' of l, the carrier of l:] is non empty Relation-like set
bool [: the carrier' of l, the carrier of l:] is non empty set
K122( the carrier' of l, the carrier of l, the ResultSort of l,d) is Element of the carrier of l
the_arity_of d is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
f is Element of the carrier' of l
the_result_sort_of f is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,f) is Element of the carrier of l
the_arity_of f is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
ast l is OperSymbol of a_Type l
a_Type l is Element of the carrier of l
the_arity_of (ast l) is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,(ast l)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
an_Adj l is Element of the carrier of l
<*(an_Adj l),(a_Type l)*> is non empty Relation-like NAT -defined the carrier of l -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of l
<*(an_Adj l)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(an_Adj l)] is non empty pair set
{1,(an_Adj l)} is non empty finite set
{{1,(an_Adj l)},{1}} is non empty finite V32() set
{[1,(an_Adj l)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(a_Type l)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(a_Type l)] is non empty pair set
{1,(a_Type l)} is non empty finite set
{{1,(a_Type l)},{1}} is non empty finite V32() set
{[1,(a_Type l)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(an_Adj l)*> ^ <*(a_Type l)*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like set
non_op l is OperSymbol of an_Adj l
the_arity_of (non_op l) is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,(non_op l)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
<*(an_Adj l)*> is non empty trivial Relation-like NAT -defined the carrier of l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of l
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
<*> (QuasiTerms l) is empty trivial proper Relation-like non-empty empty-yielding NAT -defined QuasiTerms l -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative FinSequence of QuasiTerms l
[:NAT,(QuasiTerms l):] is non empty non trivial Relation-like non finite set
x is constructor Element of the carrier' of l
x -trm (<*> (QuasiTerms l)) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (l,(MSVars l)))
p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (l,(MSVars l)))
(l,p) is set
len (<*> (QuasiTerms l)) is empty trivial Relation-like non-empty empty-yielding NAT -defined non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative Element of NAT
the_arity_of x is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of x) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound (l) Element of Union the Sorts of (Free (l,(MSVars l)))
l is non empty non void V68() V146() ManySortedSign
the carrier of l is non empty set
d is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total set
Free (l,d) is strict non empty MSAlgebra over l
the Sorts of (Free (l,d)) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,d)) is non empty set
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,d))
proj2 f is non empty finite set
the carrier of l --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of l -defined the carrier of l -defined bool NAT -valued Function-like constant total total V25( the carrier of l, bool NAT) with_missing_variables Element of bool [: the carrier of l,(bool NAT):]
[: the carrier of l,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of l,(bool NAT):] is non empty non trivial non finite set
d \/ ( the carrier of l --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of l -defined the carrier of l -defined Function-like total total with_missing_variables set
DTConMSA (d \/ ( the carrier of l --> {0})) is L15()
the carrier' of l is non empty set
{ the carrier of l} is non empty trivial finite 1 -element set
[: the carrier' of l,{ the carrier of l}:] is non empty Relation-like set
coprod (d \/ ( the carrier of l --> {0})) is Relation-like Function-like set
Union (coprod (d \/ ( the carrier of l --> {0}))) is Relation-like set
[: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod (d \/ ( the carrier of l --> {0})))) is non empty Relation-like set
REL (d \/ ( the carrier of l --> {0})) is Relation-like [: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod (d \/ ( the carrier of l --> {0})))) -defined ([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod (d \/ ( the carrier of l --> {0}))))) * -valued Element of bool [:([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod (d \/ ( the carrier of l --> {0}))))),(([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod (d \/ ( the carrier of l --> {0}))))) *):]
([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod (d \/ ( the carrier of l --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod (d \/ ( the carrier of l --> {0}))))
[:([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod (d \/ ( the carrier of l --> {0}))))),(([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod (d \/ ( the carrier of l --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod (d \/ ( the carrier of l --> {0}))))),(([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod (d \/ ( the carrier of l --> {0}))))) *):] is non empty set
G15(([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod (d \/ ( the carrier of l --> {0}))))),(REL (d \/ ( the carrier of l --> {0})))) is V137() L15()
the carrier of (DTConMSA (d \/ ( the carrier of l --> {0}))) is set
FinTrees the carrier of (DTConMSA (d \/ ( the carrier of l --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA (d \/ ( the carrier of l --> {0})))
l -Terms (d \/ ( the carrier of l --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA (d \/ ( the carrier of l --> {0}))))
bool (FinTrees the carrier of (DTConMSA (d \/ ( the carrier of l --> {0})))) is non empty set
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound (l) Element of Union the Sorts of (Free (l,(MSVars l)))
(l,d) is set
(l,d) is set
proj2 d is non empty Relation-like finite set
proj1 (proj2 d) is non empty finite set
the carrier' of l is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is constructor Element of the carrier' of l : verum } is set
(proj1 (proj2 d)) /\ { b<sub>1</sub> where b<sub>1</sub> is constructor Element of the carrier' of l : verum } is finite set
d . {} is set
(d . {}) `1 is set
proj1 d is non empty finite V39() set
l is non empty non void V68() V146() ManySortedSign
the carrier' of l is non empty set
l is non empty non void V68() V146() ManySortedSign
the carrier' of l is non empty set
d is Element of the carrier' of l
the_arity_of d is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l is non empty set
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
the_arity_of d is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l is non empty set
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
the_arity_of d is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l is non empty set
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
l is non empty non void V68() V146() constructor ManySortedSign
non_op l is OperSymbol of an_Adj l
an_Adj l is Element of the carrier of l
the carrier of l is non empty set
the_arity_of (non_op l) is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the carrier' of l is non empty set
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,(non_op l)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
<*(an_Adj l)*> is non empty trivial Relation-like NAT -defined the carrier of l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of l
[1,(an_Adj l)] is non empty pair set
{1,(an_Adj l)} is non empty finite set
{{1,(an_Adj l)},{1}} is non empty finite V32() set
{[1,(an_Adj l)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
len (the_arity_of (non_op l)) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
ast l is OperSymbol of a_Type l
a_Type l is Element of the carrier of l
the_arity_of (ast l) is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the carrier' of l is non empty set
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,(ast l)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
<*(an_Adj l),(a_Type l)*> is non empty Relation-like NAT -defined the carrier of l -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of l
<*(an_Adj l)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(an_Adj l)] is non empty pair set
{1,(an_Adj l)} is non empty finite set
{{1,(an_Adj l)},{1}} is non empty finite V32() set
{[1,(an_Adj l)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(a_Type l)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(a_Type l)] is non empty pair set
{1,(a_Type l)} is non empty finite set
{{1,(a_Type l)},{1}} is non empty finite V32() set
{[1,(a_Type l)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(an_Adj l)*> ^ <*(a_Type l)*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like set
len (the_arity_of (ast l)) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
l is non empty non void V68() V146() constructor ManySortedSign
the carrier' of l is non empty set
d is Element of the carrier' of l
the_arity_of d is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l is non empty set
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
ast l is (l) OperSymbol of a_Type l
a_Type l is Element of the carrier of l
the_arity_of (ast l) is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,(ast l)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
an_Adj l is Element of the carrier of l
<*(an_Adj l),(a_Type l)*> is non empty Relation-like NAT -defined the carrier of l -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of l
<*(an_Adj l)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(an_Adj l)] is non empty pair set
{1,(an_Adj l)} is non empty finite set
{{1,(an_Adj l)},{1}} is non empty finite V32() set
{[1,(an_Adj l)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(a_Type l)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(a_Type l)] is non empty pair set
{1,(a_Type l)} is non empty finite set
{{1,(a_Type l)},{1}} is non empty finite V32() set
{[1,(a_Type l)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(an_Adj l)*> ^ <*(a_Type l)*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like set
non_op l is (l) OperSymbol of an_Adj l
the_arity_of (non_op l) is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,(non_op l)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
<*(an_Adj l)*> is non empty trivial Relation-like NAT -defined the carrier of l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of l
l is non empty non void V68() V146() constructor ManySortedSign
a_Type l is Element of the carrier of l
the carrier of l is non empty set
an_Adj l is Element of the carrier of l
the carrier' of l is non empty set
d is Element of the carrier' of l
the_result_sort_of d is Element of the carrier of l
the ResultSort of l is Relation-like the carrier' of l -defined the carrier of l -valued Function-like V25( the carrier' of l, the carrier of l) Element of bool [: the carrier' of l, the carrier of l:]
[: the carrier' of l, the carrier of l:] is non empty Relation-like set
bool [: the carrier' of l, the carrier of l:] is non empty set
K122( the carrier' of l, the carrier of l, the ResultSort of l,d) is Element of the carrier of l
the_arity_of d is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
f is Element of the carrier' of l
the_result_sort_of f is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,f) is Element of the carrier of l
the_arity_of f is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
x is OperSymbol of a_Type l
T is OperSymbol of an_Adj l
p is OperSymbol of a_Type l
the_arity_of p is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,p) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
o is OperSymbol of an_Adj l
the_arity_of o is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,o) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
d is OperSymbol of a_Type l
f is OperSymbol of an_Adj l
the_result_sort_of d is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,d) is Element of the carrier of l
the_arity_of d is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the_result_sort_of f is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,f) is Element of the carrier of l
the_arity_of f is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
non_op l is (l) OperSymbol of an_Adj l
the_result_sort_of (non_op l) is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,(non_op l)) is Element of the carrier of l
ast l is (l) OperSymbol of a_Type l
the_result_sort_of (ast l) is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,(ast l)) is Element of the carrier of l
l is non empty non void V68() V146() constructor initialized ManySortedSign
a_Type l is Element of the carrier of l
the carrier of l is non empty set
an_Adj l is Element of the carrier of l
d is OperSymbol of a_Type l
f is OperSymbol of an_Adj l
an_Adj l is Element of the carrier of l
d is OperSymbol of a_Type l
f is OperSymbol of an_Adj l
l is non empty non void V68() V146() constructor initialized ManySortedSign
the carrier' of l is non empty set
a_Type l is Element of the carrier of l
the carrier of l is non empty set
the constructor (l) OperSymbol of a_Type l is constructor (l) OperSymbol of a_Type l
l is non empty non void V68() V146() ManySortedSign
the carrier of l is non empty set
the carrier' of l is non empty set
d is set
the ResultSort of l is Relation-like the carrier' of l -defined the carrier of l -valued Function-like V25( the carrier' of l, the carrier of l) Element of bool [: the carrier' of l, the carrier of l:]
[: the carrier' of l, the carrier of l:] is non empty Relation-like set
bool [: the carrier' of l, the carrier of l:] is non empty set
rng the ResultSort of l is Element of bool the carrier of l
bool the carrier of l is non empty set
f is Element of the carrier of l
{ b₁ where b₁ is Element of the carrier' of l : ( the_result_sort_of b₁ = f & len (the_arity_of b₁) = 0 ) } is set
T is non empty non trivial non finite set
the Element of T is Element of T
o is Element of the carrier' of l
the_result_sort_of o is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,o) is Element of the carrier of l
the_arity_of o is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,o) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of o) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
l is non empty non void V68() V146() constructor ManySortedSign
the carrier' of l is non empty set
a_Type l is Element of the carrier of l
the carrier of l is non empty set
{ b₁ where b₁ is Element of the carrier' of l : ( the_result_sort_of b₁ = a_Type l & len (the_arity_of b₁) = 0 ) } is set
the Element of { b₁ where b₁ is Element of the carrier' of l : ( the_result_sort_of b₁ = a_Type l & len (the_arity_of b₁) = 0 ) } is Element of { b₁ where b₁ is Element of the carrier' of l : ( the_result_sort_of b₁ = a_Type l & len (the_arity_of b₁) = 0 ) }
x is Element of the carrier' of l
the_result_sort_of x is Element of the carrier of l
the ResultSort of l is Relation-like the carrier' of l -defined the carrier of l -valued Function-like V25( the carrier' of l, the carrier of l) Element of bool [: the carrier' of l, the carrier of l:]
[: the carrier' of l, the carrier of l:] is non empty Relation-like set
bool [: the carrier' of l, the carrier of l:] is non empty set
K122( the carrier' of l, the carrier of l, the ResultSort of l,x) is Element of the carrier of l
the_arity_of x is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of x) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
an_Adj l is Element of the carrier of l
{ b₁ where b₁ is Element of the carrier' of l : ( the_result_sort_of b₁ = an_Adj l & len (the_arity_of b₁) = 0 ) } is set
the Element of { b₁ where b₁ is Element of the carrier' of l : ( the_result_sort_of b₁ = an_Adj l & len (the_arity_of b₁) = 0 ) } is Element of { b₁ where b₁ is Element of the carrier' of l : ( the_result_sort_of b₁ = an_Adj l & len (the_arity_of b₁) = 0 ) }
o is Element of the carrier' of l
the_result_sort_of o is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,o) is Element of the carrier of l
the_arity_of o is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,o) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of o) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
the carrier' of MaxConstrSign is non empty set
d is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
f is Element of the carrier of MaxConstrSign
{ b₁ where b₁ is Element of the carrier' of MaxConstrSign : ( the_result_sort_of b₁ = f & len (the_arity_of b₁) = d ) } is set
{0,1,2} is non empty finite non with_pair set
T is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
len T is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
p is Relation-like Function-like set
proj1 p is set
o is set
o is set
p . o is set
p . o is set
q is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
p . q is set
[T,q] is non empty pair set
{T,q} is non empty finite V32() set
{T} is non empty trivial functional finite V32() 1 -element set
{{T,q},{T}} is non empty finite V32() set
[f,[T,q]] is non empty pair set
{f,[T,q]} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,[T,q]},{f}} is non empty finite V32() set
B is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
p . B is set
[T,B] is non empty pair set
{T,B} is non empty finite V32() set
{{T,B},{T}} is non empty finite V32() set
[f,[T,B]] is non empty pair set
{f,[T,B]} is non empty finite set
{{f,[T,B]},{f}} is non empty finite V32() set
[T,q] is non empty pair Element of [:QuasiLoci,NAT:]
[T,B] is non empty pair Element of [:QuasiLoci,NAT:]
proj2 p is set
o is set
o is set
p . o is set
q is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[T,q] is non empty pair Element of [:QuasiLoci,NAT:]
{T,q} is non empty finite V32() set
{T} is non empty trivial functional finite V32() 1 -element set
{{T,q},{T}} is non empty finite V32() set
[T,q] is non empty pair set
[f,[T,q]] is non empty pair set
{f,[T,q]} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,[T,q]},{f}} is non empty finite V32() set
B is Element of the carrier' of MaxConstrSign
the_result_sort_of B is Element of the carrier of MaxConstrSign
the ResultSort of MaxConstrSign is Relation-like the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign -valued Function-like V25( the carrier' of MaxConstrSign, the carrier of MaxConstrSign) Element of bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:]
[: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:] is non empty Relation-like set
bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:] is non empty set
K122( the carrier' of MaxConstrSign, the carrier of MaxConstrSign, the ResultSort of MaxConstrSign,B) is Element of the carrier of MaxConstrSign
B `1 is set
the_arity_of B is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
the carrier of MaxConstrSign * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MaxConstrSign
the Arity of MaxConstrSign is Relation-like the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign * -valued Function-like V25( the carrier' of MaxConstrSign, the carrier of MaxConstrSign * ) Function-yielding V54() Element of bool [: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):]
[: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):] is non empty Relation-like set
bool [: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):] is non empty set
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,B) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
len (the_arity_of B) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
B `2 is set
(B `2) `1 is set
card ((B `2) `1) is epsilon-transitive epsilon-connected ordinal cardinal set
[T,q] `1 is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
card ([T,q] `1) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
l is non empty non void V68() V146() constructor initialized with_an_operation_for_each_sort () ManySortedSign
the carrier of l is non empty set
d is Element of the carrier of l
the carrier' of l is non empty set
{ b₁ where b₁ is Element of the carrier' of l : ( the_result_sort_of b₁ = d & len (the_arity_of b₁) = 0 ) } is set
x is set
T is set
p is Element of the carrier' of l
the_result_sort_of p is Element of the carrier of l
the ResultSort of l is Relation-like the carrier' of l -defined the carrier of l -valued Function-like V25( the carrier' of l, the carrier of l) Element of bool [: the carrier' of l, the carrier of l:]
[: the carrier' of l, the carrier of l:] is non empty Relation-like set
bool [: the carrier' of l, the carrier of l:] is non empty set
K122( the carrier' of l, the carrier of l, the ResultSort of l,p) is Element of the carrier of l
the_arity_of p is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,p) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of p) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
o is OperSymbol of d
the_arity_of o is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,o) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier' of l is non empty set
{ b₁ where b₁ is Element of the carrier' of l : ( the_result_sort_of b₁ = d & len (the_arity_of b₁) = 1 ) } is set
x is set
T is set
p is Element of the carrier' of l
the_result_sort_of p is Element of the carrier of l
the ResultSort of l is Relation-like the carrier' of l -defined the carrier of l -valued Function-like V25( the carrier' of l, the carrier of l) Element of bool [: the carrier' of l, the carrier of l:]
[: the carrier' of l, the carrier of l:] is non empty Relation-like set
bool [: the carrier' of l, the carrier of l:] is non empty set
K122( the carrier' of l, the carrier of l, the ResultSort of l,p) is Element of the carrier of l
the_arity_of p is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,p) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of p) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
o is Element of the carrier' of l
the_result_sort_of o is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,o) is Element of the carrier of l
the_arity_of o is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,o) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of o) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
o is OperSymbol of d
q is OperSymbol of d
ast l is (l) OperSymbol of a_Type l
a_Type l is Element of the carrier of l
the carrier' of l is non empty set
{ b₁ where b₁ is Element of the carrier' of l : ( the_result_sort_of b₁ = d & len (the_arity_of b₁) = 2 ) } is set
x is set
T is set
p is Element of the carrier' of l
the_result_sort_of p is Element of the carrier of l
the ResultSort of l is Relation-like the carrier' of l -defined the carrier of l -valued Function-like V25( the carrier' of l, the carrier of l) Element of bool [: the carrier' of l, the carrier of l:]
[: the carrier' of l, the carrier of l:] is non empty Relation-like set
bool [: the carrier' of l, the carrier of l:] is non empty set
K122( the carrier' of l, the carrier of l, the ResultSort of l,p) is Element of the carrier of l
the_arity_of p is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,p) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of p) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
o is Element of the carrier' of l
the_result_sort_of o is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,o) is Element of the carrier of l
the_arity_of o is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,o) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of o) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
o is OperSymbol of d
q is OperSymbol of d
non_op l is (l) OperSymbol of an_Adj l
an_Adj l is Element of the carrier of l
l is non empty non void V68() V146() constructor initialized with_an_operation_for_each_sort () ManySortedSign
the carrier' of l is non empty set
a_Type l is Element of the carrier of l
the carrier of l is non empty set
the constructor (l) OperSymbol of a_Type l is constructor (l) OperSymbol of a_Type l
a_Type l is Element of the carrier of l
the carrier of l is non empty set
the constructor (l) OperSymbol of a_Type l is constructor (l) OperSymbol of a_Type l
l is non empty non void V68() V146() constructor initialized ManySortedSign
the carrier' of l is non empty set
the carrier of l is non empty set
d is constructor (l) Element of the carrier' of l
[d, the carrier of l] is non empty pair set
{d, the carrier of l} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of l},{d}} is non empty finite V32() set
[d, the carrier of l] -tree {} is non empty Relation-like Function-like DecoratedTree-like set
the_result_sort_of d is Element of the carrier of l
the ResultSort of l is Relation-like the carrier' of l -defined the carrier of l -valued Function-like V25( the carrier' of l, the carrier of l) Element of bool [: the carrier' of l, the carrier of l:]
[: the carrier' of l, the carrier of l:] is non empty Relation-like set
bool [: the carrier' of l, the carrier of l:] is non empty set
K122( the carrier' of l, the carrier of l, the ResultSort of l,d) is Element of the carrier of l
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l --> {0} is non empty Relation-like non-empty non empty-yielding the carrier of l -defined the carrier of l -defined bool NAT -valued Function-like constant total total V25( the carrier of l, bool NAT) with_missing_variables Element of bool [: the carrier of l,(bool NAT):]
[: the carrier of l,(bool NAT):] is non empty non trivial Relation-like non finite set
bool [: the carrier of l,(bool NAT):] is non empty non trivial non finite set
(MSVars l) \/ ( the carrier of l --> {0}) is non empty Relation-like non-empty non empty-yielding the carrier of l -defined the carrier of l -defined Function-like total total with_missing_variables set
the_arity_of d is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
l -Terms ((MSVars l),((MSVars l) \/ ( the carrier of l --> {0}))) is non empty Relation-like the carrier of l -defined Function-like total ManySortedSubset of the Sorts of (FreeMSA ((MSVars l) \/ ( the carrier of l --> {0})))
FreeMSA ((MSVars l) \/ ( the carrier of l --> {0})) is MSAlgebra over l
FreeSort ((MSVars l) \/ ( the carrier of l --> {0})) is non empty Relation-like the carrier of l -defined Function-like total set
FreeOper ((MSVars l) \/ ( the carrier of l --> {0})) is non empty Relation-like the carrier' of l -defined Function-like total ManySortedFunction of the Arity of l * ((FreeSort ((MSVars l) \/ ( the carrier of l --> {0}))) #), the ResultSort of l * (FreeSort ((MSVars l) \/ ( the carrier of l --> {0})))
(FreeSort ((MSVars l) \/ ( the carrier of l --> {0}))) # is non empty Relation-like the carrier of l * -defined Function-like total set
the Arity of l * ((FreeSort ((MSVars l) \/ ( the carrier of l --> {0}))) #) is Relation-like the carrier' of l -defined Function-like set
the ResultSort of l * (FreeSort ((MSVars l) \/ ( the carrier of l --> {0}))) is Relation-like the carrier' of l -defined Function-like set
MSAlgebra(# (FreeSort ((MSVars l) \/ ( the carrier of l --> {0}))),(FreeOper ((MSVars l) \/ ( the carrier of l --> {0}))) #) is strict MSAlgebra over l
the Sorts of (FreeMSA ((MSVars l) \/ ( the carrier of l --> {0}))) is non empty Relation-like the carrier of l -defined Function-like total set
dom {} is empty trivial proper Relation-like non-empty empty-yielding NAT -defined non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative Element of bool NAT
DTConMSA ((MSVars l) \/ ( the carrier of l --> {0})) is L15()
{ the carrier of l} is non empty trivial finite 1 -element set
[: the carrier' of l,{ the carrier of l}:] is non empty Relation-like set
coprod ((MSVars l) \/ ( the carrier of l --> {0})) is Relation-like Function-like set
Union (coprod ((MSVars l) \/ ( the carrier of l --> {0}))) is Relation-like set
[: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod ((MSVars l) \/ ( the carrier of l --> {0})))) is non empty Relation-like set
REL ((MSVars l) \/ ( the carrier of l --> {0})) is Relation-like [: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod ((MSVars l) \/ ( the carrier of l --> {0})))) -defined ([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod ((MSVars l) \/ ( the carrier of l --> {0}))))) * -valued Element of bool [:([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod ((MSVars l) \/ ( the carrier of l --> {0}))))),(([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod ((MSVars l) \/ ( the carrier of l --> {0}))))) *):]
([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod ((MSVars l) \/ ( the carrier of l --> {0}))))) * is non empty functional FinSequence-membered FinSequenceSet of [: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod ((MSVars l) \/ ( the carrier of l --> {0}))))
[:([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod ((MSVars l) \/ ( the carrier of l --> {0}))))),(([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod ((MSVars l) \/ ( the carrier of l --> {0}))))) *):] is non empty Relation-like set
bool [:([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod ((MSVars l) \/ ( the carrier of l --> {0}))))),(([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod ((MSVars l) \/ ( the carrier of l --> {0}))))) *):] is non empty set
G15(([: the carrier' of l,{ the carrier of l}:] \/ (Union (coprod ((MSVars l) \/ ( the carrier of l --> {0}))))),(REL ((MSVars l) \/ ( the carrier of l --> {0})))) is V137() L15()
the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))) is set
FinTrees the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))) is non empty functional constituted-DTrees DTree-set of the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0})))
l -Terms ((MSVars l) \/ ( the carrier of l --> {0})) is non empty functional constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))))
bool (FinTrees the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0})))) is non empty set
p is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
{} . p is empty trivial Relation-like non-empty empty-yielding NAT -defined non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative set
(the_arity_of d) . p is set
Sym (d,((MSVars l) \/ ( the carrier of l --> {0}))) is Element of K424((DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))))
K424((DTConMSA ((MSVars l) \/ ( the carrier of l --> {0})))) is non empty Element of bool the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0})))
bool the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))) is non empty set
p is Relation-like NAT -defined FinTrees the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() ArgumentSeq of Sym (d,((MSVars l) \/ ( the carrier of l --> {0})))
(Sym (d,((MSVars l) \/ ( the carrier of l --> {0})))) -tree p is non empty Relation-like the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))),l -Terms ((MSVars l) \/ ( the carrier of l --> {0})))
variables_in ((Sym (d,((MSVars l) \/ ( the carrier of l --> {0})))) -tree p) is non empty Relation-like the carrier of l -defined Function-like total ManySortedSubset of (MSVars l) \/ ( the carrier of l --> {0})
l variables_in ((Sym (d,((MSVars l) \/ ( the carrier of l --> {0})))) -tree p) is non empty Relation-like the carrier of l -defined Function-like total set
o is set
(variables_in ((Sym (d,((MSVars l) \/ ( the carrier of l --> {0})))) -tree p)) . o is set
(MSVars l) . o is set
q is set
rng p is functional finite constituted-DTrees Element of bool (FinTrees the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))))
o is Element of the carrier of l
B is non empty Relation-like Function-like DecoratedTree-like set
l variables_in B is non empty Relation-like the carrier of l -defined Function-like total set
(l variables_in B) . o is set
the_sort_of ((Sym (d,((MSVars l) \/ ( the carrier of l --> {0})))) -tree p) is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (the_result_sort_of d) is set
{ b₁ where b₁ is non empty Relation-like the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))) -valued Function-like finite DecoratedTree-like M31( the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))), FinTrees the carrier of (DTConMSA ((MSVars l) \/ ( the carrier of l --> {0}))),l -Terms ((MSVars l) \/ ( the carrier of l --> {0}))) : ( the_sort_of b₁ = the_result_sort_of d & variables_in b₁ c= MSVars l ) } is set
l is non empty non void V68() V146() constructor initialized ManySortedSign
a_Type l is Element of the carrier of l
the carrier of l is non empty set
d is constructor (l) OperSymbol of a_Type l
d term is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
the_arity_of d is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
the carrier of l * is non empty functional FinSequence-membered FinSequenceSet of the carrier of l
the carrier' of l is non empty set
the Arity of l is Relation-like the carrier' of l -defined the carrier of l * -valued Function-like V25( the carrier' of l, the carrier of l * ) Function-yielding V54() Element of bool [: the carrier' of l,( the carrier of l *):]
[: the carrier' of l,( the carrier of l *):] is non empty Relation-like set
bool [: the carrier' of l,( the carrier of l *):] is non empty set
K122( the carrier' of l,( the carrier of l *), the Arity of l,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
len (the_arity_of d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[d, the carrier of l] is non empty pair set
{d, the carrier of l} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of l},{d}} is non empty finite V32() set
[d, the carrier of l] -tree {} is non empty Relation-like Function-like DecoratedTree-like set
the_result_sort_of d is Element of the carrier of l
the ResultSort of l is Relation-like the carrier' of l -defined the carrier of l -valued Function-like V25( the carrier' of l, the carrier of l) Element of bool [: the carrier' of l, the carrier of l:]
[: the carrier' of l, the carrier of l:] is non empty Relation-like set
bool [: the carrier' of l, the carrier of l:] is non empty set
K122( the carrier' of l, the carrier of l, the ResultSort of l,d) is Element of the carrier of l
x is Element of the carrier' of l
the_result_sort_of x is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,x) is Element of the carrier of l
the_arity_of x is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
T is Element of the carrier' of l
the_result_sort_of T is Element of the carrier of l
K122( the carrier' of l, the carrier of l, the ResultSort of l,T) is Element of the carrier of l
the_arity_of T is Relation-like NAT -defined the carrier of l -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
K122( the carrier' of l,( the carrier of l *), the Arity of l,T) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of l *
x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of l, a_Type l
an_Adj l is Element of the carrier of l
ast l is (l) OperSymbol of a_Type l
T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of l, an_Adj l
p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of l, a_Type l
(ast l) term (T,p) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (l,(MSVars l)))
[*, the carrier of l] is non empty pair set
{*, the carrier of l} is non empty finite set
{{*, the carrier of l},{*}} is non empty finite V32() set
<*T,p*> is non empty Relation-like NAT -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (l,(MSVars l)))
<*T*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,T] is non empty pair set
{1,T} is non empty finite V32() non with_pair set
{{1,T},{1}} is non empty finite V32() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*p*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,p] is non empty pair set
{1,p} is non empty finite V32() non with_pair set
{{1,p},{1}} is non empty finite V32() set
{[1,p]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*T*> ^ <*p*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like DTree-yielding set
[*, the carrier of l] -tree <*T,p*> is non empty Relation-like Function-like DecoratedTree-like set
l is Element of Constructors
the carrier' of MaxConstrSign is non empty set
l is Element of ()
(l) is constructor Element of the carrier' of MaxConstrSign
l `1 is set
the_result_sort_of (l) is Element of the carrier of MaxConstrSign
the ResultSort of MaxConstrSign is Relation-like the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign -valued Function-like V25( the carrier' of MaxConstrSign, the carrier of MaxConstrSign) Element of bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:]
[: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:] is non empty Relation-like set
bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:] is non empty set
K122( the carrier' of MaxConstrSign, the carrier of MaxConstrSign, the ResultSort of MaxConstrSign,(l)) is Element of the carrier of MaxConstrSign
(()) is constructor OperSymbol of a_Type MaxConstrSign
the_arity_of (()) is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
the carrier of MaxConstrSign * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MaxConstrSign
the Arity of MaxConstrSign is Relation-like the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign * -valued Function-like V25( the carrier' of MaxConstrSign, the carrier of MaxConstrSign * ) Function-yielding V54() Element of bool [: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):]
[: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):] is non empty Relation-like set
bool [: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):] is non empty set
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,(())) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
len (the_arity_of (())) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
card ((() `2) `1) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
[{},0] `1 is set
card ([{},0] `1) is epsilon-transitive epsilon-connected ordinal cardinal set
card 0 is empty trivial Relation-like non-empty empty-yielding NAT -defined non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative Element of omega
the_arity_of (()) is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
the carrier of MaxConstrSign * is non empty functional FinSequence-membered FinSequenceSet of the carrier of MaxConstrSign
the Arity of MaxConstrSign is Relation-like the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign * -valued Function-like V25( the carrier' of MaxConstrSign, the carrier of MaxConstrSign * ) Function-yielding V54() Element of bool [: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):]
[: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):] is non empty Relation-like set
bool [: the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *):] is non empty set
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,(())) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
{} (QuasiAdjs MaxConstrSign) is empty trivial proper Relation-like non-empty empty-yielding NAT -defined non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative Element of bool (QuasiAdjs MaxConstrSign)
(MaxConstrSign,(())) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
({} (QuasiAdjs MaxConstrSign)) ast (MaxConstrSign,(())) is non empty pair quasi-type of MaxConstrSign
{({} (QuasiAdjs MaxConstrSign)),(MaxConstrSign,(()))} is non empty functional finite V32() non with_pair set
{({} (QuasiAdjs MaxConstrSign))} is non empty trivial functional finite V32() 1 -element non with_pair set
{{({} (QuasiAdjs MaxConstrSign)),(MaxConstrSign,(()))},{({} (QuasiAdjs MaxConstrSign))}} is non empty finite V32() set
() is non empty pair quasi-type of MaxConstrSign
adjs () is functional finite constituted-DTrees Element of bool (QuasiAdjs MaxConstrSign)
the_base_of () is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
l is Relation-like NAT -defined Vars -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of Vars
len l is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
dom l is finite Element of bool NAT
d is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len d is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
dom d is finite Element of bool NAT
proj2 d is finite set
f is set
x is set
d . x is set
T is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
l /. T is non empty pair Element of Vars
(l /. T) -term MaxConstrSign is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MaxConstrSign , a_Term MaxConstrSign
[(l /. T),a_Term] is non empty pair set
{(l /. T),a_Term} is non empty finite set
{(l /. T)} is non empty trivial Relation-like finite 1 -element set
{{(l /. T),a_Term},{(l /. T)}} is non empty finite V32() set
root-tree [(l /. T),a_Term] is non empty Relation-like Function-like DecoratedTree-like set
f is Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of QuasiTerms MaxConstrSign
len f is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
x is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
f . x is set
l /. x is non empty pair Element of Vars
(l /. x) -term MaxConstrSign is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MaxConstrSign , a_Term MaxConstrSign
[(l /. x),a_Term] is non empty pair set
{(l /. x),a_Term} is non empty finite set
{(l /. x)} is non empty trivial Relation-like finite 1 -element set
{{(l /. x),a_Term},{(l /. x)}} is non empty finite V32() set
root-tree [(l /. x),a_Term] is non empty Relation-like Function-like DecoratedTree-like set
d is Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of QuasiTerms MaxConstrSign
len d is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
f is Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of QuasiTerms MaxConstrSign
len f is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
dom d is finite Element of bool NAT
dom f is finite Element of bool NAT
x is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
d . x is set
l /. x is non empty pair Element of Vars
(l /. x) -term MaxConstrSign is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MaxConstrSign , a_Term MaxConstrSign
[(l /. x),a_Term] is non empty pair set
{(l /. x),a_Term} is non empty finite set
{(l /. x)} is non empty trivial Relation-like finite 1 -element set
{{(l /. x),a_Term},{(l /. x)}} is non empty finite V32() set
root-tree [(l /. x),a_Term] is non empty Relation-like Function-like DecoratedTree-like set
f . x is set
l is Element of Constructors
(l) is constructor Element of the carrier' of MaxConstrSign
loci_of l is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
l `2 is Element of [:QuasiLoci,NAT:]
(l `2) `1 is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
((loci_of l)) is Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of QuasiTerms MaxConstrSign
(l) -trm ((loci_of l)) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
l is Element of the carrier' of MaxConstrSign
d is constructor ( MaxConstrSign ) Element of the carrier' of MaxConstrSign
d term is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
(MaxConstrSign,(d term)) is set
the_arity_of d is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
len (the_arity_of d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
len {} is empty trivial Relation-like non-empty empty-yielding NAT -defined non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative Element of NAT
[d, the carrier of MaxConstrSign] is non empty pair set
{d, the carrier of MaxConstrSign} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MaxConstrSign},{d}} is non empty finite V32() set
[d, the carrier of MaxConstrSign] -tree {} is non empty Relation-like Function-like DecoratedTree-like set
<*> (QuasiTerms MaxConstrSign) is empty trivial proper Relation-like non-empty empty-yielding NAT -defined QuasiTerms MaxConstrSign -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative FinSequence of QuasiTerms MaxConstrSign
[:NAT,(QuasiTerms MaxConstrSign):] is non empty non trivial Relation-like non finite set
d -trm (<*> (QuasiTerms MaxConstrSign)) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
(d term) . {} is non empty pair set
((d term) . {}) `1 is set
[d, the carrier of MaxConstrSign] `1 is set
d is constructor ( MaxConstrSign ) Element of the carrier' of MaxConstrSign
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MaxConstrSign , a_Term MaxConstrSign
d term f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
(MaxConstrSign,(d term f)) is set
x is non empty Relation-like Function-like DecoratedTree-like Element of QuasiTerms MaxConstrSign
<*x*> is non empty trivial Relation-like NAT -defined QuasiTerms MaxConstrSign -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() FinSequence of QuasiTerms MaxConstrSign
[1,x] is non empty pair set
{1,x} is non empty finite set
{{1,x},{1}} is non empty finite V32() set
{[1,x]} is non empty trivial Relation-like Function-like constant finite 1 -element set
the_arity_of d is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
len (the_arity_of d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
1 |-> a_Term is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
<*a_Term*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,a_Term] is non empty pair set
{1,a_Term} is non empty finite set
{{1,a_Term},{1}} is non empty finite V32() set
{[1,a_Term]} is non empty trivial Relation-like Function-like constant finite 1 -element set
T is Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of QuasiTerms MaxConstrSign
len T is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
(the_arity_of d) . 1 is set
[d, the carrier of MaxConstrSign] is non empty pair set
{d, the carrier of MaxConstrSign} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MaxConstrSign},{d}} is non empty finite V32() set
<*f*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
[1,f] is non empty pair set
{1,f} is non empty finite V32() non with_pair set
{{1,f},{1}} is non empty finite V32() set
{[1,f]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[d, the carrier of MaxConstrSign] -tree <*f*> is non empty Relation-like Function-like DecoratedTree-like set
d -trm T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
(d term f) . {} is non empty pair set
((d term f) . {}) `1 is set
[d, the carrier of MaxConstrSign] `1 is set
non_op MaxConstrSign is ( MaxConstrSign ) OperSymbol of an_Adj MaxConstrSign
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign
(non_op MaxConstrSign) term f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
(MaxConstrSign,((non_op MaxConstrSign) term f)) is set
the_arity_of (non_op MaxConstrSign) is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,(non_op MaxConstrSign)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
len (the_arity_of (non_op MaxConstrSign)) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
(the_arity_of (non_op MaxConstrSign)) . 1 is set
[(non_op MaxConstrSign), the carrier of MaxConstrSign] is non empty pair set
{(non_op MaxConstrSign), the carrier of MaxConstrSign} is non empty finite set
{(non_op MaxConstrSign)} is non empty trivial finite 1 -element set
{{(non_op MaxConstrSign), the carrier of MaxConstrSign},{(non_op MaxConstrSign)}} is non empty finite V32() set
<*f*> is non empty trivial Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
[1,f] is non empty pair set
{1,f} is non empty finite V32() non with_pair set
{{1,f},{1}} is non empty finite V32() set
{[1,f]} is non empty trivial Relation-like Function-like constant finite 1 -element set
[(non_op MaxConstrSign), the carrier of MaxConstrSign] -tree <*f*> is non empty Relation-like Function-like DecoratedTree-like set
((non_op MaxConstrSign) term f) . {} is non empty pair set
(((non_op MaxConstrSign) term f) . {}) `1 is set
[(non_op MaxConstrSign), the carrier of MaxConstrSign] `1 is set
d is constructor ( MaxConstrSign ) Element of the carrier' of MaxConstrSign
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MaxConstrSign , a_Term MaxConstrSign
x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MaxConstrSign , a_Term MaxConstrSign
d term (f,x) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
(MaxConstrSign,(d term (f,x))) is set
T is non empty Relation-like Function-like DecoratedTree-like Element of QuasiTerms MaxConstrSign
p is non empty Relation-like Function-like DecoratedTree-like Element of QuasiTerms MaxConstrSign
<*T,p*> is non empty Relation-like NAT -defined QuasiTerms MaxConstrSign -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding Function-yielding V54() FinSequence of QuasiTerms MaxConstrSign
<*T*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[1,T] is non empty pair set
{1,T} is non empty finite set
{{1,T},{1}} is non empty finite V32() set
{[1,T]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*p*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding set
[1,p] is non empty pair set
{1,p} is non empty finite set
{{1,p},{1}} is non empty finite V32() set
{[1,p]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*T*> ^ <*p*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like DTree-yielding set
the_arity_of d is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,d) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
len (the_arity_of d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
2 |-> a_Term is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
<*a_Term,a_Term*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like set
<*a_Term*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,a_Term] is non empty pair set
{1,a_Term} is non empty finite set
{{1,a_Term},{1}} is non empty finite V32() set
{[1,a_Term]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*a_Term*> ^ <*a_Term*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like set
(the_arity_of d) . 1 is set
(the_arity_of d) . 2 is set
o is Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of QuasiTerms MaxConstrSign
len o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
[d, the carrier of MaxConstrSign] is non empty pair set
{d, the carrier of MaxConstrSign} is non empty finite set
{d} is non empty trivial finite 1 -element set
{{d, the carrier of MaxConstrSign},{d}} is non empty finite V32() set
<*f,x*> is non empty Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
<*f*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f] is non empty pair set
{1,f} is non empty finite V32() non with_pair set
{{1,f},{1}} is non empty finite V32() set
{[1,f]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x] is non empty pair set
{1,x} is non empty finite V32() non with_pair set
{{1,x},{1}} is non empty finite V32() set
{[1,x]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f*> ^ <*x*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like DTree-yielding set
[d, the carrier of MaxConstrSign] -tree <*f,x*> is non empty Relation-like Function-like DecoratedTree-like set
d -trm o is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
[d, the carrier of MaxConstrSign] -tree o is non empty Relation-like Function-like DecoratedTree-like set
(d term (f,x)) . {} is non empty pair set
((d term (f,x)) . {}) `1 is set
[d, the carrier of MaxConstrSign] `1 is set
ast MaxConstrSign is ( MaxConstrSign ) OperSymbol of a_Type MaxConstrSign
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MaxConstrSign , a_Type MaxConstrSign
x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign
(ast MaxConstrSign) term (x,f) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
(MaxConstrSign,((ast MaxConstrSign) term (x,f))) is set
the_arity_of (ast MaxConstrSign) is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,(ast MaxConstrSign)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
len (the_arity_of (ast MaxConstrSign)) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
<*(an_Adj MaxConstrSign),(a_Type MaxConstrSign)*> is non empty Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of MaxConstrSign
<*(an_Adj MaxConstrSign)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(an_Adj MaxConstrSign)] is non empty pair set
{1,(an_Adj MaxConstrSign)} is non empty finite set
{{1,(an_Adj MaxConstrSign)},{1}} is non empty finite V32() set
{[1,(an_Adj MaxConstrSign)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(a_Type MaxConstrSign)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
[1,(a_Type MaxConstrSign)] is non empty pair set
{1,(a_Type MaxConstrSign)} is non empty finite set
{{1,(a_Type MaxConstrSign)},{1}} is non empty finite V32() set
{[1,(a_Type MaxConstrSign)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*(an_Adj MaxConstrSign)*> ^ <*(a_Type MaxConstrSign)*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like set
(the_arity_of (ast MaxConstrSign)) . 1 is set
(the_arity_of (ast MaxConstrSign)) . 2 is set
[(ast MaxConstrSign), the carrier of MaxConstrSign] is non empty pair set
{(ast MaxConstrSign), the carrier of MaxConstrSign} is non empty finite set
{(ast MaxConstrSign)} is non empty trivial finite 1 -element set
{{(ast MaxConstrSign), the carrier of MaxConstrSign},{(ast MaxConstrSign)}} is non empty finite V32() set
<*x,f*> is non empty Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding FinSequence of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
<*x*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,x] is non empty pair set
{1,x} is non empty finite V32() non with_pair set
{{1,x},{1}} is non empty finite V32() set
{[1,x]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*f*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like DTree-yielding nonpair-yielding set
[1,f] is non empty pair set
{1,f} is non empty finite V32() non with_pair set
{{1,f},{1}} is non empty finite V32() set
{[1,f]} is non empty trivial Relation-like Function-like constant finite 1 -element set
<*x*> ^ <*f*> is non empty Relation-like NAT -defined Function-like finite K747(1,1) -element FinSequence-like FinSubsequence-like DTree-yielding set
[(ast MaxConstrSign), the carrier of MaxConstrSign] -tree <*x,f*> is non empty Relation-like Function-like DecoratedTree-like set
((ast MaxConstrSign) term (x,f)) . {} is non empty pair set
(((ast MaxConstrSign) term (x,f)) . {}) `1 is set
[(ast MaxConstrSign), the carrier of MaxConstrSign] `1 is set
l is non empty pair quasi-type of MaxConstrSign
the_base_of l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
(MaxConstrSign,(the_base_of l)) is set
proj2 (the_base_of l) is non empty Relation-like finite set
proj1 (proj2 (the_base_of l)) is non empty finite set
{ b₁ where b₁ is constructor Element of the carrier' of MaxConstrSign : verum } is set
(proj1 (proj2 (the_base_of l))) /\ { b₁ where b₁ is constructor Element of the carrier' of MaxConstrSign : verum } is finite set
adjs l is functional finite constituted-DTrees Element of bool (QuasiAdjs MaxConstrSign)
{ (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs l } is set
union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs l } is set
(MaxConstrSign,(the_base_of l)) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs l } ) is set
d is functional finite constituted-DTrees Element of bool (QuasiAdjs MaxConstrSign)
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
d ast l is non empty pair quasi-type of MaxConstrSign
{d,l} is non empty finite V32() set
{d} is non empty trivial finite V32() 1 -element set
{{d,l},{d}} is non empty finite V32() set
((d ast l)) is set
the_base_of (d ast l) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
(MaxConstrSign,(the_base_of (d ast l))) is set
proj2 (the_base_of (d ast l)) is non empty Relation-like finite set
proj1 (proj2 (the_base_of (d ast l))) is non empty finite set
(proj1 (proj2 (the_base_of (d ast l)))) /\ { b₁ where b₁ is constructor Element of the carrier' of MaxConstrSign : verum } is finite set
adjs (d ast l) is functional finite constituted-DTrees Element of bool (QuasiAdjs MaxConstrSign)
{ (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs (d ast l) } is set
union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs (d ast l) } is set
(MaxConstrSign,(the_base_of (d ast l))) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs (d ast l) } ) is set
(MaxConstrSign,l) is set
proj2 l is non empty Relation-like finite set
proj1 (proj2 l) is non empty finite set
(proj1 (proj2 l)) /\ { b₁ where b₁ is constructor Element of the carrier' of MaxConstrSign : verum } is finite set
{ (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in d } is set
union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in d } is set
(MaxConstrSign,l) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in d } ) is set
l is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign
(MaxConstrSign,l) is set
proj2 l is non empty Relation-like finite set
proj1 (proj2 l) is non empty finite set
(proj1 (proj2 l)) /\ { b₁ where b₁ is constructor Element of the carrier' of MaxConstrSign : verum } is finite set
d is non empty pair quasi-type of MaxConstrSign
l ast d is non empty pair quasi-type of MaxConstrSign
{l} is non empty trivial functional finite V32() 1 -element non with_pair Element of bool (Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))))
adjs d is functional finite constituted-DTrees Element of bool (QuasiAdjs MaxConstrSign)
{l} \/ (adjs d) is non empty finite set
the_base_of d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
[({l} \/ (adjs d)),(the_base_of d)] is non empty pair set
{({l} \/ (adjs d)),(the_base_of d)} is non empty finite V32() set
{({l} \/ (adjs d))} is non empty trivial finite V32() 1 -element set
{{({l} \/ (adjs d)),(the_base_of d)},{({l} \/ (adjs d))}} is non empty finite V32() set
((l ast d)) is set
the_base_of (l ast d) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
(MaxConstrSign,(the_base_of (l ast d))) is set
proj2 (the_base_of (l ast d)) is non empty Relation-like finite set
proj1 (proj2 (the_base_of (l ast d))) is non empty finite set
(proj1 (proj2 (the_base_of (l ast d)))) /\ { b₁ where b₁ is constructor Element of the carrier' of MaxConstrSign : verum } is finite set
adjs (l ast d) is functional finite constituted-DTrees Element of bool (QuasiAdjs MaxConstrSign)
{ (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs (l ast d) } is set
union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs (l ast d) } is set
(MaxConstrSign,(the_base_of (l ast d))) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs (l ast d) } ) is set
(d) is set
(MaxConstrSign,(the_base_of d)) is set
proj2 (the_base_of d) is non empty Relation-like finite set
proj1 (proj2 (the_base_of d)) is non empty finite set
(proj1 (proj2 (the_base_of d))) /\ { b₁ where b₁ is constructor Element of the carrier' of MaxConstrSign : verum } is finite set
{ (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs d } is set
union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs d } is set
(MaxConstrSign,(the_base_of d)) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs d } ) is set
(MaxConstrSign,l) \/ (d) is set
{ (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in {l} \/ (adjs d) } is set
{(MaxConstrSign,l)} is non empty trivial finite 1 -element set
{ (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs d } \/ {(MaxConstrSign,l)} is non empty set
T is set
p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign
(MaxConstrSign,p) is set
proj2 p is non empty Relation-like finite set
proj1 (proj2 p) is non empty finite set
(proj1 (proj2 p)) /\ { b₁ where b₁ is constructor Element of the carrier' of MaxConstrSign : verum } is finite set
T is set
p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign
(MaxConstrSign,p) is set
proj2 p is non empty Relation-like finite set
proj1 (proj2 p) is non empty finite set
(proj1 (proj2 p)) /\ { b₁ where b₁ is constructor Element of the carrier' of MaxConstrSign : verum } is finite set
union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in {l} \/ (adjs d) } is set
(MaxConstrSign,(the_base_of (l ast d))) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in {l} \/ (adjs d) } ) is set
(MaxConstrSign,(the_base_of d)) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in {l} \/ (adjs d) } ) is set
union {(MaxConstrSign,l)} is set
(union {(MaxConstrSign,l)}) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs d } ) is set
(MaxConstrSign,(the_base_of d)) \/ ((union {(MaxConstrSign,l)}) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs d } )) is set
(MaxConstrSign,l) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs d } ) is set
(MaxConstrSign,(the_base_of d)) \/ ((MaxConstrSign,l) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs d } )) is set
(MaxConstrSign,(the_base_of d)) \/ (MaxConstrSign,l) is set
((MaxConstrSign,(the_base_of d)) \/ (MaxConstrSign,l)) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs d } ) is set
(MaxConstrSign,l) \/ ((MaxConstrSign,(the_base_of d)) \/ (union { (MaxConstrSign,b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274( MaxConstrSign ) expression of MaxConstrSign , an_Adj MaxConstrSign : b₁ in adjs d } )) is set
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
the empty trivial proper Relation-like non-empty empty-yielding Vars -defined QuasiTerms l -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair irrelevant ext-real non negative Element of bool [:Vars,(QuasiTerms l):] is empty trivial proper Relation-like non-empty empty-yielding Vars -defined QuasiTerms l -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair irrelevant ext-real non negative Element of bool [:Vars,(QuasiTerms l):]
T is empty trivial proper Relation-like non-empty empty-yielding Vars -defined QuasiTerms l -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair irrelevant ext-real non negative Element of bool [:Vars,(QuasiTerms l):]
x at T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
T # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(T #),x) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
T is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
f at T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
T # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(T #),f) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
p is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
x at p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
p # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(p #),x) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
p at T is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
x at (p at T) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
(p at T) # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),((p at T) #),x) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
l is non empty non void V68() V146() constructor initialized ManySortedSign
QuasiAdjs l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
an_Adj l is Element of the carrier of l
{ b₁ where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of l, an_Adj l : b₁ is V274(l) } is set
bool (QuasiAdjs l) is non empty set
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
x is functional constituted-DTrees Element of bool (QuasiAdjs l)
the empty trivial proper Relation-like non-empty empty-yielding Vars -defined QuasiTerms l -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair irrelevant ext-real non negative Element of bool [:Vars,(QuasiTerms l):] is empty trivial proper Relation-like non-empty empty-yielding Vars -defined QuasiTerms l -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair irrelevant ext-real non negative Element of bool [:Vars,(QuasiTerms l):]
T is empty trivial proper Relation-like non-empty empty-yielding Vars -defined QuasiTerms l -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair irrelevant ext-real non negative Element of bool [:Vars,(QuasiTerms l):]
x at T is functional constituted-DTrees Element of bool (QuasiAdjs l)
{ (b₁ at T) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l : b₁ in x } is set
p is set
o is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l
o at T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l
T # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(T #),o) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
l is non empty non void V68() V146() constructor initialized ManySortedSign
QuasiAdjs l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
an_Adj l is Element of the carrier of l
{ b₁ where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of l, an_Adj l : b₁ is V274(l) } is set
bool (QuasiAdjs l) is non empty set
d is functional constituted-DTrees Element of bool (QuasiAdjs l)
f is functional constituted-DTrees Element of bool (QuasiAdjs l)
x is functional constituted-DTrees Element of bool (QuasiAdjs l)
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
T is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
f at T is functional constituted-DTrees Element of bool (QuasiAdjs l)
{ (b₁ at T) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l : b₁ in f } is set
p is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
x at p is functional constituted-DTrees Element of bool (QuasiAdjs l)
{ (b₁ at p) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l : b₁ in x } is set
p at T is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
x at (p at T) is functional constituted-DTrees Element of bool (QuasiAdjs l)
{ (b₁ at (p at T)) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l : b₁ in x } is set
(x at p) at T is functional constituted-DTrees Element of bool (QuasiAdjs l)
{ (b₁ at T) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l : b₁ in x at p } is set
l is non empty non void V68() V146() constructor initialized ManySortedSign
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
x is non empty pair quasi-type of l
adjs x is functional finite constituted-DTrees Element of bool (QuasiAdjs l)
QuasiAdjs l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
an_Adj l is Element of the carrier of l
{ b₁ where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of l, an_Adj l : b₁ is V274(l) } is set
bool (QuasiAdjs l) is non empty set
the_base_of x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of l, a_Type l
a_Type l is Element of the carrier of l
the empty trivial proper Relation-like non-empty empty-yielding Vars -defined QuasiTerms l -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair irrelevant ext-real non negative Element of bool [:Vars,(QuasiTerms l):] is empty trivial proper Relation-like non-empty empty-yielding Vars -defined QuasiTerms l -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair irrelevant ext-real non negative Element of bool [:Vars,(QuasiTerms l):]
T is empty trivial proper Relation-like non-empty empty-yielding Vars -defined QuasiTerms l -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair irrelevant ext-real non negative Element of bool [:Vars,(QuasiTerms l):]
(adjs x) at T is functional finite constituted-DTrees Element of bool (QuasiAdjs l)
{ (b₁ at T) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l : b₁ in adjs x } is set
(the_base_of x) at T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of l, a_Type l
T # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(T #),(the_base_of x)) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
p is set
o is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l
o at T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(T #),o) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
l is non empty non void V68() V146() constructor initialized ManySortedSign
d is non empty pair quasi-type of l
f is non empty pair quasi-type of l
x is non empty pair quasi-type of l
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
adjs f is functional finite constituted-DTrees Element of bool (QuasiAdjs l)
QuasiAdjs l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
an_Adj l is Element of the carrier of l
{ b₁ where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of l, an_Adj l : b₁ is V274(l) } is set
bool (QuasiAdjs l) is non empty set
adjs d is functional finite constituted-DTrees Element of bool (QuasiAdjs l)
the_base_of f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of l, a_Type l
a_Type l is Element of the carrier of l
the_base_of d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of l, a_Type l
T is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
(adjs f) at T is functional finite constituted-DTrees Element of bool (QuasiAdjs l)
{ (b₁ at T) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l : b₁ in adjs f } is set
(the_base_of f) at T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of l, a_Type l
T # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(T #),(the_base_of f)) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
adjs x is functional finite constituted-DTrees Element of bool (QuasiAdjs l)
the_base_of x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of l, a_Type l
p is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
(adjs x) at p is functional finite constituted-DTrees Element of bool (QuasiAdjs l)
{ (b₁ at p) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l : b₁ in adjs x } is set
(the_base_of x) at p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of l, a_Type l
p # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(p #),(the_base_of x)) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
p at T is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
(adjs x) at (p at T) is functional finite constituted-DTrees Element of bool (QuasiAdjs l)
{ (b₁ at (p at T)) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l : b₁ in adjs x } is set
(the_base_of x) at (p at T) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of l, a_Type l
(p at T) # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),((p at T) #),(the_base_of x)) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
((adjs x) at p) at T is functional finite constituted-DTrees Element of bool (QuasiAdjs l)
{ (b₁ at T) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching V274(l) expression of l, an_Adj l : b₁ in (adjs x) at p } is set
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
x is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
d at x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
x # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(x #),d) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
f at x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(x #),f) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
the Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):] is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
x at the Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):] is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
the Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):] # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),( the Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):] #),x) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
p is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
T at p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
p # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(p #),T) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
x at p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(p #),x) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
variables_in x is finite Element of bool Vars
l variables_in x is non empty Relation-like the carrier of l -defined Function-like total set
(l variables_in x) . (a_Term l) is finite set
l idval (variables_in x) is Relation-like Vars -defined QuasiTerms l -valued Function-like one-to-one Function-yielding V54() irrelevant Element of bool [:Vars,(QuasiTerms l):]
{ [b₁,(b₁ -term l)] where b₁ is Element of Vars : b₁ in variables_in x } is set
dom (l idval (variables_in x)) is Element of bool Vars
x at (l idval (variables_in x)) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
(l idval (variables_in x)) # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),((l idval (variables_in x)) #),x) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
x is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
variables_in f is finite Element of bool Vars
l variables_in f is non empty Relation-like the carrier of l -defined Function-like total set
(l variables_in f) . (a_Term l) is finite set
l idval (variables_in f) is Relation-like Vars -defined QuasiTerms l -valued Function-like one-to-one Function-yielding V54() irrelevant Element of bool [:Vars,(QuasiTerms l):]
{ [b₁,(b₁ -term l)] where b₁ is Element of Vars : b₁ in variables_in f } is set
T is Relation-like Vars -defined QuasiTerms l -valued Function-like one-to-one Function-yielding V54() irrelevant Element of bool [:Vars,(QuasiTerms l):]
dom T is Element of bool Vars
f at T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
T # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(T #),f) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
T is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
d at T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
T # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(T #),d) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
f at T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(T #),f) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
d is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
f is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
QuasiTerms l is non empty functional constituted-DTrees Element of bool (Union the Sorts of (Free (l,(MSVars l))))
bool (Union the Sorts of (Free (l,(MSVars l)))) is non empty set
a_Term l is Element of the carrier of l
the Sorts of (Free (l,(MSVars l))) . (a_Term l) is set
[:Vars,(QuasiTerms l):] is non empty Relation-like set
bool [:Vars,(QuasiTerms l):] is non empty set
T is Relation-like Vars -defined QuasiTerms l -valued Function-like Function-yielding V54() Element of bool [:Vars,(QuasiTerms l):]
d at T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
T # is Relation-like Union the Sorts of (Free (l,(MSVars l))) -defined Union the Sorts of (Free (l,(MSVars l))) -valued Function-like V25( Union the Sorts of (Free (l,(MSVars l))), Union the Sorts of (Free (l,(MSVars l)))) substitution term-transformation of l, MSVars l
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(T #),d) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
f at T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
K122((Union the Sorts of (Free (l,(MSVars l)))),(Union the Sorts of (Free (l,(MSVars l)))),(T #),f) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching Element of Union the Sorts of (Free (l,(MSVars l)))
l is non empty non void V68() V146() constructor initialized ManySortedSign
MSVars l is non empty Relation-like non empty-yielding the carrier of l -defined Function-like total with_missing_variables set
the carrier of l is non empty set
Free (l,(MSVars l)) is strict non-empty non empty MSAlgebra over l
the Sorts of (Free (l,(MSVars l))) is non empty Relation-like the carrier of l -defined Function-like total set
Union the Sorts of (Free (l,(MSVars l))) is non empty set
d is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
f is Element of the carrier of MaxConstrSign
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len x is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
dom x is finite Element of bool NAT
T is set
proj1 x is finite set
p is set
x . T is set
x . p is set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
x . o is set
[{},o] is non empty pair set
{{},o} is non empty finite V32() non with_pair set
{{{},o},{{}}} is non empty finite V32() set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
[{},o] is non empty pair set
{{},o} is non empty finite V32() non with_pair set
{{{},o},{{}}} is non empty finite V32() set
H₁(o) `2 is set
proj2 x is finite set
T is set
p is set
x . p is set
o is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
[{},o] is non empty pair set
{{},o} is non empty finite V32() non with_pair set
{{{},o},{{}}} is non empty finite V32() set
T is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like FinSequence of Vars
dom T is finite Element of bool NAT
p is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative set
T . p is set
o is non empty pair Element of Vars
vars o is finite Element of bool Vars
[{},p] is non empty pair set
{{},p} is non empty finite V32() non with_pair set
{{{},p},{{}}} is non empty finite V32() set
o is non empty pair Element of Vars
p is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
[p,0] is non empty pair Element of [:QuasiLoci,NAT:]
{p,0} is non empty functional finite V32() set
{p} is non empty trivial functional finite V32() 1 -element set
{{p,0},{p}} is non empty finite V32() set
[f,[p,0]] is non empty pair Element of [: the carrier of MaxConstrSign,[:QuasiLoci,NAT:]:]
[: the carrier of MaxConstrSign,[:QuasiLoci,NAT:]:] is non empty non trivial Relation-like non finite set
{f,[p,0]} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,[p,0]},{f}} is non empty finite V32() set
o is constructor Element of the carrier' of MaxConstrSign
the_result_sort_of o is Element of the carrier of MaxConstrSign
the ResultSort of MaxConstrSign is Relation-like the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign -valued Function-like V25( the carrier' of MaxConstrSign, the carrier of MaxConstrSign) Element of bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:]
[: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:] is non empty Relation-like set
bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:] is non empty set
K122( the carrier' of MaxConstrSign, the carrier of MaxConstrSign, the ResultSort of MaxConstrSign,o) is Element of the carrier of MaxConstrSign
o `1 is set
q is constructor OperSymbol of f
the_arity_of q is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,q) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
len (the_arity_of q) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
q `2 is set
(q `2) `1 is set
card ((q `2) `1) is epsilon-transitive epsilon-connected ordinal cardinal set
[p,0] `1 is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
card ([p,0] `1) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
card p is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of omega
l is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
len l is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
(l) is Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of QuasiTerms MaxConstrSign
rng l is finite Element of bool Vars
T is Element of the carrier of MaxConstrSign
p is constructor OperSymbol of T
the_arity_of p is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,p) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
len (the_arity_of p) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
p -trm (l) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
variables_in (p -trm (l)) is finite Element of bool Vars
MaxConstrSign variables_in (p -trm (l)) is non empty Relation-like the carrier of MaxConstrSign -defined Function-like total with_missing_variables set
(MaxConstrSign variables_in (p -trm (l))) . (a_Term MaxConstrSign) is finite set
rng (l) is finite Element of bool (Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))))
{ (variables_in b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MaxConstrSign , a_Term MaxConstrSign : b₁ in rng (l) } is set
len (l) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
union { (variables_in b₁) where b₁ is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MaxConstrSign , a_Term MaxConstrSign : b₁ in rng (l) } is set
dom (l) is finite Element of bool NAT
dom l is finite Element of bool NAT
q is set
B is set
T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching expression of MaxConstrSign , a_Term MaxConstrSign
variables_in T is finite Element of bool Vars
MaxConstrSign variables_in T is non empty Relation-like the carrier of MaxConstrSign -defined Function-like total with_missing_variables set
(MaxConstrSign variables_in T) . (a_Term MaxConstrSign) is finite set
c₁₃ is set
(l) . c₁₃ is set
z is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
l . z is set
l /. z is non empty pair Element of Vars
(l) . z is set
(l /. z) -term MaxConstrSign is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MaxConstrSign , a_Term MaxConstrSign
[(l /. z),a_Term] is non empty pair set
{(l /. z),a_Term} is non empty finite set
{(l /. z)} is non empty trivial Relation-like finite 1 -element set
{{(l /. z),a_Term},{(l /. z)}} is non empty finite V32() set
root-tree [(l /. z),a_Term] is non empty Relation-like Function-like DecoratedTree-like set
{(l /. z)} is non empty trivial Relation-like finite 1 -element Element of bool Vars
q is set
B is set
l . B is set
T is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
l /. T is non empty pair Element of Vars
(l /. T) -term MaxConstrSign is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching non compound expression of MaxConstrSign , a_Term MaxConstrSign
[(l /. T),a_Term] is non empty pair set
{(l /. T),a_Term} is non empty finite set
{(l /. T)} is non empty trivial Relation-like finite 1 -element set
{{(l /. T),a_Term},{(l /. T)}} is non empty finite V32() set
root-tree [(l /. T),a_Term] is non empty Relation-like Function-like DecoratedTree-like set
(l) . T is set
l . T is set
variables_in ((l /. T) -term MaxConstrSign) is finite Element of bool Vars
MaxConstrSign variables_in ((l /. T) -term MaxConstrSign) is non empty Relation-like the carrier of MaxConstrSign -defined Function-like total with_missing_variables set
(MaxConstrSign variables_in ((l /. T) -term MaxConstrSign)) . (a_Term MaxConstrSign) is finite set
{q} is non empty trivial finite 1 -element set
l is finite Element of bool Vars
varcl l is set
d is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
rng d is finite Element of bool Vars
len d is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
T is Element of the carrier of MaxConstrSign
p is constructor OperSymbol of T
the_arity_of p is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,p) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
len (the_arity_of p) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
(d) is Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of QuasiTerms MaxConstrSign
len (d) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
p -trm (d) is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
vars (p -trm (d)) is finite Element of bool Vars
variables_in (p -trm (d)) is finite Element of bool Vars
MaxConstrSign variables_in (p -trm (d)) is non empty Relation-like the carrier of MaxConstrSign -defined Function-like total with_missing_variables set
(MaxConstrSign variables_in (p -trm (d))) . (a_Term MaxConstrSign) is finite set
varcl (variables_in (p -trm (d))) is set
[:Vars,():] is non empty Relation-like set
bool [:Vars,():] is non empty set
l is Relation-like NAT -defined Vars -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Element of QuasiLoci
rng l is finite Element of bool Vars
f is set
x is non empty pair Element of Vars
vars x is finite Element of bool Vars
varcl (vars x) is set
p is Relation-like NAT -defined Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -valued Function-like finite FinSequence-like FinSubsequence-like DTree-yielding FinSequence of QuasiTerms MaxConstrSign
len p is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
T is constructor OperSymbol of a_Type MaxConstrSign
the_arity_of T is Relation-like NAT -defined the carrier of MaxConstrSign -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
K122( the carrier' of MaxConstrSign,( the carrier of MaxConstrSign *), the Arity of MaxConstrSign,T) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of MaxConstrSign *
len (the_arity_of T) is non pair epsilon-transitive epsilon-connected ordinal natural finite cardinal V105() V106() ext-real non negative Element of NAT
T -trm p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching compound Element of Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))
vars (T -trm p) is finite Element of bool Vars
variables_in (T -trm p) is finite Element of bool Vars
MaxConstrSign variables_in (T -trm p) is non empty Relation-like the carrier of MaxConstrSign -defined Function-like total with_missing_variables set
(MaxConstrSign variables_in (T -trm p)) . (a_Term MaxConstrSign) is finite set
varcl (variables_in (T -trm p)) is set
the ResultSort of MaxConstrSign is Relation-like the carrier' of MaxConstrSign -defined the carrier of MaxConstrSign -valued Function-like V25( the carrier' of MaxConstrSign, the carrier of MaxConstrSign) Element of bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:]
[: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:] is non empty Relation-like set
bool [: the carrier' of MaxConstrSign, the carrier of MaxConstrSign:] is non empty set
rng the ResultSort of MaxConstrSign is Element of bool the carrier of MaxConstrSign
bool the carrier of MaxConstrSign is non empty set
dom the ResultSort of MaxConstrSign is Element of bool the carrier' of MaxConstrSign
bool the carrier' of MaxConstrSign is non empty set
o is set
the ResultSort of MaxConstrSign . o is set
o is Element of the carrier' of MaxConstrSign
the_result_sort_of o is Element of the carrier of MaxConstrSign
K122( the carrier' of MaxConstrSign, the carrier of MaxConstrSign, the ResultSort of MaxConstrSign,o) is Element of the carrier of MaxConstrSign
the_result_sort_of T is Element of the carrier of MaxConstrSign
K122( the carrier' of MaxConstrSign, the carrier of MaxConstrSign, the ResultSort of MaxConstrSign,T) is Element of the carrier of MaxConstrSign
q is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
({} (QuasiAdjs MaxConstrSign)) ast q is non empty pair quasi-type of MaxConstrSign
{({} (QuasiAdjs MaxConstrSign)),q} is non empty functional finite V32() non with_pair set
{{({} (QuasiAdjs MaxConstrSign)),q},{({} (QuasiAdjs MaxConstrSign))}} is non empty finite V32() set
T is non empty pair quasi-type of MaxConstrSign
vars T is finite Element of bool Vars
variables_in T is finite Element of bool Vars
(MSVars MaxConstrSign) . (a_Term MaxConstrSign) is set
K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) is non empty Element of bool (bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))
bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign)) is non empty set
bool (bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) is non empty set
((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in is Relation-like Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -defined K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) -valued Function-like V25( Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))) Element of bool [:(Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))):]
[:(Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))):] is non empty set
adjs T is functional finite constituted-DTrees Element of bool (QuasiAdjs MaxConstrSign)
(((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs T) is finite Element of bool K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))
bool K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) is non empty set
K565(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)),((((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs T))) is Element of bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign))
the_base_of T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
variables_in (the_base_of T) is finite Element of bool Vars
MaxConstrSign variables_in (the_base_of T) is non empty Relation-like the carrier of MaxConstrSign -defined Function-like total with_missing_variables set
(MaxConstrSign variables_in (the_base_of T)) . (a_Term MaxConstrSign) is finite set
K565(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)),((((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs T))) \/ (variables_in (the_base_of T)) is set
varcl (variables_in T) is set
d is Relation-like Function-like set
proj1 d is set
proj2 d is set
f is set
x is set
d . x is set
T is non empty pair Element of Vars
p is non empty pair quasi-type of MaxConstrSign
vars p is finite Element of bool Vars
variables_in p is finite Element of bool Vars
(MSVars MaxConstrSign) . (a_Term MaxConstrSign) is set
K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) is non empty Element of bool (bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))
bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign)) is non empty set
bool (bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) is non empty set
((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in is Relation-like Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -defined K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) -valued Function-like V25( Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))) Element of bool [:(Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))):]
[:(Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))):] is non empty set
adjs p is functional finite constituted-DTrees Element of bool (QuasiAdjs MaxConstrSign)
(((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs p) is finite Element of bool K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))
bool K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) is non empty set
K565(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)),((((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs p))) is Element of bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign))
the_base_of p is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
variables_in (the_base_of p) is finite Element of bool Vars
MaxConstrSign variables_in (the_base_of p) is non empty Relation-like the carrier of MaxConstrSign -defined Function-like total with_missing_variables set
(MaxConstrSign variables_in (the_base_of p)) . (a_Term MaxConstrSign) is finite set
K565(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)),((((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs p))) \/ (variables_in (the_base_of p)) is set
varcl (variables_in p) is set
vars T is finite Element of bool Vars
f is Relation-like Vars -defined () -valued Function-like Element of bool [:Vars,():]
dom f is Element of bool Vars
x is non empty pair Element of Vars
f . x is set
vars x is finite Element of bool Vars
T is non empty pair quasi-type of MaxConstrSign
vars T is finite Element of bool Vars
variables_in T is finite Element of bool Vars
(MSVars MaxConstrSign) . (a_Term MaxConstrSign) is set
K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) is non empty Element of bool (bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))
bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign)) is non empty set
bool (bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) is non empty set
((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in is Relation-like Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -defined K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) -valued Function-like V25( Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))) Element of bool [:(Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))):]
[:(Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))):] is non empty set
adjs T is functional finite constituted-DTrees Element of bool (QuasiAdjs MaxConstrSign)
(((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs T) is finite Element of bool K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))
bool K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) is non empty set
K565(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)),((((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs T))) is Element of bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign))
the_base_of T is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
variables_in (the_base_of T) is finite Element of bool Vars
MaxConstrSign variables_in (the_base_of T) is non empty Relation-like the carrier of MaxConstrSign -defined Function-like total with_missing_variables set
(MaxConstrSign variables_in (the_base_of T)) . (a_Term MaxConstrSign) is finite set
K565(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)),((((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs T))) \/ (variables_in (the_base_of T)) is set
varcl (variables_in T) is set
p is non empty pair Element of Vars
o is non empty pair quasi-type of MaxConstrSign
vars o is finite Element of bool Vars
variables_in o is finite Element of bool Vars
adjs o is functional finite constituted-DTrees Element of bool (QuasiAdjs MaxConstrSign)
(((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs o) is finite Element of bool K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))
K565(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)),((((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs o))) is Element of bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign))
the_base_of o is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
variables_in (the_base_of o) is finite Element of bool Vars
MaxConstrSign variables_in (the_base_of o) is non empty Relation-like the carrier of MaxConstrSign -defined Function-like total with_missing_variables set
(MaxConstrSign variables_in (the_base_of o)) . (a_Term MaxConstrSign) is finite set
K565(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)),((((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs o))) \/ (variables_in (the_base_of o)) is set
varcl (variables_in o) is set
vars p is finite Element of bool Vars
l is empty trivial Relation-like non-empty empty-yielding NAT -defined Vars -valued non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair ext-real non negative Element of QuasiLoci
d is Relation-like Vars -defined () -valued Function-like Element of bool [:Vars,():]
dom d is Element of bool Vars
f is non empty pair Element of Vars
x is non empty pair quasi-type of MaxConstrSign
d . f is set
vars x is finite Element of bool Vars
variables_in x is finite Element of bool Vars
(MSVars MaxConstrSign) . (a_Term MaxConstrSign) is set
K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) is non empty Element of bool (bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))
bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign)) is non empty set
bool (bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) is non empty set
((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in is Relation-like Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))) -defined K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) -valued Function-like V25( Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))) Element of bool [:(Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))):]
[:(Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))):] is non empty Relation-like set
bool [:(Union the Sorts of (Free (MaxConstrSign,(MSVars MaxConstrSign)))),K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))):] is non empty set
adjs x is functional finite constituted-DTrees Element of bool (QuasiAdjs MaxConstrSign)
(((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs x) is finite Element of bool K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)))
bool K569(((MSVars MaxConstrSign) . (a_Term MaxConstrSign))) is non empty set
K565(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)),((((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs x))) is Element of bool ((MSVars MaxConstrSign) . (a_Term MaxConstrSign))
the_base_of x is non empty Relation-like non pair Function-like finite DecoratedTree-like finite-branching pure expression of MaxConstrSign , a_Type MaxConstrSign
variables_in (the_base_of x) is finite Element of bool Vars
MaxConstrSign variables_in (the_base_of x) is non empty Relation-like the carrier of MaxConstrSign -defined Function-like total with_missing_variables set
(MaxConstrSign variables_in (the_base_of x)) . (a_Term MaxConstrSign) is finite set
K565(((MSVars MaxConstrSign) . (a_Term MaxConstrSign)),((((MSVars MaxConstrSign),(a_Term MaxConstrSign)) variables_in) .: (adjs x))) \/ (variables_in (the_base_of x)) is set
varcl (variables_in x) is set
vars f is finite Element of bool Vars
rng l is empty trivial proper Relation-like non-empty empty-yielding NAT -defined non pair Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V32() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V105() V106() non with_pair V209() ext-real non negative Element of bool Vars