:: FOMODEL2 semantic presentation

REAL is non empty non trivial non finite V167() set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V167() Element of bool REAL
bool REAL is non empty non trivial non finite V167() set
omega is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V167() set
bool omega is non empty non trivial non finite V167() set
K135() is set
bool NAT is non empty non trivial non finite V167() set
COMPLEX is non empty non trivial non finite V167() set
RAT is non empty non trivial non finite V167() set
INT is non empty non trivial non finite V167() set
{} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
{{}} is non empty trivial functional finite V25() 1 -element V167() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
{} * is non empty functional V25() FinSequence-membered FinSequenceSet of {}
the empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
[:{{}},NAT:] is non empty non trivial Relation-like non finite V167() set
[{},{}] is non empty V34() set
{[{},{}]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
[:{{}},NAT:] \ {[{},{}]} is non empty non trivial Relation-like {{}} -defined NAT -valued non finite V167() Element of bool [:{{}},NAT:]
bool [:{{}},NAT:] is non empty non trivial non finite V167() set
[:{{}},NAT:] typed\ {[{},{}]} is Relation-like {{}} -defined NAT -valued Element of bool [:{{}},NAT:]
NAT \/ ([:{{}},NAT:] \ {[{},{}]}) is non empty non trivial non finite V167() set
[:REAL,REAL:] is non empty non trivial Relation-like non finite V167() set
bool [:REAL,REAL:] is non empty non trivial non finite V167() set
K293() is V47() V75() L8()
the U1 of K293() is set
<REAL,+> is V47() L8()
K299() is V47() V75() SubStr of <REAL,+>
<NAT,+> is V47() V75() V97() uniquely-decomposable SubStr of K299()
<REAL,*> is V47() V75() V97() V99() V101() L8()
<NAT,*> is V47() V75() V97() uniquely-decomposable SubStr of <REAL,*>
2 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
{{},1} is non empty finite V25() set
[:1,1:] is non empty Relation-like finite set
bool [:1,1:] is non empty finite V25() set
[:[:1,1:],1:] is non empty Relation-like finite set
bool [:[:1,1:],1:] is non empty finite V25() set
BOOLEAN is non empty set
0 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
{0,1} is non empty finite V25() set
[:COMPLEX,COMPLEX:] is non empty non trivial Relation-like non finite V167() set
bool [:COMPLEX,COMPLEX:] is non empty non trivial non finite V167() set
3 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
Seg 1 is non empty trivial finite 1 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : ( 1 <= b₁ & b₁ <= 1 ) } is set
{1} is non empty trivial finite V25() 1 -element V166() V167() Element of bool NAT
- 2 is non empty complex ext-real non positive negative V40() V41() set
X is V51() V53() eligible Language-like
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite V167() set
X is non empty set
X * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of X
[:(X *),(X *):] is non empty non trivial Relation-like non finite V167() set
X -concatenation is non empty Relation-like [:(X *),(X *):] -defined X * -valued Function-like total quasi_total Function-yielding V164() V198() V201(X * ) Element of bool [:[:(X *),(X *):],(X *):]
[:[:(X *),(X *):],(X *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X *),(X *):],(X *):] is non empty non trivial non finite V167() set
1 -tuples_on X is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of X
id (1 -tuples_on X) is non empty Relation-like non empty-yielding 1 -tuples_on X -defined 1 -tuples_on X -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on X),(1 -tuples_on X):]
[:(1 -tuples_on X),(1 -tuples_on X):] is non empty Relation-like set
bool [:(1 -tuples_on X),(1 -tuples_on X):] is non empty set
(X -concatenation) .: (id (1 -tuples_on X)) is functional V25() FinSequence-membered Element of bool (X *)
bool (X *) is non empty non trivial non finite V167() set
2 -tuples_on X is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of X
chi (((X -concatenation) .: (id (1 -tuples_on X))),(2 -tuples_on X)) is non empty Relation-like 2 -tuples_on X -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on X),BOOLEAN:]
[:(2 -tuples_on X),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on X),BOOLEAN:] is non empty set
X is set
id X is Relation-like X -defined X -valued Function-like one-to-one total V155() V157() V158() V162() set
[:X,X:] is Relation-like set
bool [:X,X:] is non empty set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
phi is ofAtomicFormula Element of AllSymbolsOf X
ar phi is complex ext-real V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . phi is set
abs (ar phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
S is non empty set
(abs (ar phi)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
[:((abs (ar phi)) -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:((abs (ar phi)) -tuples_on S),BOOLEAN:] is non empty set
[:((abs (ar phi)) -tuples_on S),S:] is non empty Relation-like set
bool [:((abs (ar phi)) -tuples_on S),S:] is non empty set
the non empty Relation-like (abs (ar phi)) -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:((abs (ar phi)) -tuples_on S),BOOLEAN:] is non empty Relation-like (abs (ar phi)) -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:((abs (ar phi)) -tuples_on S),BOOLEAN:]
the non empty Relation-like (abs (ar phi)) -tuples_on S -defined S -valued Function-like total quasi_total Element of bool [:((abs (ar phi)) -tuples_on S),S:] is non empty Relation-like (abs (ar phi)) -tuples_on S -defined S -valued Function-like total quasi_total Element of bool [:((abs (ar phi)) -tuples_on S),S:]
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
S is non empty set
phi is ofAtomicFormula Element of AllSymbolsOf X
ar phi is complex ext-real V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . phi is set
abs (ar phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar phi)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
S \/ BOOLEAN is non empty set
[:((abs (ar phi)) -tuples_on S),(S \/ BOOLEAN):] is non empty Relation-like set
bool [:((abs (ar phi)) -tuples_on S),(S \/ BOOLEAN):] is non empty set
I is (X,S,phi)
((abs (ar phi)) -tuples_on S) \/ {} is non empty functional V25() set
bool ((abs (ar phi)) -tuples_on S) is non empty set
bool (S \/ BOOLEAN) is non empty set
phi is functional V25() FinSequence-membered Element of bool ((abs (ar phi)) -tuples_on S)
A is Element of bool (S \/ BOOLEAN)
[:phi,A:] is Relation-like set
bool [:phi,A:] is non empty set
[:phi,A:] is Relation-like (abs (ar phi)) -tuples_on S -defined S \/ BOOLEAN -valued Element of bool [:((abs (ar phi)) -tuples_on S),(S \/ BOOLEAN):]
A2 is Relation-like phi -defined A -valued Function-like quasi_total Element of bool [:phi,A:]
h is Relation-like (abs (ar phi)) -tuples_on S -defined S \/ BOOLEAN -valued Element of bool [:((abs (ar phi)) -tuples_on S),(S \/ BOOLEAN):]
phi is functional V25() FinSequence-membered Element of bool ((abs (ar phi)) -tuples_on S)
A1 is Element of bool (S \/ BOOLEAN)
[:phi,A1:] is Relation-like set
bool [:phi,A1:] is non empty set
[:phi,A1:] is Relation-like (abs (ar phi)) -tuples_on S -defined S \/ BOOLEAN -valued Element of bool [:((abs (ar phi)) -tuples_on S),(S \/ BOOLEAN):]
A2 is Relation-like phi -defined A1 -valued Function-like quasi_total Element of bool [:phi,A1:]
h is Relation-like (abs (ar phi)) -tuples_on S -defined S \/ BOOLEAN -valued Element of bool [:((abs (ar phi)) -tuples_on S),(S \/ BOOLEAN):]
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
phi is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
ar phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . phi is set
abs (ar phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
S is non empty set
(abs (ar phi)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
S \/ BOOLEAN is non empty set
I is non empty Relation-like (abs (ar phi)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,phi)
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
S is Element of AllSymbolsOf X
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
S is non empty set
S \/ BOOLEAN is non empty set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
I is set
N is own ofAtomicFormula Element of AllSymbolsOf X
ar N is complex ext-real V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . N is set
abs (ar N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar N)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
the non empty Relation-like (abs (ar N)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,N) is non empty Relation-like (abs (ar N)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,N)
v1 is non empty Relation-like (abs (ar N)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,N)
I is Relation-like Function-like set
proj1 I is set
N is own ofAtomicFormula Element of AllSymbolsOf X
I . N is set
ar N is complex ext-real V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . N is set
abs (ar N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar N)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
v1 is own ofAtomicFormula Element of AllSymbolsOf X
ar v1 is complex ext-real V40() V41() Element of INT
the adicity of X . v1 is set
abs (ar v1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar v1)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
X is V51() V53() eligible Language-like
S is non empty set
phi is Relation-like Function-like set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
phi is own ofAtomicFormula Element of AllSymbolsOf X
ar phi is complex ext-real V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . phi is set
abs (ar phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
S is non empty set
(abs (ar phi)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
S \/ BOOLEAN is non empty set
I is non empty Relation-like (abs (ar phi)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,phi)
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
v1 is Relation-like Function-like (X,S)
proj1 v1 is set
psi is set
phi is own ofAtomicFormula Element of AllSymbolsOf X
v1 . phi is set
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
phi is Relation-like Function-like set
proj1 phi is set
X is V51() V53() eligible Language-like
S is non empty set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
AllSymbolsOf X is non empty non trivial non finite V167() set
the Relation-like Function-like (X,S) is Relation-like Function-like (X,S)
the Relation-like Function-like (X,S) | (OwnSymbolsOf X) is Relation-like OwnSymbolsOf X -defined Function-like set
v1 is Relation-like Function-like set
proj1 v1 is set
proj1 the Relation-like Function-like (X,S) is set
(OwnSymbolsOf X) /\ (proj1 the Relation-like Function-like (X,S)) is Element of bool (AllSymbolsOf X)
(OwnSymbolsOf X) typed/\ (proj1 the Relation-like Function-like (X,S)) is Element of bool (OwnSymbolsOf X)
bool (OwnSymbolsOf X) is non empty set
(OwnSymbolsOf X) /\ (proj1 the Relation-like Function-like (X,S)) is set
(OwnSymbolsOf X) /\typed (proj1 the Relation-like Function-like (X,S)) is Element of bool (proj1 the Relation-like Function-like (X,S))
bool (proj1 the Relation-like Function-like (X,S)) is non empty set
S \/ BOOLEAN is non empty set
psi is own ofAtomicFormula Element of AllSymbolsOf X
v1 . psi is set
ar psi is complex ext-real V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . psi is set
abs (ar psi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar psi)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
the Relation-like Function-like (X,S) . psi is set
phi is set
psi is Relation-like Function-like (X,S)
A is own ofAtomicFormula Element of AllSymbolsOf X
psi . A is set
psi . phi is set
X is V51() V53() eligible Language-like
S is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
phi is Relation-like Function-like Function-yielding V164() (X,S) set
I is own ofAtomicFormula Element of AllSymbolsOf X
phi . I is Relation-like Function-like set
ar I is complex ext-real V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . I is set
abs (ar I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar I)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
S \/ BOOLEAN is non empty set
N is Relation-like Function-like (X,S)
N . I is set
X is V51() V53() eligible Language-like
S is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
I is own ofAtomicFormula Element of AllSymbolsOf X
ar I is complex ext-real V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . I is set
abs (ar I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar I)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
S \/ BOOLEAN is non empty set
phi is Relation-like Function-like Function-yielding V164() (X,S) set
N is non empty Relation-like (abs (ar I)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,I)
I .--> N is trivial Relation-like AllSymbolsOf X -defined {I} -defined bool [:((abs (ar I)) -tuples_on S),(S \/ BOOLEAN):] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{I} is non empty trivial finite 1 -element set
[:((abs (ar I)) -tuples_on S),(S \/ BOOLEAN):] is non empty Relation-like set
bool [:((abs (ar I)) -tuples_on S),(S \/ BOOLEAN):] is non empty set
{I} --> N is non empty Relation-like non-empty non empty-yielding {I} -defined {N} -valued bool [:((abs (ar I)) -tuples_on S),(S \/ BOOLEAN):] -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{I},{N}:]
{N} is non empty trivial functional finite 1 -element V166() V167() set
[:{I},{N}:] is non empty Relation-like finite set
bool [:{I},{N}:] is non empty finite V25() set
phi +* (I .--> N) is Relation-like Function-like Function-yielding V164() set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
proj1 phi is set
dom (I .--> N) is trivial finite Element of bool {I}
bool {I} is non empty finite V25() set
(proj1 phi) \/ (dom (I .--> N)) is set
A1 is own ofAtomicFormula Element of AllSymbolsOf X
(phi +* (I .--> N)) . A1 is Relation-like Function-like set
(I .--> N) . A1 is Relation-like Function-like set
ar A1 is complex ext-real V40() V41() Element of INT
the adicity of X . A1 is set
abs (ar A1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar A1)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
(phi +* (I .--> N)) . A1 is Relation-like Function-like set
A is Relation-like Function-like (X,S)
A . A1 is set
ar A1 is complex ext-real V40() V41() Element of INT
the adicity of X . A1 is set
abs (ar A1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar A1)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
X is Relation-like Function-like set
S is set
phi is set
{} .--> phi is trivial Relation-like {{}} -defined Function-like one-to-one constant finite V199() set
{{}} --> phi is non empty Relation-like {{}} -defined {phi} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{phi}:]
{phi} is non empty trivial finite 1 -element set
[:{{}},{phi}:] is non empty Relation-like finite set
bool [:{{}},{phi}:] is non empty finite V25() set
S .--> ({} .--> phi) is trivial Relation-like {S} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{S} is non empty trivial finite 1 -element set
{S} --> ({} .--> phi) is non empty Relation-like {S} -defined {({} .--> phi)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{S},{({} .--> phi)}:]
{({} .--> phi)} is non empty trivial functional finite V25() 1 -element set
[:{S},{({} .--> phi)}:] is non empty Relation-like finite set
bool [:{S},{({} .--> phi)}:] is non empty finite V25() set
X +* (S .--> ({} .--> phi)) is Relation-like Function-like set
X is V51() V53() eligible Language-like
S is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
phi is Relation-like Function-like Function-yielding V164() (X,S) set
I is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
N is Element of S
(phi,I,N) is Relation-like Function-like set
{} .--> N is trivial Relation-like {{}} -defined S -valued Function-like one-to-one constant finite V199() set
{{}} --> N is non empty Relation-like {{}} -defined S -valued {N} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{N}:]
{N} is non empty trivial finite 1 -element set
[:{{}},{N}:] is non empty Relation-like finite set
bool [:{{}},{N}:] is non empty finite V25() set
I .--> ({} .--> N) is trivial Relation-like AllSymbolsOf X -defined {I} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{I} is non empty trivial finite 1 -element set
{I} --> ({} .--> N) is non empty Relation-like {I} -defined {({} .--> N)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{I},{({} .--> N)}:]
{({} .--> N)} is non empty trivial functional finite V25() 1 -element set
[:{I},{({} .--> N)}:] is non empty Relation-like finite set
bool [:{I},{({} .--> N)}:] is non empty finite V25() set
phi +* (I .--> ({} .--> N)) is Relation-like Function-like Function-yielding V164() set
ar I is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . I is set
abs (ar I) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
0 -tuples_on S is non empty functional V25() FinSequence-membered V167() FinSequenceSet of S
(abs (ar I)) -tuples_on S is non empty functional V25() FinSequence-membered V167() FinSequenceSet of S
[:((abs (ar I)) -tuples_on S),S:] is non empty Relation-like set
bool [:((abs (ar I)) -tuples_on S),S:] is non empty set
{{}} --> N is non empty Relation-like {{}} -defined S -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},S:]
[:{{}},S:] is non empty Relation-like set
bool [:{{}},S:] is non empty set
S \/ BOOLEAN is non empty set
phi is non empty Relation-like (abs (ar I)) -tuples_on S -defined S -valued Function-like total quasi_total Element of bool [:((abs (ar I)) -tuples_on S),S:]
A is non empty Relation-like (abs (ar I)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,I)
I .--> A is trivial Relation-like AllSymbolsOf X -defined {I} -defined bool [:((abs (ar I)) -tuples_on S),(S \/ BOOLEAN):] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
[:((abs (ar I)) -tuples_on S),(S \/ BOOLEAN):] is non empty Relation-like set
bool [:((abs (ar I)) -tuples_on S),(S \/ BOOLEAN):] is non empty set
{I} --> A is non empty Relation-like non-empty non empty-yielding {I} -defined {A} -valued bool [:((abs (ar I)) -tuples_on S),(S \/ BOOLEAN):] -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{I},{A}:]
{A} is non empty trivial functional finite 1 -element V166() V167() set
[:{I},{A}:] is non empty Relation-like finite set
bool [:{I},{A}:] is non empty finite V25() set
phi +* (I .--> A) is Relation-like Function-like Function-yielding V164() (X,S) set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
S is non empty set
X is set
phi is non empty set
Funcs (X,phi) is non empty functional FUNCTION_DOMAIN of X,phi
[:S,(Funcs (X,phi)):] is non empty Relation-like set
bool [:S,(Funcs (X,phi)):] is non empty set
I is non empty Relation-like S -defined Funcs (X,phi) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:S,(Funcs (X,phi)):]
X is non empty set
S is non empty set
phi is non empty set
Funcs (S,phi) is non empty functional FUNCTION_DOMAIN of S,phi
[:X,(Funcs (S,phi)):] is non empty Relation-like set
bool [:X,(Funcs (S,phi)):] is non empty set
the non empty Relation-like X -defined Funcs (S,phi) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:X,(Funcs (S,phi)):] is non empty Relation-like X -defined Funcs (S,phi) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:X,(Funcs (S,phi)):]
X is Relation-like Function-like Function-yielding V164() set
proj1 X is set
S is Relation-like Function-like set
phi is Relation-like Function-like set
proj1 phi is set
I is set
phi . I is set
X . I is Relation-like Function-like set
S (*) (X . I) is Relation-like Function-like set
phi is Relation-like Function-like set
proj1 phi is set
I is Relation-like Function-like set
proj1 I is set
N is set
phi . N is set
X . N is Relation-like Function-like set
S (*) (X . N) is Relation-like Function-like set
I . N is set
X is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
S is Relation-like Function-like set
(X,S) is Relation-like Function-like set
proj1 (X,S) is set
dom X is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool NAT
X is Relation-like Function-like Function-yielding V164() set
proj1 X is set
S is Relation-like Function-like set
proj1 S is set
(proj1 X) /\ (proj1 S) is set
(proj1 X) typed/\ (proj1 S) is Element of bool (proj1 X)
bool (proj1 X) is non empty set
(proj1 X) /\typed (proj1 S) is Element of bool (proj1 S)
bool (proj1 S) is non empty set
I is Relation-like Function-like set
proj1 I is set
N is set
I . N is set
X . N is Relation-like Function-like set
S . N is set
(X . N) . (S . N) is set
I is Relation-like Function-like set
proj1 I is set
N is Relation-like Function-like set
proj1 N is set
v1 is set
I . v1 is set
X . v1 is Relation-like Function-like set
S . v1 is set
(X . v1) . (S . v1) is set
N . v1 is set
X is Relation-like Function-like Function-yielding V164() set
S is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(X,S) is Relation-like Function-like set
proj1 (X,S) is set
proj1 X is set
dom S is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool NAT
(proj1 X) /\ (dom S) is Relation-like finite Element of bool NAT
(proj1 X) typed/\ (dom S) is Element of bool (proj1 X)
bool (proj1 X) is non empty set
(proj1 X) /\ (dom S) is Relation-like finite set
(proj1 X) /\typed (dom S) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural non proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool (dom S)
bool (dom S) is non empty finite V25() set
X is functional V25() FinSequence-membered set
S is Relation-like Function-like set
S is non empty set
X is non empty set
[:S,X:] is non empty Relation-like set
bool [:S,X:] is non empty set
phi is Relation-like NAT -defined S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
I is non empty Relation-like S -defined X -valued Function-like total quasi_total Element of bool [:S,X:]
I (*) phi is Relation-like NAT -defined X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
len phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
N is Relation-like NAT -defined S -valued Function-like finite FinSequence-like FinSubsequence-like V199() FinSequence of S
I * N is Relation-like NAT -defined X -valued Function-like finite FinSequence-like FinSubsequence-like V199() FinSequence of X
len (I * N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
len N is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
v1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
X is non empty set
S is non empty set
[:X,S:] is non empty Relation-like set
bool [:X,S:] is non empty set
I is Relation-like NAT -defined X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
phi is non empty Relation-like X -defined S -valued Function-like total quasi_total Element of bool [:X,S:]
phi (*) I is Relation-like NAT -defined S -valued Function-like finite len I -element FinSequence-like FinSubsequence-like V199() set
len I is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
S is non empty set
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is non empty set
[:S,X:] is non empty Relation-like set
bool [:S,X:] is non empty set
I is Relation-like NAT -defined S -valued Function-like finite phi -element FinSequence-like FinSubsequence-like V199() set
N is non empty Relation-like S -defined X -valued Function-like total quasi_total Element of bool [:S,X:]
N (*) I is Relation-like NAT -defined X -valued Function-like finite phi -element len I -element FinSequence-like FinSubsequence-like V199() set
len I is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
v1 is Relation-like NAT -defined X -valued Function-like finite FinSequence-like FinSubsequence-like V199() FinSequence of X
S is V51() V53() eligible Language-like
X is non empty set
TermSymbolsOf S is non empty set
the U1 of S is set
the U3 of S is Element of the U1 of S
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
I is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of ((AllSymbolsOf S) *) \ {{}}
ar I is complex ext-real V40() V41() Element of INT
S -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
[:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V167() set
(AllSymbolsOf S) -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(AllSymbolsOf S) -pr1 is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total V201( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf S),(AllSymbolsOf S)) is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
MultPlace ((AllSymbolsOf S) -pr1) is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(S -firstChar) . I is non relational termal own ofAtomicFormula Element of AllSymbolsOf S
ar ((S -firstChar) . I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of S . ((S -firstChar) . I) is set
abs (ar I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar I)) -tuples_on X is non empty functional V25() FinSequence-membered FinSequenceSet of X
abs (ar ((S -firstChar) . I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar ((S -firstChar) . I))) -tuples_on X is non empty functional V25() FinSequence-membered FinSequenceSet of X
phi is Relation-like Function-like Function-yielding V164() (S,X) set
(S,X,phi,((S -firstChar) . I)) is non empty Relation-like (abs (ar ((S -firstChar) . I))) -tuples_on X -defined X \/ BOOLEAN -valued Function-like total quasi_total (S,X,(S -firstChar) . I)
X \/ BOOLEAN is non empty set
dom (S,X,phi,((S -firstChar) . I)) is non empty functional V25() FinSequence-membered Element of bool ((abs (ar ((S -firstChar) . I))) -tuples_on X)
bool ((abs (ar ((S -firstChar) . I))) -tuples_on X) is non empty set
X is V51() V53() eligible Language-like
TermSymbolsOf X is non empty set
the U1 of X is set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
S is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
<*((X -firstChar) . S)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,((X -firstChar) . S)] is non empty V34() set
{[1,((X -firstChar) . S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
{} .--> {} is trivial Relation-like {{}} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite set
bool [:{{}},{{}}:] is non empty finite V25() set
(AllSymbolsOf X) -concatenation is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() V201((AllSymbolsOf X) * ) Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
MultPlace ((AllSymbolsOf X) -concatenation) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf X) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
SubTerms S is empty trivial Relation-like non-empty empty-yielding NAT -defined (proj2 S) * -valued AllTermsOf X -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element abs (ar S) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of (AllTermsOf X) *
proj2 S is non empty trivial finite 1 -element set
(proj2 S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 S
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
ar S is complex ext-real V40() V41() Element of INT
ar ((X -firstChar) . S) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of INT
the adicity of X . ((X -firstChar) . S) is set
abs (ar S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
(X -multiCat) . (SubTerms S) is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of (AllSymbolsOf X) *
phi is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
<*((X -firstChar) . S)*> ^ phi is non empty Relation-like NAT -defined Function-like finite 1 + {} -element FinSequence-like FinSubsequence-like V199() set
1 + {} is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
<*((X -firstChar) . S)*> null phi is Relation-like NAT -defined phi \/ (proj1 <*((X -firstChar) . S)*>) -defined Seg (1 + phi) -defined phi \/ (proj2 <*((X -firstChar) . S)*>) -valued Function-like finite len <*((X -firstChar) . S)*> -element total FinSequence-like FinSubsequence-like V199() set
proj1 <*((X -firstChar) . S)*> is non empty trivial finite 1 -element set
phi \/ (proj1 <*((X -firstChar) . S)*>) is non empty finite set
1 + phi is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
Seg (1 + phi) is non empty finite 1 + phi -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : ( 1 <= b₁ & b₁ <= 1 + phi ) } is set
proj2 <*((X -firstChar) . S)*> is non empty trivial finite 1 -element set
phi \/ (proj2 <*((X -firstChar) . S)*>) is non empty finite set
len <*((X -firstChar) . S)*> is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
<*((X -firstChar) . S)*> \typed/ phi is Relation-like NAT -defined finite Element of bool (<*((X -firstChar) . S)*> \/ phi)
<*((X -firstChar) . S)*> \/ phi is non empty Relation-like NAT -defined finite set
bool (<*((X -firstChar) . S)*> \/ phi) is non empty finite V25() set
phi ^ <*((X -firstChar) . S)*> is non empty Relation-like NAT -defined Function-like finite {} + 1 -element {} + 1 -element FinSequence-like FinSubsequence-like V199() set
{} + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
{} + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
X is V51() V53() eligible Language-like
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
X -subTerms is non empty Relation-like AllTermsOf X -defined (AllTermsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(AllTermsOf X),((AllTermsOf X) *):]
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite V167() set
[:(AllTermsOf X),((AllTermsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(AllTermsOf X),((AllTermsOf X) *):] is non empty non trivial non finite V167() set
S is non empty set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
Funcs ((AllTermsOf X),S) is non empty functional FUNCTION_DOMAIN of AllTermsOf X,S
phi is Relation-like Function-like Function-yielding V164() (X,S) set
phi (*) (X -firstChar) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined Function-like Function-yielding V164() set
dom (phi (*) (X -firstChar)) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
AtomicTermsOf X is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
LettersOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
{0} is non empty trivial functional finite V25() 1 -element V167() Element of bool NAT
0 * is non empty functional V25() FinSequence-membered FinSequenceSet of 0
{0} is non empty trivial functional finite V25() 1 -element V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
1 -tuples_on (LettersOf X) is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of LettersOf X
X -termsOfMaxDepth is non empty Relation-like NAT -defined K365((((AllSymbolsOf X) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):]
[:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial non finite V167() set
dom (X -firstChar) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
A1 is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
((X -subTerms),A1) is Relation-like Function-like set
((phi (*) (X -firstChar)),((X -subTerms),A1)) is Relation-like Function-like set
proj1 ((X -subTerms),A1) is set
dom (X -subTerms) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (AllTermsOf X)
bool (AllTermsOf X) is non empty set
proj1 ((phi (*) (X -firstChar)),((X -subTerms),A1)) is set
t is set
((phi (*) (X -firstChar)),((X -subTerms),A1)) . t is set
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
H is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of ((AllSymbolsOf X) *) \ {{}}
ar H is complex ext-real V40() V41() Element of INT
(X -firstChar) . H is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
ar ((X -firstChar) . H) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of X . ((X -firstChar) . H) is set
abs (ar H) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
m1 is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
s2 is own ofAtomicFormula Element of AllSymbolsOf X
i2 is Element of OwnSymbolsOf X
proj1 phi is set
ar s2 is complex ext-real V40() V41() Element of INT
the adicity of X . s2 is set
abs (ar s2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar s2)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
S \/ BOOLEAN is non empty set
(X,S,phi,s2) is non empty Relation-like (abs (ar s2)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,s2)
m2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of AllTermsOf X
(X -subTerms) . m2 is Relation-like NAT -defined AllTermsOf X -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
SubTerms H is Relation-like NAT -defined (proj2 H) * -valued AllTermsOf X -valued Function-like finite abs (ar H) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
proj2 H is non empty finite set
(proj2 H) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 H
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
q is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar H) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() FinSequence of AllTermsOf X
A1 * q is Relation-like NAT -defined S -valued Function-like finite abs (ar H) -element len q -element FinSequence-like FinSubsequence-like V199() FinSequence of S
len q is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
qq is Relation-like NAT -defined S -valued Function-like finite abs (ar H) -element FinSequence-like FinSubsequence-like V199() FinSequence of S
len qq is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar H)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
phi . i2 is Relation-like Function-like set
proj1 (phi . i2) is set
p is Relation-like NAT -defined S -valued Function-like finite abs (ar H) -element FinSequence-like FinSubsequence-like V199() Element of (abs (ar H)) -tuples_on S
m1 is non empty Relation-like (abs (ar s2)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,s2)
dom m1 is non empty functional V25() FinSequence-membered Element of bool ((abs (ar s2)) -tuples_on S)
bool ((abs (ar s2)) -tuples_on S) is non empty set
((phi (*) (X -firstChar)),((X -subTerms),A1)) . H is set
(phi (*) (X -firstChar)) . H is Relation-like Function-like set
((X -subTerms),A1) . H is set
((phi (*) (X -firstChar)) . H) . (((X -subTerms),A1) . H) is set
(X,S,phi,s2) . (((X -subTerms),A1) . H) is set
m1 . p is set
t is set
(dom (phi (*) (X -firstChar))) /\ (AllTermsOf X) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
(dom (phi (*) (X -firstChar))) typed/\ (AllTermsOf X) is functional V25() FinSequence-membered V166() Element of bool (dom (phi (*) (X -firstChar)))
bool (dom (phi (*) (X -firstChar))) is non empty set
(dom (phi (*) (X -firstChar))) /\ (AllTermsOf X) is set
(dom (phi (*) (X -firstChar))) /\typed (AllTermsOf X) is functional V25() FinSequence-membered V166() Element of bool (AllTermsOf X)
t is set
((phi (*) (X -firstChar)),((X -subTerms),A1)) . t is set
S is non empty set
X is V51() V53() eligible Language-like
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
Funcs ((AllTermsOf X),S) is non empty functional FUNCTION_DOMAIN of AllTermsOf X,S
[:NAT,(Funcs ((AllTermsOf X),S)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(Funcs ((AllTermsOf X),S)):] is non empty non trivial non finite V167() set
phi is Element of S
(AllTermsOf X) --> phi is non empty Relation-like AllTermsOf X -defined S -valued Function-like constant total quasi_total Element of bool [:(AllTermsOf X),S:]
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
{phi} is non empty trivial finite 1 -element set
[:(AllTermsOf X),{phi}:] is non empty Relation-like set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
I is Relation-like Function-like Function-yielding V164() (X,S) set
I (*) (X -firstChar) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined Function-like Function-yielding V164() set
X -subTerms is non empty Relation-like AllTermsOf X -defined (AllTermsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(AllTermsOf X),((AllTermsOf X) *):]
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite V167() set
[:(AllTermsOf X),((AllTermsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(AllTermsOf X),((AllTermsOf X) *):] is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
AtomicTermsOf X is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
LettersOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
{0} is non empty trivial functional finite V25() 1 -element V167() Element of bool NAT
0 * is non empty functional V25() FinSequence-membered FinSequenceSet of 0
{0} is non empty trivial functional finite V25() 1 -element V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
1 -tuples_on (LettersOf X) is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of LettersOf X
X -termsOfMaxDepth is non empty Relation-like NAT -defined K365((((AllSymbolsOf X) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):]
[:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial non finite V167() set
h is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
H is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
T is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X -subTerms),T) is Relation-like Function-like set
((I (*) (X -firstChar)),((X -subTerms),T)) is Relation-like Function-like set
m1 is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
((X -subTerms),m1) is Relation-like Function-like set
((I (*) (X -firstChar)),((X -subTerms),m1)) is Relation-like Function-like set
s2 is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
i2 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
t is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
H is non empty Relation-like NAT -defined Funcs ((AllTermsOf X),S) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf X),S)):]
H . 0 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
T is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
T + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
H . (T + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
H . T is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X -subTerms),(H . T)) is Relation-like Function-like set
((I (*) (X -firstChar)),((X -subTerms),(H . T))) is Relation-like Function-like set
AllSymbolsOf X is non empty non trivial non finite V167() set
AtomicTermsOf X is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
LettersOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
{0} is non empty trivial functional finite V25() 1 -element V167() Element of bool NAT
0 * is non empty functional V25() FinSequence-membered FinSequenceSet of 0
{0} is non empty trivial functional finite V25() 1 -element V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
1 -tuples_on (LettersOf X) is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of LettersOf X
X -termsOfMaxDepth is non empty Relation-like NAT -defined K365((((AllSymbolsOf X) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):]
[:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial non finite V167() set
t is non empty Relation-like NAT -defined Funcs ((AllTermsOf X),S) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf X),S)):]
t . 0 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
H is non empty Relation-like NAT -defined Funcs ((AllTermsOf X),S) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf X),S)):]
H . 0 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
h is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
T is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
t . T is Relation-like Function-like Element of Funcs ((AllTermsOf X),S)
T + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
t . (T + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
s2 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X -subTerms),s2) is Relation-like Function-like set
((I (*) (X -firstChar)),((X -subTerms),s2)) is Relation-like Function-like set
m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
t . m1 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
T is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
H . T is Relation-like Function-like Element of Funcs ((AllTermsOf X),S)
T + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
H . (T + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
s2 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X -subTerms),s2) is Relation-like Function-like set
((I (*) (X -firstChar)),((X -subTerms),s2)) is Relation-like Function-like set
m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
H . m1 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
T is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
m1 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
s2 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
i2 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X -subTerms),m1) is Relation-like Function-like set
((I (*) (X -firstChar)),((X -subTerms),m1)) is Relation-like Function-like set
X is V51() V53() eligible Language-like
TermSymbolsOf X is non empty set
the U1 of X is set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
S is non empty set
Funcs ((AllTermsOf X),S) is non empty functional FUNCTION_DOMAIN of AllTermsOf X,S
phi is Element of S
I is Relation-like Function-like Function-yielding V164() (X,S) set
(X,S,phi,I) is non empty Relation-like NAT -defined Funcs ((AllTermsOf X),S) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf X),S)):]
[:NAT,(Funcs ((AllTermsOf X),S)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(Funcs ((AllTermsOf X),S)):] is non empty non trivial non finite V167() set
N is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . N is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,S,I,((X -firstChar) . N)) is non empty Relation-like (abs (ar ((X -firstChar) . N))) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,(X -firstChar) . N)
ar ((X -firstChar) . N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of X . ((X -firstChar) . N) is set
abs (ar ((X -firstChar) . N)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar ((X -firstChar) . N))) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
S \/ BOOLEAN is non empty set
SubTerms N is Relation-like NAT -defined (proj2 N) * -valued AllTermsOf X -valued Function-like finite abs (ar N) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
proj2 N is non empty finite set
(proj2 N) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 N
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
ar N is complex ext-real V40() V41() Element of INT
abs (ar N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(X,S,I,((X -firstChar) . N)) . {} is set
v1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
v1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,phi,I) . (v1 + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,phi,I) . (v1 + 1)) . N is set
(X,S,phi,I) . v1 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,phi,I) . v1) (*) (SubTerms N) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,I,((X -firstChar) . N)) . (((X,S,phi,I) . v1) (*) (SubTerms N)) is set
X -subTerms is non empty Relation-like AllTermsOf X -defined (AllTermsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(AllTermsOf X),((AllTermsOf X) *):]
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite V167() set
[:(AllTermsOf X),((AllTermsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(AllTermsOf X),((AllTermsOf X) *):] is non empty non trivial non finite V167() set
I (*) (X -firstChar) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined Function-like Function-yielding V164() set
dom (I (*) (X -firstChar)) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
((X -subTerms),((X,S,phi,I) . v1)) is Relation-like Function-like set
((I (*) (X -firstChar)),((X -subTerms),((X,S,phi,I) . v1))) is Relation-like Function-like set
dom (X -subTerms) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (AllTermsOf X)
bool (AllTermsOf X) is non empty set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
proj1 ((I (*) (X -firstChar)),((X -subTerms),((X,S,phi,I) . v1))) is set
((I (*) (X -firstChar)),((X -subTerms),((X,S,phi,I) . v1))) . N is set
(I (*) (X -firstChar)) . N is Relation-like Function-like set
((X -subTerms),((X,S,phi,I) . v1)) . N is set
((I (*) (X -firstChar)) . N) . (((X -subTerms),((X,S,phi,I) . v1)) . N) is set
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of AllTermsOf X
(X -subTerms) . A2 is Relation-like NAT -defined AllTermsOf X -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
((X,S,phi,I) . v1) (*) ((X -subTerms) . A2) is Relation-like NAT -defined S -valued Function-like finite len ((X -subTerms) . A2) -element FinSequence-like FinSubsequence-like V199() set
len ((X -subTerms) . A2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
((I (*) (X -firstChar)) . N) . (((X,S,phi,I) . v1) (*) ((X -subTerms) . A2)) is set
((I (*) (X -firstChar)) . N) . (((X,S,phi,I) . v1) (*) (SubTerms N)) is set
AllSymbolsOf X is non empty non trivial non finite V167() set
t is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . t is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
H is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
ar H is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of INT
the adicity of X . H is set
abs (ar H) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(abs (ar H)) -tuples_on S is non empty functional V25() FinSequence-membered V167() FinSequenceSet of S
(X,S,I,H) is non empty Relation-like (abs (ar H)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,H)
T is non empty Relation-like (abs (ar H)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,H)
T . {} is set
X is V51() V53() eligible Language-like
TermSymbolsOf X is non empty set
the U1 of X is set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
S is non empty set
Funcs ((AllTermsOf X),S) is non empty functional FUNCTION_DOMAIN of AllTermsOf X,S
phi is Relation-like Function-like Function-yielding V164() (X,S) set
I is Element of S
(X,S,I,phi) is non empty Relation-like NAT -defined Funcs ((AllTermsOf X),S) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf X),S)):]
[:NAT,(Funcs ((AllTermsOf X),S)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(Funcs ((AllTermsOf X),S)):] is non empty non trivial non finite V167() set
N is Element of S
(X,S,N,phi) is non empty Relation-like NAT -defined Funcs ((AllTermsOf X),S) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf X),S)):]
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
X -subTerms is non empty Relation-like AllTermsOf X -defined (AllTermsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(AllTermsOf X),((AllTermsOf X) *):]
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite V167() set
[:(AllTermsOf X),((AllTermsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(AllTermsOf X),((AllTermsOf X) *):] is non empty non trivial non finite V167() set
X -termsOfMaxDepth is non empty Relation-like NAT -defined K365((((AllSymbolsOf X) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):]
[:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,I,phi) . (0 + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
t is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
((X,S,I,phi) . (0 + 1)) . t is set
H is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(0 + 1) + H is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,N,phi) . ((0 + 1) + H) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,N,phi) . ((0 + 1) + H)) . t is set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,I,phi) . (0 + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,I,phi) . (0 + 1)) . t is set
(X -firstChar) . t is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,S,phi,((X -firstChar) . t)) is non empty Relation-like (abs (ar ((X -firstChar) . t))) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,(X -firstChar) . t)
ar ((X -firstChar) . t) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of INT
the adicity of X . ((X -firstChar) . t) is set
abs (ar ((X -firstChar) . t)) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(abs (ar ((X -firstChar) . t))) -tuples_on S is non empty functional V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
(X,S,phi,((X -firstChar) . t)) . {} is set
T is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(0 + 1) + T is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,N,phi) . ((0 + 1) + T) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,N,phi) . ((0 + 1) + T)) . t is set
t is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
t + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,I,phi) . (t + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
t + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(t + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,I,phi) . ((t + 1) + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
T is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal t + 1 -termal Element of ((AllSymbolsOf X) *) \ {{}}
((X,S,I,phi) . ((t + 1) + 1)) . T is set
m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
((t + 1) + 1) + m1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,N,phi) . (((t + 1) + 1) + m1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,N,phi) . (((t + 1) + 1) + m1)) . T is set
H is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
H + m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
SubTerms T is Relation-like NAT -defined (X -termsOfMaxDepth) . t -valued (proj2 T) * -valued AllTermsOf X -valued Function-like finite abs (ar T) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
K365(((AllSymbolsOf X) *)) is non empty non trivial non finite V167() Element of bool (bool ((AllSymbolsOf X) *))
bool (bool ((AllSymbolsOf X) *)) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is non empty Relation-like NAT -defined K365(((AllSymbolsOf X) *)) -valued Function-like total quasi_total Element of bool [:NAT,K365(((AllSymbolsOf X) *)):]
[:NAT,K365(((AllSymbolsOf X) *)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365(((AllSymbolsOf X) *)):] is non empty non trivial non finite V167() set
(X -termsOfMaxDepth) . t is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365(((AllSymbolsOf X) *))
proj2 T is non empty finite set
(proj2 T) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 T
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
ar T is complex ext-real V40() V41() Element of INT
(X -firstChar) . T is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
ar ((X -firstChar) . T) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of X . ((X -firstChar) . T) is set
abs (ar T) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(X,S,I,phi) . H is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,I,phi) . H) (*) (SubTerms T) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,N,phi) . (H + m1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,N,phi) . (H + m1)) (*) (SubTerms T) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X -termsOfMaxDepth) . t is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
q is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar T) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() FinSequence of AllTermsOf X
len q is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
qq is Relation-like (X -termsOfMaxDepth) . t -valued Function-like Function-yielding V164() V198() set
proj1 qq is set
Seg (abs (ar T)) is finite abs (ar T) -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : ( 1 <= b₁ & b₁ <= abs (ar T) ) } is set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
s2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S,N,phi) . s2 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
p is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
p * q is Relation-like NAT -defined S -valued Function-like finite abs (ar T) -element len q -element FinSequence-like FinSubsequence-like V199() FinSequence of S
STT is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
STT * q is Relation-like NAT -defined S -valued Function-like finite abs (ar T) -element len q -element FinSequence-like FinSubsequence-like V199() FinSequence of S
qqq is Relation-like NAT -defined S -valued Function-like finite abs (ar T) -element FinSequence-like FinSubsequence-like V199() FinSequence of S
len qqq is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
tq is Relation-like NAT -defined S -valued Function-like finite abs (ar T) -element FinSequence-like FinSubsequence-like V199() FinSequence of S
len tq is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
dom qqq is finite abs (ar T) -element Element of bool NAT
dom tq is finite abs (ar T) -element Element of bool NAT
g1 is set
qqq . g1 is set
tq . g1 is set
qq . g1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
g2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal t -termal Element of ((AllSymbolsOf X) *) \ {{}}
((X,S,I,phi) . H) . g2 is set
STT . (qq . g1) is set
H + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,I,phi) . (H + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
i2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of ((AllSymbolsOf X) *) \ {{}}
((X,S,I,phi) . (H + 1)) . i2 is set
(X -firstChar) . i2 is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,S,phi,((X -firstChar) . i2)) is non empty Relation-like (abs (ar ((X -firstChar) . i2))) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,(X -firstChar) . i2)
ar ((X -firstChar) . i2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of X . ((X -firstChar) . i2) is set
abs (ar ((X -firstChar) . i2)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar ((X -firstChar) . i2))) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
S \/ BOOLEAN is non empty set
s2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S,N,phi) . s2 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,N,phi) . s2) (*) (SubTerms T) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,phi,((X -firstChar) . i2)) . (((X,S,N,phi) . s2) (*) (SubTerms T)) is set
s2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,N,phi) . (s2 + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,N,phi) . (s2 + 1)) . i2 is set
t is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
H is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
H + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,I,phi) . (H + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
T is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal H -termal Element of ((AllSymbolsOf X) *) \ {{}}
((X,S,I,phi) . (H + 1)) . T is set
m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(H + 1) + m1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,N,phi) . ((H + 1) + m1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,N,phi) . ((H + 1) + m1)) . T is set
t + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,I,phi) . (t + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
T is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal t -termal Element of ((AllSymbolsOf X) *) \ {{}}
((X,S,I,phi) . (t + 1)) . T is set
m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(t + 1) + m1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,N,phi) . ((t + 1) + m1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,N,phi) . ((t + 1) + m1)) . T is set
t is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
t + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,I,phi) . (t + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
H is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal t -termal Element of ((AllSymbolsOf X) *) \ {{}}
((X,S,I,phi) . (t + 1)) . H is set
T is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(t + 1) + T is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,N,phi) . ((t + 1) + T) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,N,phi) . ((t + 1) + T)) . H is set
X is V51() V53() eligible Language-like
S is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of AllTermsOf X
X -termsOfMaxDepth is non empty Relation-like NAT -defined K365((((AllSymbolsOf X) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):]
[:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial non finite V167() set
Funcs ((AllTermsOf X),S) is non empty functional FUNCTION_DOMAIN of AllTermsOf X,S
phi is Relation-like Function-like Function-yielding V164() (X,S) set
psi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X -termsOfMaxDepth) . psi is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
the Element of S is Element of S
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
psi + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
(X,S, the Element of S,phi) is non empty Relation-like NAT -defined Funcs ((AllTermsOf X),S) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf X),S)):]
[:NAT,(Funcs ((AllTermsOf X),S)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(Funcs ((AllTermsOf X),S)):] is non empty non trivial non finite V167() set
A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S, the Element of S,phi) . A2 is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
h is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
h . I is Element of S
t is Element of S
H is Element of S
(X,S,H,phi) is non empty Relation-like NAT -defined Funcs ((AllTermsOf X),S) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf X),S)):]
T is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X -termsOfMaxDepth) . T is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
T + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,H,phi) . (T + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S,H,phi) . (T + 1)) . I is Element of S
(psi + 1) + T is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,H,phi) . ((psi + 1) + T) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
A1 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal psi -termal Element of ((AllSymbolsOf X) *) \ {{}}
((X,S,H,phi) . ((psi + 1) + T)) . A1 is set
(T + 1) + psi is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,H,phi) . ((T + 1) + psi) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
m1 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal T -termal Element of ((AllSymbolsOf X) *) \ {{}}
((X,S,H,phi) . ((T + 1) + psi)) . m1 is set
((X,S,H,phi) . (T + 1)) . m1 is set
psi is Element of S
phi is Element of S
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X -termsOfMaxDepth) . A is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
the Element of S is Element of S
(X,S, the Element of S,phi) is non empty Relation-like NAT -defined Funcs ((AllTermsOf X),S) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf X),S)):]
[:NAT,(Funcs ((AllTermsOf X),S)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(Funcs ((AllTermsOf X),S)):] is non empty non trivial non finite V167() set
A + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S, the Element of S,phi) . (A + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S, the Element of S,phi) . (A + 1)) . I is Element of S
X is V51() V53() eligible Language-like
S is non empty set
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
phi is Relation-like Function-like Function-yielding V164() (X,S) set
N is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of AllTermsOf X
N . v1 is Element of S
(X,S,phi,v1) is Element of S
N is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
v1 is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of AllTermsOf X
N . psi is Element of S
(X,S,phi,psi) is Element of S
v1 . psi is Element of S
X is V51() V53() eligible Language-like
S is non empty set
phi is Relation-like Function-like Function-yielding V164() (X,S) set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
the U2 of X is Element of the U1 of X
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
phi +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
X is V51() V53() eligible Language-like
S is non empty set
X is V51() V53() eligible Language-like
S is non empty set
phi is Relation-like Function-like Function-yielding V164() (X,S) set
(X,S,phi) is Relation-like Function-like set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
the U2 of X is Element of the U1 of X
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
phi +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
I is Relation-like Function-like set
I is set
X is V51() V53() eligible Language-like
S is non empty set
phi is Relation-like Function-like Function-yielding V164() (X,S) set
(X,S,phi) is Relation-like Function-like (X,S,phi) set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
the U2 of X is Element of the U1 of X
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
phi +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
I is Relation-like Function-like (X,S,phi) set
X is V51() V53() eligible Language-like
S is non empty set
phi is Relation-like Function-like Function-yielding V164() (X,S) set
(X,S,phi) is Relation-like Function-like (X,S,phi) set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
the U2 of X is Element of the U1 of X
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
phi +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
phi is own ofAtomicFormula Element of AllSymbolsOf X
(AtomicFormulaSymbolsOf X) \ (OwnSymbolsOf X) is Element of bool (AllSymbolsOf X)
(AtomicFormulaSymbolsOf X) typed\ (OwnSymbolsOf X) is Element of bool (AtomicFormulaSymbolsOf X)
bool (AtomicFormulaSymbolsOf X) is non empty set
(AtomicFormulaSymbolsOf X) \ (OwnSymbolsOf X) is Element of bool (AtomicFormulaSymbolsOf X)
{(TheEqSymbOf X)} is non empty trivial finite 1 -element Element of bool (AtomicFormulaSymbolsOf X)
dom ((TheEqSymbOf X) .--> (S)) is trivial finite Element of bool {(TheEqSymbOf X)}
bool {(TheEqSymbOf X)} is non empty finite V25() set
(X,S,phi) . phi is set
(X,S,phi,phi) is non empty Relation-like (abs (ar phi)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,phi)
ar phi is complex ext-real V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . phi is set
abs (ar phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar phi)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
S \/ BOOLEAN is non empty set
X is V51() V53() eligible Language-like
S is non empty set
phi is Relation-like Function-like Function-yielding V164() (X,S) set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
I is Relation-like Function-like (X,S,phi) set
N is ofAtomicFormula Element of AllSymbolsOf X
I . N is set
ar N is complex ext-real V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . N is set
abs (ar N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar N)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
S \/ BOOLEAN is non empty set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
the U2 of X is Element of the U1 of X
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
H is ofAtomicFormula Element of AllSymbolsOf X
ar H is complex ext-real V40() V41() Element of INT
the adicity of X . H is set
abs (ar H) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
- (- 2) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(X,S,phi) is Relation-like Function-like Function-yielding V164() (X,S) (X,S,phi) set
phi +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
T is own ofAtomicFormula Element of AllSymbolsOf X
(X,S,(X,S,phi),T) is non empty Relation-like (abs (ar T)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,T)
ar T is complex ext-real V40() V41() Element of INT
the adicity of X . T is set
abs (ar T) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar T)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
t is Element of AtomicFormulaSymbolsOf X
(AtomicFormulaSymbolsOf X) \ (OwnSymbolsOf X) is Element of bool (AllSymbolsOf X)
(AtomicFormulaSymbolsOf X) typed\ (OwnSymbolsOf X) is Element of bool (AtomicFormulaSymbolsOf X)
bool (AtomicFormulaSymbolsOf X) is non empty set
(AtomicFormulaSymbolsOf X) \ (OwnSymbolsOf X) is Element of bool (AtomicFormulaSymbolsOf X)
{(TheEqSymbOf X)} is non empty trivial finite 1 -element Element of bool (AtomicFormulaSymbolsOf X)
[:((abs (ar N)) -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:((abs (ar N)) -tuples_on S),BOOLEAN:] is non empty set
X is V51() V53() eligible Language-like
S is non empty set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi is Relation-like Function-like Function-yielding V164() (X,S) set
(X,S,phi) is Relation-like Function-like Function-yielding V164() (X,S) (X,S,phi) set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
the U2 of X is Element of the U1 of X
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
phi +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
I is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . I is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(X,S,phi,(X,S,phi),((X -firstChar) . I)) is non empty Relation-like (abs (ar ((X -firstChar) . I))) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,(X -firstChar) . I)
ar ((X -firstChar) . I) is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . ((X -firstChar) . I) is set
abs (ar ((X -firstChar) . I)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((X -firstChar) . I))) -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
SubTerms I is Relation-like NAT -defined (proj2 I) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . I)) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
proj2 I is non empty finite set
(proj2 I) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 I
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(TermSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(X,S,phi) is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
(X,S,phi) (*) (SubTerms I) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,phi,(X,S,phi),((X -firstChar) . I)) . ((X,S,phi) (*) (SubTerms I)) is set
X is V51() V53() eligible Language-like
S is non empty set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi is Relation-like Function-like Function-yielding V164() (X,S) set
I is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff Element of ((AllSymbolsOf X) *) \ {{}}
(X,S,phi,I) is set
(X,S,phi) is Relation-like Function-like Function-yielding V164() (X,S) (X,S,phi) set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
the U2 of X is Element of the U1 of X
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
phi +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X -firstChar) . I is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(X,S,phi,(X,S,phi),((X -firstChar) . I)) is non empty Relation-like (abs (ar ((X -firstChar) . I))) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,(X -firstChar) . I)
ar ((X -firstChar) . I) is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . ((X -firstChar) . I) is set
abs (ar ((X -firstChar) . I)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((X -firstChar) . I))) -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
SubTerms I is Relation-like NAT -defined (proj2 I) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . I)) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
proj2 I is non empty finite set
(proj2 I) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 I
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(TermSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(X,S,phi) is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
(X,S,phi) (*) (SubTerms I) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,phi,(X,S,phi),((X -firstChar) . I)) . ((X,S,phi) (*) (SubTerms I)) is set
phi is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
ar phi is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X . phi is set
abs (ar phi) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar phi)) -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
(X,S,phi,(X,S,phi),phi) is non empty Relation-like (abs (ar phi)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,phi)
[:((abs (ar phi)) -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:((abs (ar phi)) -tuples_on S),BOOLEAN:] is non empty set
A1 is non empty Relation-like (abs (ar phi)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,phi)
h is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar phi) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() FinSequence of AllTermsOf X
(X,S,phi) * h is Relation-like NAT -defined S -valued Function-like finite abs (ar phi) -element len h -element FinSequence-like FinSubsequence-like V199() FinSequence of S
len h is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
t is Relation-like NAT -defined S -valued Function-like finite abs (ar phi) -element FinSequence-like FinSubsequence-like V199() FinSequence of S
len t is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
A2 is non empty Relation-like (abs (ar phi)) -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:((abs (ar phi)) -tuples_on S),BOOLEAN:]
H is non empty Relation-like NAT -defined S -valued Function-like finite abs (ar phi) -element FinSequence-like FinSubsequence-like V199() Element of (abs (ar phi)) -tuples_on S
A2 . H is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
S is non empty set
phi is Relation-like Function-like Function-yielding V164() (X,S) set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
phi | (OwnSymbolsOf X) is Relation-like OwnSymbolsOf X -defined Function-like Function-yielding V164() set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
dom (phi | (OwnSymbolsOf X)) is Element of bool (OwnSymbolsOf X)
bool (OwnSymbolsOf X) is non empty set
phi is set
proj2 (phi | (OwnSymbolsOf X)) is set
(phi | (OwnSymbolsOf X)) .: (dom (phi | (OwnSymbolsOf X))) is set
A is set
(phi | (OwnSymbolsOf X)) . A is Relation-like Function-like set
AllSymbolsOf X is non empty non trivial non finite V167() set
A1 is own ofAtomicFormula Element of AllSymbolsOf X
ar A1 is complex ext-real V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . A1 is set
abs (ar A1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
bool (S *) is non empty non trivial non finite V167() set
A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
A2 -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
bool (S \/ BOOLEAN) is non empty set
(X,S,phi,A1) is non empty Relation-like (abs (ar A1)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,A1)
(abs (ar A1)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
h is functional V25() FinSequence-membered Element of bool (S *)
t is Element of bool (S \/ BOOLEAN)
[:h,t:] is Relation-like set
bool [:h,t:] is non empty set
[:h,t:] is Relation-like S * -defined S \/ BOOLEAN -valued Element of bool [:(S *),(S \/ BOOLEAN):]
[:(S *),(S \/ BOOLEAN):] is non empty non trivial Relation-like non finite V167() set
bool [:(S *),(S \/ BOOLEAN):] is non empty non trivial non finite V167() set
H is Relation-like h -defined t -valued Function-like quasi_total Element of bool [:h,t:]
T is Relation-like S * -defined S \/ BOOLEAN -valued Element of bool [:(S *),(S \/ BOOLEAN):]
phi is Relation-like Function-like set
dom (phi | (OwnSymbolsOf X)) is Element of bool (OwnSymbolsOf X)
bool (OwnSymbolsOf X) is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
phi is own ofAtomicFormula Element of AllSymbolsOf X
(phi | (OwnSymbolsOf X)) . phi is Relation-like Function-like set
(X,S,phi,phi) is non empty Relation-like (abs (ar phi)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,phi)
ar phi is complex ext-real V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . phi is set
abs (ar phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar phi)) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
phi is Relation-like Function-like set
X is V51() V53() eligible Language-like
S is non empty set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
phi is Relation-like Function-like Function-yielding V164() (X,S) set
phi | (OwnSymbolsOf X) is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like Function-yielding V164() (X,S) set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
dom (phi | (OwnSymbolsOf X)) is Element of bool (OwnSymbolsOf X)
bool (OwnSymbolsOf X) is non empty set
phi is Relation-like OwnSymbolsOf X -defined set
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
X is V51() V53() eligible Language-like
S is non empty set
(X,S) is set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : S₁[b₁] } is set
X is V51() V53() eligible Language-like
S is non empty set
(X,S) is functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
the Relation-like Function-like Function-yielding V164() (X,S) set is Relation-like Function-like Function-yielding V164() (X,S) set
the Relation-like Function-like Function-yielding V164() (X,S) set | (OwnSymbolsOf X) is Relation-like OwnSymbolsOf X -defined OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total Function-yielding V164() (X,S) set
dom ( the Relation-like Function-like Function-yielding V164() (X,S) set | (OwnSymbolsOf X)) is Element of bool (OwnSymbolsOf X)
bool (OwnSymbolsOf X) is non empty set
rng ( the Relation-like Function-like Function-yielding V164() (X,S) set | (OwnSymbolsOf X)) is functional Element of bool (PFuncs ((S *),(S \/ BOOLEAN)))
bool (PFuncs ((S *),(S \/ BOOLEAN))) is non empty set
[:(OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))):] is non empty Relation-like set
bool [:(OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))):] is non empty set
psi is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Element of bool [:(OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))):]
phi is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))
A is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
v1 is Relation-like Function-like Element of (X,S)
psi is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b₁ is 0wff } is set
[:(X,S),(AtomicFormulasOf X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
[:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:] is non empty Relation-like set
bool [:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:] is non empty set
N is non empty Relation-like [:(X,S),(AtomicFormulasOf X):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:]
v1 is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() 0wff Element of AtomicFormulasOf X
N . (v1,psi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
[v1,psi] is non empty V34() set
N . [v1,psi] is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
(X,S,v1,psi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,v1) is Relation-like Function-like Function-yielding V164() (X,S) (X,S,v1) set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
v1 +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X -firstChar) . psi is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(X,S,v1,(X,S,v1),((X -firstChar) . psi)) is non empty Relation-like (abs (ar ((X -firstChar) . psi))) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,(X -firstChar) . psi)
ar ((X -firstChar) . psi) is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . ((X -firstChar) . psi) is set
abs (ar ((X -firstChar) . psi)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((X -firstChar) . psi))) -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
SubTerms psi is Relation-like NAT -defined (proj2 psi) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . psi)) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
proj2 psi is non empty finite set
(proj2 psi) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 psi
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(TermSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(X,S,v1) is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
(X,S,v1) (*) (SubTerms psi) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,v1,(X,S,v1),((X -firstChar) . psi)) . ((X,S,v1) (*) (SubTerms psi)) is set
v1 is non empty Relation-like [:(X,S),(AtomicFormulasOf X):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:]
psi is non empty Relation-like [:(X,S),(AtomicFormulasOf X):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:]
phi is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() 0wff Element of AtomicFormulasOf X
v1 . (phi,A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
[phi,A] is non empty V34() set
v1 . [phi,A] is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
(X,S,phi,A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,phi) is Relation-like Function-like Function-yielding V164() (X,S) (X,S,phi) set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
phi +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X -firstChar) . A is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(X,S,phi,(X,S,phi),((X -firstChar) . A)) is non empty Relation-like (abs (ar ((X -firstChar) . A))) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,(X -firstChar) . A)
ar ((X -firstChar) . A) is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . ((X -firstChar) . A) is set
abs (ar ((X -firstChar) . A)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((X -firstChar) . A))) -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
SubTerms A is Relation-like NAT -defined (proj2 A) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . A)) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
proj2 A is non empty finite set
(proj2 A) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 A
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(TermSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(X,S,phi) is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
(X,S,phi) (*) (SubTerms A) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,phi,(X,S,phi),((X -firstChar) . A)) . ((X,S,phi) (*) (SubTerms A)) is set
psi . (phi,A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
psi . [phi,A] is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
X is V51() V53() eligible Language-like
S is non empty set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
[:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
N . 1 is set
I is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
phi is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
N /^ 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
TRUE is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
FALSE is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
psi is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
v1 is Element of S
(phi,psi,v1) is Relation-like Function-like Function-yielding V164() (X,S) set
{} .--> v1 is trivial Relation-like {{}} -defined S -valued Function-like one-to-one constant finite V199() set
{{}} --> v1 is non empty Relation-like {{}} -defined S -valued {v1} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{v1}:]
{v1} is non empty trivial finite 1 -element set
[:{{}},{v1}:] is non empty Relation-like finite set
bool [:{{}},{v1}:] is non empty finite V25() set
psi .--> ({} .--> v1) is trivial Relation-like AllSymbolsOf X -defined {psi} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{psi} is non empty trivial finite 1 -element set
{psi} --> ({} .--> v1) is non empty Relation-like {psi} -defined {({} .--> v1)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{psi},{({} .--> v1)}:]
{({} .--> v1)} is non empty trivial functional finite V25() 1 -element set
[:{psi},{({} .--> v1)}:] is non empty Relation-like finite set
bool [:{psi},{({} .--> v1)}:] is non empty finite V25() set
phi +* (psi .--> ({} .--> v1)) is Relation-like Function-like Function-yielding V164() set
I . ((phi,psi,v1),(N /^ 1)) is set
[(phi,psi,v1),(N /^ 1)] is non empty V34() set
I . [(phi,psi,v1),(N /^ 1)] is set
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,S),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
[:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
dom phi is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
psi is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[psi,A1] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
A is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
<*A*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,A] is non empty V34() set
{[1,A]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
<*A*> ^ A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,S,psi,phi,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
psi is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom psi is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
phi is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[phi,A] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
A1 is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[A1,t] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
h is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
<*h*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,h] is non empty V34() set
{[1,h]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
<*h*> ^ t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
[A1,A2] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
H is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[H,T] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
psi . (H,T) is set
[H,T] is non empty V34() set
psi . [H,T] is set
(X,S,H,phi,T) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
phi is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom phi is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
A is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom A is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
A1 is set
A2 is Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
h is set
t is set
[h,t] is non empty V34() set
H is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[H,s2] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
m1 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
<*m1*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,m1] is non empty V34() set
{[1,m1]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
<*m1*> ^ s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
A1 is set
A2 is Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
h is set
t is set
[h,t] is non empty V34() set
H is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[H,s2] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
m1 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
<*m1*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,m1] is non empty V34() set
{[1,m1]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
<*m1*> ^ s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
A1 is set
A2 is Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
h is set
t is set
[h,t] is non empty V34() set
phi . A1 is set
H is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
phi . (H,T) is set
[H,T] is non empty V34() set
phi . [H,T] is set
(X,S,H,phi,T) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
A . (H,T) is set
A . [H,T] is set
A . A1 is set
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
[:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
I is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
phi is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom phi is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X) is non low-compounding non own Element of AllSymbolsOf X
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[I,v1] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
phi . (I,v1) is set
[I,v1] is non empty V34() set
phi . [I,v1] is set
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
phi . (I,psi) is set
[I,psi] is non empty V34() set
phi . [I,psi] is set
<*(X)*> ^ v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(<*(X)*> ^ v1) ^ psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,S),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
[:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
(X) is non low-compounding non own Element of AllSymbolsOf X
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
dom phi is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
psi is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom psi is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
<*(X)*> ^ A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(X)*> ^ A1) ^ A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
phi is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
[phi,A1] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
[phi,A2] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
(X,S,psi,phi,A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
phi is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom phi is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
A is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[A,A1] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
<*(X)*> ^ t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(X)*> ^ t) ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
A2 is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
[A2,t] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[A2,H] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[A2,h] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
T is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[T,m1] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
phi . (T,m1) is set
[T,m1] is non empty V34() set
phi . [T,m1] is set
(X,S,phi,T,m1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
phi is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom phi is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
A is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom A is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
A1 is set
A2 is Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
h is set
t is set
[h,t] is non empty V34() set
H is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
<*(X)*> ^ m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(X)*> ^ m1) ^ s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
[H,m1] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
[H,s2] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
A1 is set
A2 is Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
h is set
t is set
[h,t] is non empty V34() set
H is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
<*(X)*> ^ m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(X)*> ^ m1) ^ s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
[H,m1] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
[H,s2] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
A1 is set
A2 is Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
h is set
t is set
[h,t] is non empty V34() set
phi . A1 is set
H is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
phi . (H,T) is set
[H,T] is non empty V34() set
phi . [H,T] is set
(X,S,phi,H,T) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
A . (H,T) is set
A . [H,T] is set
A . A1 is set
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,S),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
[:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
(X,S) is non empty Relation-like [:(X,S),(AtomicFormulasOf X):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:]
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b₁ is 0wff } is set
[:(X,S),(AtomicFormulasOf X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
[:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:] is non empty Relation-like set
bool [:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:] is non empty set
bool (X,S) is non empty set
bool BOOLEAN is non empty set
bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
phi is functional Element of bool (X,S)
[:phi,(AtomicFormulasOf X):] is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
A1 is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
A is Element of bool BOOLEAN
[:A1,A:] is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
[:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
h is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
t is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,S,t) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,t) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,t) +* (X,S,t) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
((X,S,t) +* (X,S,t)) +* t is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
H is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
T is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
A2 is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
h is non empty Relation-like NAT -defined PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
h . 0 is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
t is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
t + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
h . (t + 1) is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
h . t is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,S,(h . t)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,(h . t)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,(h . t)) +* (X,S,(h . t)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
((X,S,(h . t)) +* (X,S,(h . t))) +* (h . t) is Relation-like Function-like set
dom (X,S) is non empty Relation-like non empty-yielding (X,S) -defined AtomicFormulasOf X -valued Element of bool [:(X,S),(AtomicFormulasOf X):]
bool [:(X,S),(AtomicFormulasOf X):] is non empty set
rng (X,S) is non empty Element of bool BOOLEAN
bool BOOLEAN is non empty set
[:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
A1 is non empty Relation-like NAT -defined PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
A1 . 0 is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
A2 is non empty Relation-like NAT -defined PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
A2 . 0 is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
A is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
h is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
A1 . h is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
h + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
A1 . (h + 1) is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
H is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,S,H) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,H) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,H) +* (X,S,H) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
((X,S,H) +* (X,S,H)) +* H is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
t is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
t + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
A1 . (t + 1) is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
h is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
A2 . h is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
h + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
A2 . (h + 1) is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
H is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,S,H) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,H) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,H) +* (X,S,H) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
((X,S,H) +* (X,S,H)) +* H is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
t is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
t + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
A2 . (t + 1) is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
h is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
t is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
H is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
T is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,S,t) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,t) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,t) +* (X,S,t) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
((X,S,t) +* (X,S,t)) +* t is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
phi is Relation-like Function-like Function-yielding V164() (X,S) set
phi | (OwnSymbolsOf X) is Relation-like OwnSymbolsOf X -defined OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total Function-yielding V164() (X,S) set
dom (phi | (OwnSymbolsOf X)) is Element of bool (OwnSymbolsOf X)
bool (OwnSymbolsOf X) is non empty set
rng (phi | (OwnSymbolsOf X)) is functional Element of bool (PFuncs ((S *),(S \/ BOOLEAN)))
bool (PFuncs ((S *),(S \/ BOOLEAN))) is non empty set
[:(OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))):] is non empty Relation-like set
bool [:(OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))):] is non empty set
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((phi *),(phi \/ BOOLEAN))
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
(X,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (X,phi) } is set
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,phi) is non empty Relation-like NAT -defined PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
N is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,phi) . N is Relation-like Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
v1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,phi) . v1 is Relation-like Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
psi is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
phi is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,phi) . A is Relation-like Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is set
phi is V51() V53() eligible Language-like
OwnSymbolsOf phi is non empty Element of bool (AllSymbolsOf phi)
AllSymbolsOf phi is non empty non trivial non finite V167() set
the U1 of phi is set
bool (AllSymbolsOf phi) is non empty non trivial non finite V167() set
the U2 of phi is Element of the U1 of phi
the U3 of phi is Element of the U1 of phi
{ the U2 of phi, the U3 of phi} is non empty finite set
the U1 of phi \ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
bool the U1 of phi is non empty set
the U1 of phi typed\ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
AllSymbolsOf phi is non empty non trivial non finite V167() set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite V167() set
((AllSymbolsOf phi) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
I is non empty set
I * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of I
I \/ BOOLEAN is non empty set
PFuncs ((I *),(I \/ BOOLEAN)) is non empty functional M26(I * ,I \/ BOOLEAN)
Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf phi, PFuncs ((I *),(I \/ BOOLEAN))
(phi,I) is non empty functional Element of bool (Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf phi -defined PFuncs ((I *),(I \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN)))) : b₁ is (phi,I) } is set
[:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN)))) -defined (AllSymbolsOf phi) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf phi) *):]
[:(Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf phi) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf phi) *):] is non empty non trivial non finite V167() set
(phi,X,I) is Relation-like [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)
PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):], BOOLEAN )
dom (phi,X,I) is Relation-like (phi,I) -defined ((AllSymbolsOf phi) *) \ {{}} -valued Element of bool [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):]
bool [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] is non empty non trivial non finite V167() set
(phi,X,I) . S is set
(phi,I) is non empty Relation-like NAT -defined PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
X + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(phi,(X + 0),I) is Relation-like [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)
dom (phi,(X + 0),I) is Relation-like (phi,I) -defined ((AllSymbolsOf phi) *) \ {{}} -valued Element of bool [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):]
(phi,(X + 0),I) . S is set
v1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + v1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(phi,(X + v1),I) is Relation-like [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)
dom (phi,(X + v1),I) is Relation-like (phi,I) -defined ((AllSymbolsOf phi) *) \ {{}} -valued Element of bool [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):]
(phi,(X + v1),I) . S is set
v1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
X + (v1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(phi,(X + (v1 + 1)),I) is Relation-like [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)
dom (phi,(X + (v1 + 1)),I) is Relation-like (phi,I) -defined ((AllSymbolsOf phi) *) \ {{}} -valued Element of bool [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):]
(phi,(X + (v1 + 1)),I) . S is set
(X + v1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(phi,((X + v1) + 1),I) is Relation-like [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)
psi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(phi,I) . psi is Relation-like Function-like Element of PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(phi,I) . phi is Relation-like Function-like Element of PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)
(phi,I,((phi,I) . psi)) is Relation-like [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN:]
[:[:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
(phi,I,((phi,I) . psi)) is Relation-like [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN:]
(phi,I,((phi,I) . psi)) +* (phi,I,((phi,I) . psi)) is Relation-like [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN:]
((phi,I,((phi,I) . psi)) +* (phi,I,((phi,I) . psi))) +* ((phi,I) . psi) is Relation-like Function-like set
proj1 ((phi,I) . phi) is set
dom ((phi,I,((phi,I) . psi)) +* (phi,I,((phi,I) . psi))) is Relation-like (phi,I) -defined ((AllSymbolsOf phi) *) \ {{}} -valued Element of bool [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):]
proj1 ((phi,I) . psi) is set
(dom ((phi,I,((phi,I) . psi)) +* (phi,I,((phi,I) . psi)))) \/ (proj1 ((phi,I) . psi)) is set
X + (v1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(phi,(X + (v1 + 1)),I) is Relation-like [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)
dom (phi,(X + (v1 + 1)),I) is Relation-like (phi,I) -defined ((AllSymbolsOf phi) *) \ {{}} -valued Element of bool [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):]
X is set
S is set
phi is set
S \/ phi is set
I is set
(S \/ phi) \/ I is set
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((phi *),(phi \/ BOOLEAN))
(X,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (X,phi) } is set
[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
(X) is non low-compounding non own Element of AllSymbolsOf X
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b₁ is 0wff } is set
(X,0,S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,S),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
dom (X,0,S) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
(X,0,phi) is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
dom (X,0,phi) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
(X,S) is non empty Relation-like NAT -defined PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S) . A2 is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,phi) is non empty Relation-like NAT -defined PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
(X,phi) . A2 is Relation-like Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
h is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
t is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,S) is non empty Relation-like [:(X,S),(AtomicFormulasOf X):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:]
[:(X,S),(AtomicFormulasOf X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
[:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:] is non empty Relation-like set
bool [:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:] is non empty set
(X,phi) is non empty Relation-like [:(X,phi),(AtomicFormulasOf X):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(X,phi),(AtomicFormulasOf X):],BOOLEAN:]
[:(X,phi),(AtomicFormulasOf X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
[:[:(X,phi),(AtomicFormulasOf X):],BOOLEAN:] is non empty Relation-like set
bool [:[:(X,phi),(AtomicFormulasOf X):],BOOLEAN:] is non empty set
H is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
T is Relation-like Function-like Function-yielding V164() (X,phi) Element of (X,phi)
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[H,m1] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
[T,m1] is non empty V34() Element of [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,A,S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
dom (X,A,S) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
(X,A,phi) is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
dom (X,A,phi) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
A + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,(A + 1),S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
dom (X,(A + 1),S) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
(X,(A + 1),phi) is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
dom (X,(A + 1),phi) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
h is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
t is Relation-like Function-like Function-yielding V164() (X,phi) Element of (X,phi)
(X,S,(X,A,S)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
[:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
dom (X,S,(X,A,S)) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
(X,S,(X,A,S)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom (X,S,(X,A,S)) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
(dom (X,S,(X,A,S))) \/ (dom (X,S,(X,A,S))) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
((dom (X,S,(X,A,S))) \/ (dom (X,S,(X,A,S)))) \/ (dom (X,A,S)) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
(X,S) is non empty Relation-like NAT -defined PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S) . A2 is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
A1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S) . A1 is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
m2 is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
i2 is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,S,m2) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,m2) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,m2) +* (X,S,m2) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
((X,S,m2) +* (X,S,m2)) +* m2 is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom ((X,S,m2) +* (X,S,m2)) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
dom m2 is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
(dom ((X,S,m2) +* (X,S,m2))) \/ (dom m2) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
dom (X,S,m2) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
dom (X,S,m2) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
(dom (X,S,m2)) \/ (dom (X,S,m2)) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
((dom (X,S,m2)) \/ (dom (X,S,m2))) \/ (dom m2) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
(X,phi,(X,A,phi)) is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
[:[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
dom (X,phi,(X,A,phi)) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
(X,phi,(X,A,phi)) is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom (X,phi,(X,A,phi)) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
(dom (X,phi,(X,A,phi))) \/ (dom (X,phi,(X,A,phi))) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
((dom (X,phi,(X,A,phi))) \/ (dom (X,phi,(X,A,phi)))) \/ (dom (X,A,phi)) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
(X,phi) is non empty Relation-like NAT -defined PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,phi) . A2 is Relation-like Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
A1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,phi) . A1 is Relation-like Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
m2 is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
i2 is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,phi,m2) is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,phi,m2) is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,phi,m2) +* (X,phi,m2) is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
((X,phi,m2) +* (X,phi,m2)) +* m2 is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom ((X,phi,m2) +* (X,phi,m2)) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
dom m2 is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
(dom ((X,phi,m2) +* (X,phi,m2))) \/ (dom m2) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
dom (X,phi,m2) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
dom (X,phi,m2) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
(dom (X,phi,m2)) \/ (dom (X,phi,m2)) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
((dom (X,phi,m2)) \/ (dom (X,phi,m2))) \/ (dom m2) is Relation-like (X,phi) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
i2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[h,i2] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
[t,i2] is non empty V34() Element of [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
q is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[h,q] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
m1 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
<*m1*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,m1] is non empty V34() set
{[1,m1]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
<*m1*> ^ q is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
[t,q] is non empty V34() Element of [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
<*(X)*> ^ m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
q is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(X)*> ^ m1) ^ q is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
[h,m1] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[h,q] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[t,m1] is non empty V34() Element of [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
[t,q] is non empty V34() Element of [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):]
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf S) *) \ {{}}, BOOLEAN )
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (S,phi) } is set
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
(S,phi) is non empty Relation-like NAT -defined PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
(S,phi) . X is Relation-like Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
curry ((S,phi) . X) is Relation-like Function-like set
[:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):] is non empty Relation-like set
bool [:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):] is non empty set
AtomicFormulasOf S is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}} : b₁ is 0wff } is set
PFuncs ((S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN))) is non empty functional M26((S,phi), PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN))
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() 0wff Element of AtomicFormulasOf S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() 0wff Element of AtomicFormulasOf S
[:(S,phi),(AtomicFormulasOf S):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
(S,phi) is non empty Relation-like [:(S,phi),(AtomicFormulasOf S):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(S,phi),(AtomicFormulasOf S):],BOOLEAN:]
[:[:(S,phi),(AtomicFormulasOf S):],BOOLEAN:] is non empty Relation-like set
bool [:[:(S,phi),(AtomicFormulasOf S):],BOOLEAN:] is non empty set
dom (S,phi) is non empty Relation-like non empty-yielding (S,phi) -defined AtomicFormulasOf S -valued Element of bool [:(S,phi),(AtomicFormulasOf S):]
bool [:(S,phi),(AtomicFormulasOf S):] is non empty set
(S,phi) . 0 is Relation-like Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
proj1 ((S,phi) . 0) is set
h is set
[h, the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() 0wff Element of AtomicFormulasOf S] is non empty V34() set
(S,0,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
dom (S,0,phi) is Relation-like (S,phi) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
0 + X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S,(0 + X),phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
dom (S,(0 + X),phi) is Relation-like (S,phi) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
proj1 ((S,phi) . X) is set
A is Relation-like (S,phi) -defined PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN) -valued Function-like Function-yielding V164() Element of PFuncs ((S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)))
dom A is functional Element of bool (S,phi)
bool (S,phi) is non empty set
h is non empty Relation-like (S,phi) -defined PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):]
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf S) *) \ {{}}, BOOLEAN )
phi is non empty set
(S,X,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (S,phi) } is set
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
curry (S,X,phi) is Relation-like Function-like set
[:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):] is non empty Relation-like set
bool [:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):] is non empty set
I is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S,I,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
(S,phi) is non empty Relation-like NAT -defined PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
(S,phi) . I is Relation-like Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
curry (S,I,phi) is Relation-like Function-like set
curry ((S,phi) . I) is Relation-like Function-like set
X is V51() V53() eligible Language-like
S is non empty set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,phi,S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,S),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
curry (X,phi,S) is Relation-like Function-like set
I is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
(curry (X,phi,S)) . I is set
PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf X) *) \ {{}}, BOOLEAN )
psi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,psi,S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
curry (X,psi,S) is Relation-like Function-like set
(X,S) is non empty Relation-like NAT -defined PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
(X,S) . psi is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
curry ((X,S) . psi) is Relation-like Function-like set
[:(X,S),(PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)):] is non empty Relation-like set
bool [:(X,S),(PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)):] is non empty set
phi is non empty Relation-like (X,S) -defined PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:(X,S),(PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)):]
phi . I is Relation-like Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is V51() V53() eligible Language-like
OwnSymbolsOf phi is non empty Element of bool (AllSymbolsOf phi)
AllSymbolsOf phi is non empty non trivial non finite V167() set
the U1 of phi is set
bool (AllSymbolsOf phi) is non empty non trivial non finite V167() set
the U2 of phi is Element of the U1 of phi
the U3 of phi is Element of the U1 of phi
{ the U2 of phi, the U3 of phi} is non empty finite set
the U1 of phi \ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
bool the U1 of phi is non empty set
the U1 of phi typed\ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
AllSymbolsOf phi is non empty non trivial non finite V167() set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite V167() set
((AllSymbolsOf phi) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
I is non empty set
I * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of I
I \/ BOOLEAN is non empty set
PFuncs ((I *),(I \/ BOOLEAN)) is non empty functional M26(I * ,I \/ BOOLEAN)
Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf phi, PFuncs ((I *),(I \/ BOOLEAN))
(phi,I) is non empty functional Element of bool (Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf phi -defined PFuncs ((I *),(I \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN)))) : b₁ is (phi,I) } is set
psi is Relation-like Function-like Function-yielding V164() (phi,I) Element of (phi,I)
(phi,I,X,psi) is Relation-like ((AllSymbolsOf phi) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf phi) *) \ {{}}, BOOLEAN )
(phi,X,I) is Relation-like [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)
[:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN)))) -defined (AllSymbolsOf phi) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf phi) *):]
[:(Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf phi) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf phi),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf phi) *):] is non empty non trivial non finite V167() set
PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):], BOOLEAN )
curry (phi,X,I) is Relation-like Function-like set
(curry (phi,X,I)) . psi is set
(phi,I,(X + S),psi) is Relation-like ((AllSymbolsOf phi) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN)
(phi,(X + S),I) is Relation-like [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)
curry (phi,(X + S),I) is Relation-like Function-like set
(curry (phi,(X + S),I)) . psi is set
[:(phi,I),(PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN)):] is non empty Relation-like set
bool [:(phi,I),(PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN)):] is non empty set
h is non empty Relation-like (phi,I) -defined PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:(phi,I),(PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN)):]
h . psi is Relation-like Function-like Element of PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN)
t is non empty Relation-like (phi,I) -defined PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:(phi,I),(PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN)):]
t . psi is Relation-like Function-like Element of PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN)
dom h is non empty functional Element of bool (phi,I)
bool (phi,I) is non empty set
dom (phi,I,X,psi) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite V167() set
dom (phi,I,(X + S),psi) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
H is set
(phi,I,X,psi) . H is set
(phi,I,(X + S),psi) . H is set
[psi,H] is non empty V34() set
dom (phi,X,I) is Relation-like (phi,I) -defined ((AllSymbolsOf phi) *) \ {{}} -valued Element of bool [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):]
bool [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):] is non empty non trivial non finite V167() set
dom (phi,(X + S),I) is Relation-like (phi,I) -defined ((AllSymbolsOf phi) *) \ {{}} -valued Element of bool [:(phi,I),(((AllSymbolsOf phi) *) \ {{}}):]
(phi,(X + S),I) . [psi,H] is set
(phi,X,I) . [psi,H] is set
(phi,(X + S),I) . (psi,H) is set
(phi,X,I) . (psi,H) is set
H is set
T is set
(phi,I,X,psi) . T is set
(phi,I,(X + S),psi) . T is set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (S,phi) } is set
I is non empty set
I * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of I
I \/ BOOLEAN is non empty set
PFuncs ((I *),(I \/ BOOLEAN)) is non empty functional M26(I * ,I \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((I *),(I \/ BOOLEAN))
(S,I) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((I *),(I \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) : b₁ is (S,I) } is set
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
(S,phi) is non empty Relation-like NAT -defined PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
N is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S,phi) . N is Relation-like Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
(S,N,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
(S,N,I) is Relation-like [:(S,I),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
[:(S,I),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
PFuncs ([:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,I),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
(S,I) is non empty Relation-like NAT -defined PFuncs ([:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
(S,I) . N is Relation-like Function-like Element of PFuncs ([:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
t is Relation-like Function-like Function-yielding V164() (S,phi) Element of (S,phi)
(S,phi,X,t) is Relation-like ((AllSymbolsOf S) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf S) *) \ {{}}, BOOLEAN )
(S,X,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
curry (S,X,phi) is Relation-like Function-like set
(curry (S,X,phi)) . t is set
dom (S,phi,X,t) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
H is Relation-like Function-like Function-yielding V164() (S,I) Element of (S,I)
(S,I,X,H) is Relation-like ((AllSymbolsOf S) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)
(S,X,I) is Relation-like [:(S,I),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
curry (S,X,I) is Relation-like Function-like set
(curry (S,X,I)) . H is set
dom (S,I,X,H) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
curry ((S,phi) . N) is Relation-like Function-like set
(curry ((S,phi) . N)) . t is set
curry ((S,I) . N) is Relation-like Function-like set
(curry ((S,I) . N)) . H is set
[:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):] is non empty Relation-like set
bool [:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):] is non empty set
proj1 ((S,phi) . N) is set
m2 is non empty Relation-like (S,phi) -defined PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):]
uncurry m2 is Relation-like Function-like set
m1 is set
s2 is Relation-like ((AllSymbolsOf S) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)
dom s2 is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
dom m2 is non empty functional Element of bool (S,phi)
bool (S,phi) is non empty set
m2 . t is Relation-like Function-like Element of PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)
q is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[t,q] is non empty V34() Element of [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
dom (S,N,phi) is Relation-like (S,phi) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
[H,m1] is non empty V34() set
proj1 ((S,I) . N) is set
i2 is Relation-like ((AllSymbolsOf S) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)
dom i2 is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (S,phi) } is set
I is non empty set
I * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of I
I \/ BOOLEAN is non empty set
PFuncs ((I *),(I \/ BOOLEAN)) is non empty functional M26(I * ,I \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((I *),(I \/ BOOLEAN))
(S,I) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((I *),(I \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) : b₁ is (S,I) } is set
psi is Relation-like Function-like Function-yielding V164() (S,phi) Element of (S,phi)
(S,phi,X,psi) is Relation-like ((AllSymbolsOf S) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf S) *) \ {{}}, BOOLEAN )
(S,X,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
curry (S,X,phi) is Relation-like Function-like set
(curry (S,X,phi)) . psi is set
dom (S,phi,X,psi) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
phi is Relation-like Function-like Function-yielding V164() (S,I) Element of (S,I)
(S,I,X,phi) is Relation-like ((AllSymbolsOf S) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)
(S,X,I) is Relation-like [:(S,I),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
[:(S,I),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
PFuncs ([:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,I),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
curry (S,X,I) is Relation-like Function-like set
(curry (S,X,I)) . phi is set
dom (S,I,X,phi) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
the non empty set is non empty set
the non empty set * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of the non empty set
the non empty set \/ BOOLEAN is non empty set
PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)) is non empty functional M26( the non empty set * , the non empty set \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))
(X, the non empty set ) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) : b₁ is (X, the non empty set ) } is set
the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set ) is Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set )
v1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X, the non empty set ,v1, the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set )) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf X) *) \ {{}}, BOOLEAN )
(X,v1, the non empty set ) is Relation-like [:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
[:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
curry (X,v1, the non empty set ) is Relation-like Function-like set
(curry (X,v1, the non empty set )) . the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set ) is set
dom (X, the non empty set ,v1, the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set )) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
psi is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((phi *),(phi \/ BOOLEAN))
(X,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (X,phi) } is set
A1 is Relation-like Function-like Function-yielding V164() (X,phi) Element of (X,phi)
A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,phi,A2,A1) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
(X,A2,phi) is Relation-like [:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
[:(X,phi),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,phi),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
curry (X,A2,phi) is Relation-like Function-like set
(curry (X,A2,phi)) . A1 is set
dom (X,phi,A2,A1) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
I is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
N is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
the non empty set is non empty set
the non empty set * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of the non empty set
the non empty set \/ BOOLEAN is non empty set
PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)) is non empty functional M26( the non empty set * , the non empty set \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))
(X, the non empty set ) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) : b₁ is (X, the non empty set ) } is set
the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set ) is Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set )
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X, the non empty set ,phi, the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set )) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf X) *) \ {{}}, BOOLEAN )
(X,phi, the non empty set ) is Relation-like [:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
[:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
curry (X,phi, the non empty set ) is Relation-like Function-like set
(curry (X,phi, the non empty set )) . the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set ) is set
dom (X, the non empty set ,phi, the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set )) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is V51() V53() eligible Language-like
(phi,X) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite V167() set
the U1 of phi is set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite V167() set
((AllSymbolsOf phi) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite V167() set
(phi,(X + S)) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
the non empty set is non empty set
(phi, the non empty set ) is non empty functional Element of bool (Funcs ((OwnSymbolsOf phi),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))))
OwnSymbolsOf phi is non empty Element of bool (AllSymbolsOf phi)
AllSymbolsOf phi is non empty non trivial non finite V167() set
bool (AllSymbolsOf phi) is non empty non trivial non finite V167() set
the U2 of phi is Element of the U1 of phi
the U3 of phi is Element of the U1 of phi
{ the U2 of phi, the U3 of phi} is non empty finite set
the U1 of phi \ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
bool the U1 of phi is non empty set
the U1 of phi typed\ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
the non empty set * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of the non empty set
the non empty set \/ BOOLEAN is non empty set
PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)) is non empty functional M26( the non empty set * , the non empty set \/ BOOLEAN)
Funcs ((OwnSymbolsOf phi),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf phi, PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf phi),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf phi -defined PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf phi),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) : b₁ is (phi, the non empty set ) } is set
the Relation-like Function-like Function-yielding V164() (phi, the non empty set ) Element of (phi, the non empty set ) is Relation-like Function-like Function-yielding V164() (phi, the non empty set ) Element of (phi, the non empty set )
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(phi, the non empty set ,A, the Relation-like Function-like Function-yielding V164() (phi, the non empty set ) Element of (phi, the non empty set )) is Relation-like ((AllSymbolsOf phi) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf phi) *) \ {{}}, BOOLEAN )
(phi,A, the non empty set ) is Relation-like [:(phi, the non empty set ),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(phi, the non empty set ),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)
[:(phi, the non empty set ),(((AllSymbolsOf phi) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf phi),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) -defined (AllSymbolsOf phi) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf phi),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf phi) *):]
[:(Funcs ((OwnSymbolsOf phi),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf phi) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf phi),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf phi) *):] is non empty non trivial non finite V167() set
PFuncs ([:(phi, the non empty set ),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(phi, the non empty set ),(((AllSymbolsOf phi) *) \ {{}}):], BOOLEAN )
curry (phi,A, the non empty set ) is Relation-like Function-like set
(curry (phi,A, the non empty set )) . the Relation-like Function-like Function-yielding V164() (phi, the non empty set ) Element of (phi, the non empty set ) is set
A1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(phi, the non empty set ,A1, the Relation-like Function-like Function-yielding V164() (phi, the non empty set ) Element of (phi, the non empty set )) is Relation-like ((AllSymbolsOf phi) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf phi) *) \ {{}}),BOOLEAN)
(phi,A1, the non empty set ) is Relation-like [:(phi, the non empty set ),(((AllSymbolsOf phi) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(phi, the non empty set ),(((AllSymbolsOf phi) *) \ {{}}):],BOOLEAN)
curry (phi,A1, the non empty set ) is Relation-like Function-like set
(curry (phi,A1, the non empty set )) . the Relation-like Function-like Function-yielding V164() (phi, the non empty set ) Element of (phi, the non empty set ) is set
dom (phi, the non empty set ,A, the Relation-like Function-like Function-yielding V164() (phi, the non empty set ) Element of (phi, the non empty set )) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
dom (phi, the non empty set ,A1, the Relation-like Function-like Function-yielding V164() (phi, the non empty set ) Element of (phi, the non empty set )) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
X is V51() V53() eligible Language-like
(X,0) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b₁ is 0wff } is set
the non empty set is non empty set
(X, the non empty set ) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
the non empty set * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of the non empty set
the non empty set \/ BOOLEAN is non empty set
PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)) is non empty functional M26( the non empty set * , the non empty set \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) : b₁ is (X, the non empty set ) } is set
the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set ) is Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set )
[:(X, the non empty set ),(AtomicFormulasOf X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
(X, the non empty set ) is non empty Relation-like [:(X, the non empty set ),(AtomicFormulasOf X):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(X, the non empty set ),(AtomicFormulasOf X):],BOOLEAN:]
[:[:(X, the non empty set ),(AtomicFormulasOf X):],BOOLEAN:] is non empty Relation-like set
bool [:[:(X, the non empty set ),(AtomicFormulasOf X):],BOOLEAN:] is non empty set
dom (X, the non empty set ) is non empty Relation-like non empty-yielding (X, the non empty set ) -defined AtomicFormulasOf X -valued Element of bool [:(X, the non empty set ),(AtomicFormulasOf X):]
bool [:(X, the non empty set ),(AtomicFormulasOf X):] is non empty set
[:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
(X, the non empty set ) is non empty Relation-like NAT -defined PFuncs ([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
v1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X, the non empty set ) . v1 is Relation-like Function-like Element of PFuncs ([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
proj1 ((X, the non empty set ) . v1) is set
(X,0, the non empty set ) is Relation-like [:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
dom (X,0, the non empty set ) is Relation-like (X, the non empty set ) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
psi is set
[ the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set ),psi] is non empty V34() set
(X, the non empty set ,v1, the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set )) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf X) *) \ {{}}, BOOLEAN )
(X,v1, the non empty set ) is Relation-like [:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X, the non empty set ),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
curry (X,v1, the non empty set ) is Relation-like Function-like set
(curry (X,v1, the non empty set )) . the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set ) is set
dom (X, the non empty set ,v1, the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set )) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
psi is set
[:(X, the non empty set ),(PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)):] is non empty Relation-like set
bool [:(X, the non empty set ),(PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)):] is non empty set
A1 is non empty Relation-like (X, the non empty set ) -defined PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:(X, the non empty set ),(PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)):]
dom A1 is non empty functional Element of bool (X, the non empty set )
bool (X, the non empty set ) is non empty set
[ the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set ),psi] is non empty V34() set
[ the Relation-like Function-like Function-yielding V164() (X, the non empty set ) Element of (X, the non empty set ),psi] `2 is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b₁ is 0wff } is set
(X,0) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b₁ is 0wff } is set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,0) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 * phi is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
S + (0 * phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
S + phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
(X,(S + phi)) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}} is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}
0 * S is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
0 + (0 * S) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
0 + S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
X is V51() V53() eligible Language-like
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,S) (X) Element of ((AllSymbolsOf X) *) \ {{}} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,S) (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}} is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
S is non empty set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
phi is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
AllSymbolsOf X is non empty non trivial non finite V167() set
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S,A,phi) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf X) *) \ {{}}, BOOLEAN )
(X,A,S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,S),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
curry (X,A,S) is Relation-like Function-like set
(curry (X,A,S)) . phi is set
A1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,A1) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
(X,S,A1,phi) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
(X,A1,S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
curry (X,A1,S) is Relation-like Function-like set
(curry (X,A1,S)) . phi is set
dom (X,S,A1,phi) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,A) (X) Element of ((AllSymbolsOf X) *) \ {{}}
dom (X,S,A,phi) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,S,A,phi) . h is set
(X,S,A,phi) /. h is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
t is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
H is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S,H,phi) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
(X,H,S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
curry (X,H,S) is Relation-like Function-like set
(curry (X,H,S)) . phi is set
(X,S,H,phi) . I is set
H + A is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S,(H + A),phi) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
(X,(H + A),S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
curry (X,(H + A),S) is Relation-like Function-like set
(curry (X,(H + A),S)) . phi is set
A + H is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S,(A + H),phi) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
(X,(A + H),S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
curry (X,(A + H),S) is Relation-like Function-like set
(curry (X,(A + H),S)) . phi is set
(X,H) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
i2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S,i2,phi) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
(X,i2,S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
curry (X,i2,S) is Relation-like Function-like set
(curry (X,i2,S)) . phi is set
dom (X,S,i2,phi) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
m2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,m2) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,S,m2,phi) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
(X,m2,S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
curry (X,m2,S) is Relation-like Function-like set
(curry (X,m2,S)) . phi is set
dom (X,S,m2,phi) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
dom (X,S,H,phi) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,S,(H + A),phi) . I is set
N is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
v1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
psi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S,psi,phi) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf X) *) \ {{}}, BOOLEAN )
(X,psi,S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,S),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
curry (X,psi,S) is Relation-like Function-like set
(curry (X,psi,S)) . phi is set
(X,S,psi,phi) . I is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (X,b₂) } is set
X is V51() V53() eligible Language-like
(X) is set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (X,b₂) } is set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}} is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
S is V51() V53() eligible Language-like
TermSymbolsOf S is non empty set
the U1 of S is set
the U3 of S is Element of the U1 of S
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
AllTermsOf S is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365((((AllSymbolsOf S) *) \ {{}}))
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V167() set
S -termsOfMaxDepth is Relation-like Function-like set
proj2 (S -termsOfMaxDepth) is set
union (proj2 (S -termsOfMaxDepth)) is set
S -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
[:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V167() set
(AllSymbolsOf S) -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(AllSymbolsOf S) -pr1 is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total V201( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf S),(AllSymbolsOf S)) is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
MultPlace ((AllSymbolsOf S) -pr1) is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
phi is non empty set
Funcs ((AllTermsOf S),phi) is non empty functional FUNCTION_DOMAIN of AllTermsOf S,phi
I is Element of phi
N is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of ((AllSymbolsOf S) *) \ {{}}
(S -firstChar) . N is non relational termal own ofAtomicFormula Element of AllSymbolsOf S
SubTerms N is Relation-like NAT -defined (proj2 N) * -valued AllTermsOf S -valued Function-like finite abs (ar N) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf S) *
proj2 N is non empty finite set
(proj2 N) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 N
AllTermsOf S is non empty functional V25() FinSequence-membered AllSymbolsOf S -prefix S -prefix Element of bool ((AllSymbolsOf S) *)
ar N is complex ext-real V40() V41() Element of INT
ar ((S -firstChar) . N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of S . ((S -firstChar) . N) is set
abs (ar N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
((AllSymbolsOf S) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf S) *
(AllTermsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf S) *) *)
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V167() set
v1 is Relation-like Function-like Function-yielding V164() (S,phi) set
(S,phi,I,v1) is non empty Relation-like NAT -defined Funcs ((AllTermsOf S),phi) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf S),phi)):]
[:NAT,(Funcs ((AllTermsOf S),phi)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(Funcs ((AllTermsOf S),phi)):] is non empty non trivial non finite V167() set
(S,phi,I,v1) . (X + 1) is Relation-like AllTermsOf S -defined phi -valued Function-like total quasi_total Element of Funcs ((AllTermsOf S),phi)
((S,phi,I,v1) . (X + 1)) . N is set
(S,phi,v1,((S -firstChar) . N)) is non empty Relation-like (abs (ar ((S -firstChar) . N))) -tuples_on phi -defined phi \/ BOOLEAN -valued Function-like total quasi_total (S,phi,(S -firstChar) . N)
abs (ar ((S -firstChar) . N)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar ((S -firstChar) . N))) -tuples_on phi is non empty functional V25() FinSequence-membered FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
(S,phi,I,v1) . X is Relation-like Function-like Element of Funcs ((AllTermsOf S),phi)
((S,phi,I,v1) . X) (*) (SubTerms N) is Relation-like NAT -defined Function-like finite V199() set
(S,phi,v1,((S -firstChar) . N)) . (((S,phi,I,v1) . X) (*) (SubTerms N)) is set
(S,phi,v1,((S -firstChar) . N)) . {} is set
psi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
psi + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(S,phi,I,v1) . (psi + 1) is Relation-like AllTermsOf S -defined phi -valued Function-like total quasi_total Element of Funcs ((AllTermsOf S),phi)
((S,phi,I,v1) . (psi + 1)) . N is set
(S,phi,I,v1) . psi is Relation-like AllTermsOf S -defined phi -valued Function-like total quasi_total Element of Funcs ((AllTermsOf S),phi)
((S,phi,I,v1) . psi) (*) (SubTerms N) is Relation-like NAT -defined phi -valued Function-like finite V199() set
(S,phi,v1,((S -firstChar) . N)) . (((S,phi,I,v1) . psi) (*) (SubTerms N)) is set
I is non empty set
phi is V51() V53() eligible Language-like
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
TermSymbolsOf phi is non empty set
the U1 of phi is set
the U3 of phi is Element of the U1 of phi
{ the U3 of phi} is non empty trivial finite 1 -element set
the U1 of phi \ { the U3 of phi} is non empty Element of bool the U1 of phi
bool the U1 of phi is non empty set
the U1 of phi typed\ { the U3 of phi} is Element of bool the U1 of phi
the adicity of phi is non empty Relation-like the U1 of phi \ { the U3 of phi} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of phi \ { the U3 of phi}),INT:]
[:( the U1 of phi \ { the U3 of phi}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of phi \ { the U3 of phi}),INT:] is non empty non trivial non finite V167() set
the adicity of phi " NAT is Element of bool ( the U1 of phi \ { the U3 of phi})
bool ( the U1 of phi \ { the U3 of phi}) is non empty set
AllSymbolsOf phi is non empty non trivial non finite V167() set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite V167() set
((AllSymbolsOf phi) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
AllTermsOf phi is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf phi -prefix phi -prefix Element of K365((((AllSymbolsOf phi) *) \ {{}}))
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf phi) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf phi) *) \ {{}}))
bool (bool (((AllSymbolsOf phi) *) \ {{}})) is non empty non trivial non finite V167() set
phi -termsOfMaxDepth is Relation-like Function-like set
proj2 (phi -termsOfMaxDepth) is set
union (proj2 (phi -termsOfMaxDepth)) is set
Funcs ((AllTermsOf phi),I) is non empty functional FUNCTION_DOMAIN of AllTermsOf phi,I
N is Element of I
psi is Relation-like Function-like Function-yielding V164() (phi,I) set
(phi,I,N,psi) is non empty Relation-like NAT -defined Funcs ((AllTermsOf phi),I) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf phi),I)):]
[:NAT,(Funcs ((AllTermsOf phi),I)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(Funcs ((AllTermsOf phi),I)):] is non empty non trivial non finite V167() set
X + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(phi,I,N,psi) . (X + 1) is Relation-like AllTermsOf phi -defined I -valued Function-like total quasi_total Element of Funcs ((AllTermsOf phi),I)
phi is non empty Relation-like NAT -defined TermSymbolsOf phi -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal X -termal Element of ((AllSymbolsOf phi) *) \ {{}}
((phi,I,N,psi) . (X + 1)) . phi is set
v1 is Element of I
(phi,I,v1,psi) is non empty Relation-like NAT -defined Funcs ((AllTermsOf phi),I) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf phi),I)):]
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X + 1) + S is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(phi,I,v1,psi) . ((X + 1) + S) is Relation-like AllTermsOf phi -defined I -valued Function-like total quasi_total Element of Funcs ((AllTermsOf phi),I)
((phi,I,v1,psi) . ((X + 1) + S)) . phi is set
S is V51() V53() eligible Language-like
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is non empty set
(S,X,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (S,phi) } is set
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
curry (S,X,phi) is Relation-like Function-like set
PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf S) *) \ {{}}, BOOLEAN )
[:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):] is non empty Relation-like set
bool [:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):] is non empty set
X is set
S is set
phi is set
S \/ phi is set
I is set
(S \/ phi) \/ I is set
N is set
v1 is set
psi is set
phi is set
v1 \/ psi is set
(v1 \/ psi) \/ phi is set
X is V51() V53() eligible Language-like
(X,0) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b₁ is 0wff } is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
v1 is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
psi is non empty set
psi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of psi
psi \/ BOOLEAN is non empty set
PFuncs ((psi *),(psi \/ BOOLEAN)) is non empty functional M26(psi * ,psi \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((psi *),(psi \/ BOOLEAN))
(X,psi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((psi *),(psi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN)))) : b₁ is (X,psi) } is set
A is Relation-like Function-like Function-yielding V164() (X,psi) Element of (X,psi)
(X,psi,S,A) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf X) *) \ {{}}, BOOLEAN )
(X,S,psi) is Relation-like [:(X,psi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,psi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
[:(X,psi),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,psi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,psi),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
curry (X,S,psi) is Relation-like Function-like set
(curry (X,S,psi)) . A is set
dom (X,psi,S,A) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,psi,phi,A) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
(X,phi,psi) is Relation-like [:(X,psi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,psi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
curry (X,phi,psi) is Relation-like Function-like set
(curry (X,phi,psi)) . A is set
dom (X,psi,phi,A) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
psi is non empty set
psi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of psi
psi \/ BOOLEAN is non empty set
PFuncs ((psi *),(psi \/ BOOLEAN)) is non empty functional M26(psi * ,psi \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((psi *),(psi \/ BOOLEAN))
(X,psi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((psi *),(psi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN)))) : b₁ is (X,psi) } is set
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
phi is Relation-like Function-like Function-yielding V164() (X,psi) Element of (X,psi)
(X,psi,A,phi) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf X) *) \ {{}}, BOOLEAN )
(X,A,psi) is Relation-like [:(X,psi),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,psi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
[:(X,psi),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((psi *),(psi \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,psi),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,psi),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
curry (X,A,psi) is Relation-like Function-like set
(curry (X,A,psi)) . phi is set
dom (X,psi,A,phi) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
Funcs ((S,X),BOOLEAN) is non empty functional FUNCTION_DOMAIN of (S,X), BOOLEAN
phi is non empty set
(S,X,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (S,phi) } is set
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
curry (S,X,phi) is Relation-like Function-like set
[:(S,phi),(Funcs ((S,X),BOOLEAN)):] is non empty Relation-like set
bool [:(S,phi),(Funcs ((S,X),BOOLEAN)):] is non empty set
PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf S) *) \ {{}}, BOOLEAN )
[:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):] is non empty Relation-like set
bool [:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):] is non empty set
A is non empty Relation-like (S,phi) -defined PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:(S,phi),(PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)):]
dom A is non empty functional Element of bool (S,phi)
bool (S,phi) is non empty set
A1 is set
A2 is Relation-like Function-like Function-yielding V164() (S,phi) Element of (S,phi)
A . A2 is Relation-like Function-like Element of PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)
h is Relation-like ((AllSymbolsOf S) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)
(S,phi,X,A2) is Relation-like ((AllSymbolsOf S) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)
(curry (S,X,phi)) . A2 is set
dom h is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
rng h is Element of bool BOOLEAN
bool BOOLEAN is non empty set
A . A1 is Relation-like Function-like set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
phi is non empty set
(S,X,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (S,phi) } is set
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
[:(S,phi),(S,X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
Funcs ([:(S,phi),(S,X):],BOOLEAN) is non empty functional FUNCTION_DOMAIN of [:(S,phi),(S,X):], BOOLEAN
(S,phi) is non empty Relation-like NAT -defined PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
(S,phi) . X is Relation-like Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
[:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
dom (S,X,phi) is Relation-like (S,phi) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
curry (S,X,phi) is Relation-like Function-like set
uncurry (curry (S,X,phi)) is Relation-like Function-like set
Funcs ((S,X),BOOLEAN) is non empty functional FUNCTION_DOMAIN of (S,X), BOOLEAN
[:(S,phi),(Funcs ((S,X),BOOLEAN)):] is non empty Relation-like set
bool [:(S,phi),(Funcs ((S,X),BOOLEAN)):] is non empty set
A1 is non empty Relation-like (S,phi) -defined Funcs ((S,X),BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:(S,phi),(Funcs ((S,X),BOOLEAN)):]
rng A1 is non empty functional Element of bool (Funcs ((S,X),BOOLEAN))
bool (Funcs ((S,X),BOOLEAN)) is non empty set
dom A1 is non empty functional Element of bool (S,phi)
bool (S,phi) is non empty set
rng (S,X,phi) is Element of bool BOOLEAN
bool BOOLEAN is non empty set
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S,phi) . phi is Relation-like Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
{0} is non empty trivial functional finite V25() 1 -element V167() Element of bool NAT
0 * is non empty functional V25() FinSequence-membered FinSequenceSet of 0
{0} is non empty trivial functional finite V25() 1 -element V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf X, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) : verum } is set
(X) is non low-compounding non own Element of AllSymbolsOf X
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(X)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) : verum } is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
S ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
AllSymbolsOf X is non empty non trivial non finite V167() set
N is non empty Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
v1 is non empty Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
N ^ v1 is non empty Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
S is Element of AllSymbolsOf X
<*S*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() set
[1,S] is non empty V34() set
{[1,S]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
<*S*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(S,X) is set
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
(S) is non low-compounding non own Element of AllSymbolsOf S
<*(S)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf S
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(S)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (S,phi) } is set
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
(S,X,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
(S,phi,(S,X,phi)) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:]
[:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
dom (S,phi,(S,X,phi)) is Relation-like (S,phi) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
[:(S,phi),(S,X):] is Relation-like set
(S,(S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
{ H₁(b₁,b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : S₁[] } is set
[:(S,phi), { H₁(b₁,b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : S₁[] } :] is Relation-like set
[:(S,phi),(S,X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
Funcs ([:(S,phi),(S,X):],BOOLEAN) is non empty functional FUNCTION_DOMAIN of [:(S,phi),(S,X):], BOOLEAN
[:[:(S,phi),(S,X):],BOOLEAN:] is non empty Relation-like set
bool [:[:(S,phi),(S,X):],BOOLEAN:] is non empty set
H is non empty Relation-like [:(S,phi),(S,X):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(S,phi),(S,X):],BOOLEAN:]
dom H is non empty Relation-like non empty-yielding (S,phi) -defined (S,X) -valued Element of bool [:(S,phi),(S,X):]
bool [:(S,phi),(S,X):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like Function-like Function-yielding V164() (S,phi) Element of (S,phi), b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}} : verum } is set
m1 is set
s2 is Relation-like Function-like Function-yielding V164() (S,phi) Element of (S,phi)
i2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[s2,i2] is non empty V34() Element of [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
dom (S,X,phi) is Relation-like (S,phi) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
m2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),m2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),m2),m1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[s2,m2] is non empty V34() Element of [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
[s2,m1] is non empty V34() Element of [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
q is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X)
qq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X)
(S,(S)) ^ q is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
((S,(S)) ^ q) ^ qq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
[s2,H₁(q,qq)] is non empty V34() set
m1 is set
s2 is set
i2 is set
[s2,i2] is non empty V34() set
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X)
q is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X)
(S,(S)) ^ m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
((S,(S)) ^ m1) ^ q is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
qq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),qq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
p is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),qq),p) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
m2 is Relation-like Function-like Function-yielding V164() (S,phi) Element of (S,phi)
[m2,m1] is non empty V34() Element of [:(S,phi),(S,X):]
[:(S,phi),(S,X):] is non empty Relation-like set
[m2,q] is non empty V34() Element of [:(S,phi),(S,X):]
STT is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[m2,STT] is non empty V34() Element of [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(S,X) is set
LettersOf S is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " {0} is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf S, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (S,phi) } is set
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
(S,X,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
(S,phi,(S,X,phi)) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:]
[:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
dom (S,phi,(S,X,phi)) is Relation-like (S,phi) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
[:(S,phi),(S,X):] is Relation-like set
(S) is non low-compounding non own Element of AllSymbolsOf S
{ H₁(b₁,b₂) where b₁ is literal Element of LettersOf S, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : S₁[] } is set
[:(S,phi), { H₁(b₁,b₂) where b₁ is literal Element of LettersOf S, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : S₁[] } :] is Relation-like set
[:(S,phi),(S,X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
Funcs ([:(S,phi),(S,X):],BOOLEAN) is non empty functional FUNCTION_DOMAIN of [:(S,phi),(S,X):], BOOLEAN
[:[:(S,phi),(S,X):],BOOLEAN:] is non empty Relation-like set
bool [:[:(S,phi),(S,X):],BOOLEAN:] is non empty set
T is non empty Relation-like [:(S,phi),(S,X):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(S,phi),(S,X):],BOOLEAN:]
dom T is non empty Relation-like non empty-yielding (S,phi) -defined (S,X) -valued Element of bool [:(S,phi),(S,X):]
bool [:(S,phi),(S,X):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like Function-like Function-yielding V164() (S,phi) Element of (S,phi), b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}} : verum } is set
s2 is set
i2 is Relation-like Function-like Function-yielding V164() (S,phi) Element of (S,phi)
m2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[i2,m2] is non empty V34() Element of [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
dom (S,X,phi) is Relation-like (S,phi) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
q is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[i2,q] is non empty V34() Element of [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
m1 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
(S,m1) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
TermSymbolsOf S is non empty set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
[1,m1] is non empty V34() set
{[1,m1]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(S,(S,m1),q) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
p is literal Element of LettersOf S
(S,p) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
[1,p] is non empty V34() set
{[1,p]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
qq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X)
(S,(S,p),qq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
s2 is set
i2 is set
m2 is set
[i2,m2] is non empty V34() set
q is literal Element of LettersOf S
qq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X)
<*q*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() set
[1,q] is non empty V34() set
{[1,q]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
<*q*> ^ qq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
m1 is Relation-like Function-like Function-yielding V164() (S,phi) Element of (S,phi)
[m1,qq] is non empty V34() Element of [:(S,phi),(S,X):]
[:(S,phi),(S,X):] is non empty Relation-like set
p is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
(S,p) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
[1,p] is non empty V34() set
{[1,p]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
STT is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,p),STT) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
S is V51() V53() eligible Language-like
(S,(X + 1)) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
(S,X) is set
AllSymbolsOf S is non empty non trivial non finite V167() set
LettersOf S is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U3 of S is Element of the U1 of S
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " {0} is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf S, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
(S,X) is set
(S) is non low-compounding non own Element of AllSymbolsOf S
<*(S)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf S
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(S)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
(S,X) \/ (S,X) is set
((S,X) \/ (S,X)) \/ (S,X) is non empty set
the non empty set is non empty set
(S, the non empty set ) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))))
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
the U2 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
the non empty set * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of the non empty set
the non empty set \/ BOOLEAN is non empty set
PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)) is non empty functional M26( the non empty set * , the non empty set \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf S),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) : b₁ is (S, the non empty set ) } is set
the Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set ) is Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set )
(S, the non empty set ) is non empty Relation-like NAT -defined PFuncs ([:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):]
[:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
PFuncs ([:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
[:NAT,(PFuncs ([:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
A1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S, the non empty set ) . A1 is Relation-like Function-like Element of PFuncs ([:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
curry ((S, the non empty set ) . A1) is Relation-like Function-like set
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S, the non empty set ) . A is Relation-like Function-like Element of PFuncs ([:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
[:[:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
(S,(X + 1), the non empty set ) is Relation-like [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
(S,X, the non empty set ) is Relation-like [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
m1 is Relation-like [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:]
Funcs ((S,(X + 1)),BOOLEAN) is non empty functional FUNCTION_DOMAIN of (S,(X + 1)), BOOLEAN
[:(S, the non empty set ),(Funcs ((S,(X + 1)),BOOLEAN)):] is non empty Relation-like set
bool [:(S, the non empty set ),(Funcs ((S,(X + 1)),BOOLEAN)):] is non empty set
[:(S,(X + 1)),BOOLEAN:] is non empty Relation-like set
bool [:(S,(X + 1)),BOOLEAN:] is non empty set
s2 is non empty Relation-like (S, the non empty set ) -defined Funcs ((S,(X + 1)),BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:(S, the non empty set ),(Funcs ((S,(X + 1)),BOOLEAN)):]
s2 . the Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set ) is Relation-like (S,(X + 1)) -defined BOOLEAN -valued Function-like total quasi_total Element of Funcs ((S,(X + 1)),BOOLEAN)
[:(S, the non empty set ),(S,X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf S),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN)))) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs (( the non empty set *),( the non empty set \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
Funcs ([:(S, the non empty set ),(S,X):],BOOLEAN) is non empty functional FUNCTION_DOMAIN of [:(S, the non empty set ),(S,X):], BOOLEAN
[:[:(S, the non empty set ),(S,X):],BOOLEAN:] is non empty Relation-like set
bool [:[:(S, the non empty set ),(S,X):],BOOLEAN:] is non empty set
i2 is non empty Relation-like (S,(X + 1)) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(S,(X + 1)),BOOLEAN:]
dom i2 is non empty functional V25() FinSequence-membered V166() V167() Element of bool (S,(X + 1))
bool (S,(X + 1)) is non empty set
dom s2 is non empty functional Element of bool (S, the non empty set )
bool (S, the non empty set ) is non empty set
proj1 ((S, the non empty set ) . A1) is set
{ the Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set )} is non empty trivial functional finite 1 -element Element of bool (S, the non empty set )
proj2 (proj1 ((S, the non empty set ) . A1)) is set
[:{ the Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set )},(proj2 (proj1 ((S, the non empty set ) . A1))):] is Relation-like set
(proj1 ((S, the non empty set ) . A1)) /\ [:{ the Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set )},(proj2 (proj1 ((S, the non empty set ) . A1))):] is Relation-like set
(proj1 ((S, the non empty set ) . A1)) typed/\ [:{ the Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set )},(proj2 (proj1 ((S, the non empty set ) . A1))):] is Element of bool (proj1 ((S, the non empty set ) . A1))
bool (proj1 ((S, the non empty set ) . A1)) is non empty set
(proj1 ((S, the non empty set ) . A1)) /\typed [:{ the Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set )},(proj2 (proj1 ((S, the non empty set ) . A1))):] is Relation-like { the Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set )} -defined proj2 (proj1 ((S, the non empty set ) . A1)) -valued Element of bool [:{ the Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set )},(proj2 (proj1 ((S, the non empty set ) . A1))):]
bool [:{ the Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set )},(proj2 (proj1 ((S, the non empty set ) . A1))):] is non empty set
proj2 ((proj1 ((S, the non empty set ) . A1)) /\ [:{ the Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set )},(proj2 (proj1 ((S, the non empty set ) . A1))):]) is set
(S, the non empty set ,((S, the non empty set ) . A)) is Relation-like [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:]
(S, the non empty set ,((S, the non empty set ) . A)) is Relation-like [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:]
(S, the non empty set ,((S, the non empty set ) . A)) +* (S, the non empty set ,((S, the non empty set ) . A)) is Relation-like [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:]
((S, the non empty set ,((S, the non empty set ) . A)) +* (S, the non empty set ,((S, the non empty set ) . A))) +* m1 is Relation-like [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:]
[:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
m1 is Relation-like [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:]
dom m1 is Relation-like (S, the non empty set ) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):]
bool [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
dom (S, the non empty set ,((S, the non empty set ) . A)) is Relation-like (S, the non empty set ) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):]
dom m1 is Relation-like (S, the non empty set ) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):]
p is Relation-like (S, the non empty set ) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):]
m2 is non empty Relation-like [:(S, the non empty set ),(S,X):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(S, the non empty set ),(S,X):],BOOLEAN:]
dom m2 is non empty Relation-like non empty-yielding (S, the non empty set ) -defined (S,X) -valued Element of bool [:(S, the non empty set ),(S,X):]
bool [:(S, the non empty set ),(S,X):] is non empty set
dom ((S, the non empty set ,((S, the non empty set ) . A)) +* (S, the non empty set ,((S, the non empty set ) . A))) is Relation-like (S, the non empty set ) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):]
(dom ((S, the non empty set ,((S, the non empty set ) . A)) +* (S, the non empty set ,((S, the non empty set ) . A)))) \/ (dom m1) is Relation-like (S, the non empty set ) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):]
q is Relation-like (S, the non empty set ) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):]
qq is Relation-like (S, the non empty set ) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):]
q \/ qq is Relation-like (S, the non empty set ) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):]
(q \/ qq) \/ p is Relation-like (S, the non empty set ) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S, the non empty set ),(((AllSymbolsOf S) *) \ {{}}):]
[:(S, the non empty set ),(S,X):] is Relation-like set
[:(S, the non empty set ),(S,X):] is Relation-like set
[:(S, the non empty set ),((S,X) \/ (S,X)):] is Relation-like set
[:(S, the non empty set ),((S,X) \/ (S,X)):] \/ [:(S, the non empty set ),(S,X):] is non empty Relation-like set
[:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] is non empty Relation-like set
bool [:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] is non empty set
[:{ the Relation-like Function-like Function-yielding V164() (S, the non empty set ) Element of (S, the non empty set )},(((S,X) \/ (S,X)) \/ (S,X)):] is non empty Relation-like set
tq is Relation-like (S, the non empty set ) -defined ((S,X) \/ (S,X)) \/ (S,X) -valued Element of bool [:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):]
[:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] /\ tq is Relation-like (S, the non empty set ) -defined ((S,X) \/ (S,X)) \/ (S,X) -valued Element of bool [:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):]
[:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] typed/\ tq is Relation-like (S, the non empty set ) -defined ((S,X) \/ (S,X)) \/ (S,X) -valued Element of bool [:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):]
[:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] /\ tq is Relation-like (S, the non empty set ) -defined ((S,X) \/ (S,X)) \/ (S,X) -valued set
[:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] /\typed tq is Relation-like (S, the non empty set ) -defined ((S,X) \/ (S,X)) \/ (S,X) -valued Element of bool tq
bool tq is non empty set
tq null [:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] is Relation-like [:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] \/ (proj1 tq) -defined [:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] \/ (proj2 tq) -valued set
proj1 tq is set
[:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] \/ (proj1 tq) is non empty set
proj2 tq is set
[:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] \/ (proj2 tq) is non empty set
tq \typed/ [:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] is Relation-like Element of bool (tq \/ [:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):])
tq \/ [:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] is non empty Relation-like set
bool (tq \/ [:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):]) is non empty set
rng ([:(S, the non empty set ),(((S,X) \/ (S,X)) \/ (S,X)):] /\ tq) is Element of bool (((S,X) \/ (S,X)) \/ (S,X))
bool (((S,X) \/ (S,X)) \/ (S,X)) is non empty set
X is V51() V53() eligible Language-like
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b₁ is 0wff } is set
AllSymbolsOf X is non empty non trivial non finite V167() set
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
{} .--> {} is trivial Relation-like {{}} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite set
bool [:{{}},{{}}:] is non empty finite V25() set
(AllSymbolsOf X) -concatenation is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() V201((AllSymbolsOf X) * ) Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
MultPlace ((AllSymbolsOf X) -concatenation) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf X) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
v1 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
phi is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite V167() set
h is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
ar h is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . h is set
abs (ar h) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,h) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,h] is non empty V34() set
{[1,h]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
t is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar h) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
(X -multiCat) . t is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,h) ^ ((X -multiCat) . t) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
H is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
ar H is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X . H is set
abs (ar H) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,H) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,H] is non empty V34() set
{[1,H]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
T is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar H) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
(X -multiCat) . T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,H) ^ ((X -multiCat) . T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
psi is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
v1 ^ psi is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
A is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
phi ^ A is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
((X -multiCat) . t) ^ psi is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,h) ^ (((X -multiCat) . t) ^ psi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
((X,H) ^ ((X -multiCat) . T)) ^ A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
((X -multiCat) . T) ^ A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,H) ^ (((X -multiCat) . T) ^ A) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
((X,H) ^ (((X -multiCat) . T) ^ A)) . 1 is set
(abs (ar h)) -tuples_on (AllTermsOf X) is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of AllTermsOf X
(X -multiCat) .: ((abs (ar h)) -tuples_on (AllTermsOf X)) is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
dom (X -multiCat) is non empty functional V25() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
i2 is non empty Relation-like non empty-yielding NAT -defined AllTermsOf X -valued Function-like finite abs (ar h) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (abs (ar h)) -tuples_on (AllTermsOf X)
(X -multiCat) . i2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
m1 is AllSymbolsOf X -prefix X -prefix set
m2 is non empty Relation-like non empty-yielding NAT -defined AllTermsOf X -valued Function-like finite abs (ar h) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (abs (ar h)) -tuples_on (AllTermsOf X)
(X -multiCat) . m2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
q is Relation-like NAT -defined (AllSymbolsOf X) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of ((AllSymbolsOf X) *) *
(X -multiCat) . q is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of (AllSymbolsOf X) *
((X -multiCat) . q) ^ psi is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
qq is Relation-like NAT -defined (AllSymbolsOf X) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of ((AllSymbolsOf X) *) *
(X -multiCat) . qq is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of (AllSymbolsOf X) *
((X -multiCat) . qq) ^ A is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
X is V51() V53() eligible Language-like
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b₁ is 0wff } is set
S is set
X is V51() V53() eligible Language-like
(X,0) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b₁ is 0wff } is set
S is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
I is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
N is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
I is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
(S,0) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
(S,X) \ (S,0) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
(S,X) typed\ (S,0) is functional V25() FinSequence-membered V166() Element of bool (S,X)
bool (S,X) is non empty set
(S,X) \ (S,0) is functional V25() FinSequence-membered V166() Element of bool (S,X)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
v1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
v1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
AllSymbolsOf S is non empty non trivial non finite V167() set
(S) is non low-compounding non own Element of AllSymbolsOf S
the U3 of S is Element of the U1 of S
(S,(S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
(S,(X + 1)) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
LettersOf S is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " {0} is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
(S,X) is set
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf S, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
(S,X) is set
<*(S)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf S
{ ((<*(S)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
(S,X) \/ (S,X) is set
((S,X) \/ (S,X)) \/ (S,X) is non empty set
A1 is literal Element of LettersOf S
(S,A1) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
TermSymbolsOf S is non empty set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
[1,A1] is non empty V34() set
{[1,A1]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X)
(S,(S,A1),A2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
t is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
(S,t) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
[1,t] is non empty V34() set
{[1,t]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,X) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,t),h) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
A1 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
(S,A1) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
TermSymbolsOf S is non empty set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
[1,A1] is non empty V34() set
{[1,A1]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,X) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,A1),A2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X)
(S,(S,(S)),A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X)
(S,(S,(S,(S)),A1),A2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,X) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),h) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,X) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),h),t) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
X is V51() V53() eligible Language-like
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non low-compounding non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,S) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,S) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),phi),I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
S + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
(X,S) is set
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
{ ((<*(X)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) : verum } is set
(X,(S + 1)) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,S) is set
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf X, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) : verum } is set
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
(X,(X,(X)),A2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
(X,(X,(X,(X)),A2),h) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) \/ (X,S) is set
((X,S) \/ (X,S)) \/ (X,S) is non empty set
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,(S + 1))
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non low-compounding non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),S),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
v1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
psi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 * psi is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
v1 + (0 * psi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
0 * v1 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
psi + (0 * v1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
v1 + psi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,v1 + (0 * psi)) (X) Element of ((AllSymbolsOf X) *) \ {{}}
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,psi + (0 * v1)) (X) Element of ((AllSymbolsOf X) *) \ {{}}
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,v1 + psi) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,v1 + psi) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),A1),A2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,(v1 + psi) + 1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(v1 + psi) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite V167() set
I is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,I) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,I] is non empty V34() set
{[1,I]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,S) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,I),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
S + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
(X,S) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
(X,S) is set
(X) is non low-compounding non own Element of AllSymbolsOf X
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(X)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) : verum } is set
(X,(S + 1)) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,S) is set
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf X, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) : verum } is set
A2 is literal Element of LettersOf X
(X,A2) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
[1,A2] is non empty V34() set
{[1,A2]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
(X,(X,A2),h) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) \/ (X,S) is set
((X,S) \/ (X,S)) \/ (X,S) is non empty set
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,(S + 1))
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,S) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,S] is non empty V34() set
{[1,S]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,S),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
I is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,I) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,S),N) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,I + 1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
I + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite V167() set
phi is non relational Element of AllSymbolsOf X
(X,phi) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,phi] is non empty V34() set
{[1,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,phi),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X -firstChar) . (X,(X,phi),S) is Element of AllSymbolsOf X
(X,(X,phi),S) . 1 is set
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite V167() set
I is non relational Element of AllSymbolsOf X
(X,I) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,I] is non empty V34() set
{[1,I]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,I),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,I),S),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,S,phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,I),(X,S,phi)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(X) is non low-compounding non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
S is Element of AllSymbolsOf X
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,S) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,S] is non empty V34() set
{[1,S]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,S),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite V167() set
phi is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,phi) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,phi] is non empty V34() set
{[1,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,phi),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X -firstChar) . (X,(X,phi),S) is Element of AllSymbolsOf X
(X,(X,phi),S) . 1 is set
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
S is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,phi) (X) Element of ((AllSymbolsOf X) *) \ {{}} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,phi) (X) Element of ((AllSymbolsOf X) *) \ {{}}
AllSymbolsOf X is non empty non trivial non finite V167() set
the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X, the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1, the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X] is non empty V34() set
{[1, the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(X,(X, the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X), the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,phi) (X) Element of ((AllSymbolsOf X) *) \ {{}}) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,phi + 1) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,S) (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . phi is Element of AllSymbolsOf X
X is V51() V53() eligible Language-like
S is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite V167() set
the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
I is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
I + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,I) (X) Element of ((AllSymbolsOf X) *) \ {{}} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,I) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X, the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1, the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X] is non empty V34() set
{[1, the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(X,(X, the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X), the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,I) (X) Element of ((AllSymbolsOf X) *) \ {{}}) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,I + 1) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,S) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
the non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X, the non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set ) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X, the non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set ) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(X) is non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
S . 1 is set
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,v1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
A is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,A) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
[1,A] is non empty V34() set
{[1,A]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,phi) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,A),A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,phi + 1) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
A is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,A) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
[1,A] is non empty V34() set
{[1,A]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,phi) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,A),A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,phi + 1) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,phi) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),A) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,phi) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),A),A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,phi + 1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,phi) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),A) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,phi) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),A),A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,phi + 1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,A,A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),(X,A,A1)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),(X,A,A1)) . 1 is set
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite V167() set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . S is Element of AllSymbolsOf X
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(X) is non low-compounding non relational non own Element of AllSymbolsOf X
S . 1 is set
psi is literal Element of LettersOf X
phi is Element of AllSymbolsOf X
S . 1 is set
psi is Element of AllSymbolsOf X
S . 1 is set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
AtomicFormulasOf S is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}} : b₁ is 0wff } is set
(S) is non low-compounding non relational non own Element of AllSymbolsOf S
the U3 of S is Element of the U1 of S
(S,0) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
S -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
[:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V167() set
(AllSymbolsOf S) -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(AllSymbolsOf S) -pr1 is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total V201( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf S),(AllSymbolsOf S)) is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
MultPlace ((AllSymbolsOf S) -pr1) is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,phi) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
phi + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(S,(phi + 1)) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
(S,(phi + 1)) \ (S,0) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
(S,(phi + 1)) typed\ (S,0) is functional V25() FinSequence-membered V166() Element of bool (S,(phi + 1))
bool (S,(phi + 1)) is non empty set
(S,(phi + 1)) \ (S,0) is functional V25() FinSequence-membered V166() Element of bool (S,(phi + 1))
h is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,phi + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
s2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
s2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
H is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
i2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,phi + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
m2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
m2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
s2 + m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
q is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
m2 + q is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
t is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
h ^ t is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
T is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
H ^ T is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
qq is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
(S,qq) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
TermSymbolsOf S is non empty set
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
[1,qq] is non empty V34() set
{[1,qq]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
p is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,s2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,qq),p) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,s2 + 1) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
qq is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
(S,qq) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
TermSymbolsOf S is non empty set
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
[1,qq] is non empty V34() set
{[1,qq]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
p is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,s2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,qq),p) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,s2 + 1) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
STT is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
(S,STT) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
[1,STT] is non empty V34() set
{[1,STT]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
qqq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,m2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,STT),qqq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,m2 + 1) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
STT is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
(S,STT) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
[1,STT] is non empty V34() set
{[1,STT]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
qqq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,m2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,STT),qqq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,m2 + 1) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,STT),qqq) ^ T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
p ^ t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,qq) ^ (p ^ t) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
qqq ^ T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,STT) ^ (qqq ^ T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
((S,STT) ^ (qqq ^ T)) . 1 is set
(S,qq) ^ (qqq ^ T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
0 * m1 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
s2 + (0 * m1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
0 * q is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
m2 + (0 * q) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S,(S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
STT is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,m2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),STT) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf S) *) \ {{}}
qqq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,m2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),STT),qqq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,m2 + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
STT is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,m2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),STT) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf S) *) \ {{}}
qqq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,m2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),STT),qqq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,m2 + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
m1 . 1 is set
i2 ^ T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(i2 ^ T) . 1 is set
i2 . 1 is set
(S,STT,qqq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),(S,STT,qqq)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),(S,STT,qqq)) . 1 is set
(S,(S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(S,(S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
qq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,s2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),qq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf S) *) \ {{}}
p is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,s2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),qq),p) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,s2 + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
qq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,s2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),qq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf S) *) \ {{}}
p is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,s2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),qq),p) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,s2 + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
m1 . 1 is set
(S,qq,p) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),(S,qq,p)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),(S,qq,p)) . 1 is set
STT is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
(S,STT) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
TermSymbolsOf S is non empty set
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
[1,STT] is non empty V34() set
{[1,STT]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
qqq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,m2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,STT),qqq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,m2 + 1) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
STT is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
(S,STT) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
TermSymbolsOf S is non empty set
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
[1,STT] is non empty V34() set
{[1,STT]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
qqq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,m2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,STT),qqq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,m2 + 1) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
i2 ^ T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(i2 ^ T) . 1 is set
(S,(S,STT),qqq) . 1 is set
STT is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,m2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),STT) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf S) *) \ {{}}
qqq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,m2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),STT),qqq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,m2 + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
STT is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,m2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),STT) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf S) *) \ {{}}
qqq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,m2) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),STT),qqq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,m2 + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
0 * m1 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
s2 + (0 * m1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
0 * q is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
m2 + (0 * q) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S,qq,p) ^ t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,(S)) ^ ((S,qq,p) ^ t) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,(S,(S)),(S,qq,p)) ^ t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,(S,(S,(S)),STT),qqq) ^ T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,STT,qqq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),(S,STT,qqq)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),(S,STT,qqq)) ^ T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,STT,qqq) ^ T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,(S)) ^ ((S,STT,qqq) ^ T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
qqq ^ T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
STT ^ (qqq ^ T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
p ^ t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
qq ^ (p ^ t) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,(S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
h is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
H is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
t is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
h ^ t is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
T is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
H ^ T is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,phi + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
AtomicFormulaSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
TheNorSymbOf S is set
{(TheNorSymbOf S)} is non empty trivial finite 1 -element set
(AllSymbolsOf S) \ {(TheNorSymbOf S)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
(AllSymbolsOf S) typed\ {(TheNorSymbOf S)} is Element of bool (AllSymbolsOf S)
i2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (S, 0 ) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S -firstChar) . i2 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
m1 . 1 is set
s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,phi + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
s2 ^ T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(s2 ^ T) . 1 is set
s2 . 1 is set
(S -firstChar) . s2 is Element of AllSymbolsOf S
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,phi + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,phi + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S -firstChar) . s2 is Element of AllSymbolsOf S
s2 . 1 is set
m1 ^ t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(m1 ^ t) . 1 is set
m1 . 1 is set
i2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S -firstChar) . i2 is non relational Element of AllSymbolsOf S
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,phi + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
X is V51() V53() eligible Language-like
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
phi is set
X is V51() V53() eligible Language-like
(X) is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (X,b₂) } is set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
N is set
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
psi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (X,b₂) } is set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X)
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
N is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is V51() V53() eligible Language-like
(X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (X,b₂) } is set
I is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
v1 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
N is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
I ^ N is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
psi is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
v1 ^ psi is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
A1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
A1 + A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,(A1 + A2)) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
0 * A2 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
A1 + (0 * A2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
0 * A1 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
A2 + (0 * A1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,A1 + A2) (X) Element of ((AllSymbolsOf X) *) \ {{}}
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,A1 + A2) (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
(X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (X,b₂) } is set
S is set
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (S,phi) } is set
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,X,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
(S,phi,(S,X,phi)) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:]
[:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
dom (S,phi,(S,X,phi)) is Relation-like (S,phi) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
(S,X) is set
(S,X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
(S) is non low-compounding non relational non own Element of AllSymbolsOf S
<*(S)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf S
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(S)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
[:(S,phi),(S,X):] is Relation-like set
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (S,phi) } is set
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,X,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
(S,phi,(S,X,phi)) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:]
[:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
dom (S,phi,(S,X,phi)) is Relation-like (S,phi) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
(S,X) is set
LettersOf S is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " {0} is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
(S,X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf S, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
[:(S,phi),(S,X):] is Relation-like set
X is non empty set
2 -tuples_on X is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of X
(X) is non empty Relation-like 2 -tuples_on X -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on X),BOOLEAN:]
[:(2 -tuples_on X),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on X),BOOLEAN:] is non empty set
X * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of X
[:(X *),(X *):] is non empty non trivial Relation-like non finite V167() set
X -concatenation is non empty Relation-like [:(X *),(X *):] -defined X * -valued Function-like total quasi_total Function-yielding V164() V198() V201(X * ) Element of bool [:[:(X *),(X *):],(X *):]
[:[:(X *),(X *):],(X *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X *),(X *):],(X *):] is non empty non trivial non finite V167() set
1 -tuples_on X is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of X
id (1 -tuples_on X) is non empty Relation-like non empty-yielding 1 -tuples_on X -defined 1 -tuples_on X -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on X),(1 -tuples_on X):]
[:(1 -tuples_on X),(1 -tuples_on X):] is non empty Relation-like set
bool [:(1 -tuples_on X),(1 -tuples_on X):] is non empty set
(X -concatenation) .: (id (1 -tuples_on X)) is functional V25() FinSequence-membered Element of bool (X *)
bool (X *) is non empty non trivial non finite V167() set
chi (((X -concatenation) .: (id (1 -tuples_on X))),(2 -tuples_on X)) is non empty Relation-like 2 -tuples_on X -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on X),BOOLEAN:]
(X) " {1} is functional V25() FinSequence-membered V166() Element of bool (2 -tuples_on X)
bool (2 -tuples_on X) is non empty set
((1 -tuples_on X)) is non empty Relation-like non empty-yielding 1 -tuples_on X -defined 1 -tuples_on X -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on X),(1 -tuples_on X):]
(X -concatenation) .: ((1 -tuples_on X)) is functional V25() FinSequence-membered Element of bool (X *)
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(1 + 1) -tuples_on X is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of X
((X -concatenation) .: ((1 -tuples_on X))) /\ ((1 + 1) -tuples_on X) is functional V25() FinSequence-membered Element of bool (X *)
((X -concatenation) .: ((1 -tuples_on X))) typed/\ ((1 + 1) -tuples_on X) is functional V25() FinSequence-membered Element of bool ((X -concatenation) .: ((1 -tuples_on X)))
bool ((X -concatenation) .: ((1 -tuples_on X))) is non empty set
((X -concatenation) .: ((1 -tuples_on X))) /\ ((1 + 1) -tuples_on X) is set
((X -concatenation) .: ((1 -tuples_on X))) /\typed ((1 + 1) -tuples_on X) is functional V25() FinSequence-membered V166() Element of bool ((1 + 1) -tuples_on X)
bool ((1 + 1) -tuples_on X) is non empty set
(X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):] is functional V25() FinSequence-membered Element of bool (X *)
((X -concatenation) .: ((1 -tuples_on X))) /\ ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) is functional V25() FinSequence-membered Element of bool (X *)
((X -concatenation) .: ((1 -tuples_on X))) typed/\ ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) is functional V25() FinSequence-membered Element of bool ((X -concatenation) .: ((1 -tuples_on X)))
((X -concatenation) .: ((1 -tuples_on X))) /\ ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) is set
((X -concatenation) .: ((1 -tuples_on X))) /\typed ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) is functional V25() FinSequence-membered Element of bool ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):])
bool ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) is non empty set
phi is functional V25() FinSequence-membered Element of bool ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):])
phi /\ ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) is functional V25() FinSequence-membered Element of bool (X *)
phi typed/\ ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) is functional V25() FinSequence-membered Element of bool phi
bool phi is non empty set
phi /\ ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) is set
phi /\typed ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) is functional V25() FinSequence-membered Element of bool ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):])
phi null ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) is set
((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) /\ phi is functional V25() FinSequence-membered Element of bool ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):])
((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) typed/\ phi is functional V25() FinSequence-membered Element of bool ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):])
((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) /\ phi is set
((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) /\typed phi is functional V25() FinSequence-membered Element of bool phi
phi \typed/ ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) is functional V25() Element of bool (phi \/ ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]))
phi \/ ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):]) is functional V25() set
bool (phi \/ ((X -concatenation) .: [:(1 -tuples_on X),(1 -tuples_on X):])) is non empty set
X is non empty set
2 -tuples_on X is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of X
(X) is non empty Relation-like 2 -tuples_on X -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on X),BOOLEAN:]
[:(2 -tuples_on X),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on X),BOOLEAN:] is non empty set
X * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of X
[:(X *),(X *):] is non empty non trivial Relation-like non finite V167() set
X -concatenation is non empty Relation-like [:(X *),(X *):] -defined X * -valued Function-like total quasi_total Function-yielding V164() V198() V201(X * ) Element of bool [:[:(X *),(X *):],(X *):]
[:[:(X *),(X *):],(X *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X *),(X *):],(X *):] is non empty non trivial non finite V167() set
1 -tuples_on X is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of X
id (1 -tuples_on X) is non empty Relation-like non empty-yielding 1 -tuples_on X -defined 1 -tuples_on X -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on X),(1 -tuples_on X):]
[:(1 -tuples_on X),(1 -tuples_on X):] is non empty Relation-like set
bool [:(1 -tuples_on X),(1 -tuples_on X):] is non empty set
(X -concatenation) .: (id (1 -tuples_on X)) is functional V25() FinSequence-membered Element of bool (X *)
bool (X *) is non empty non trivial non finite V167() set
chi (((X -concatenation) .: (id (1 -tuples_on X))),(2 -tuples_on X)) is non empty Relation-like 2 -tuples_on X -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on X),BOOLEAN:]
(X) " {1} is functional V25() FinSequence-membered V166() Element of bool (2 -tuples_on X)
bool (2 -tuples_on X) is non empty set
{ <*b₁,b₁*> where b₁ is Element of X : verum } is set
((1 -tuples_on X)) is non empty Relation-like non empty-yielding 1 -tuples_on X -defined 1 -tuples_on X -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on X),(1 -tuples_on X):]
(X -concatenation) .: ((1 -tuples_on X)) is functional V25() FinSequence-membered Element of bool (X *)
X is V51() V53() eligible Language-like
TheEqSymbOf X is set
the U2 of X is Element of the U1 of X
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite V167() set
X is V51() V53() eligible Language-like
(X) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
the U2 of X is Element of the U1 of X
ar (X) is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . (X) is set
(ar (X)) + 2 is complex ext-real V40() V41() set
phi is set
abs (ar (X)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar (X))) - 2 is complex ext-real V40() V41() set
abs (- 2) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
- (- 2) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
phi is set
X is V51() V53() eligible Language-like
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
S is non empty set
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
phi is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . phi is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
SubTerms phi is Relation-like NAT -defined (proj2 phi) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . phi)) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
ar ((X -firstChar) . phi) is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . ((X -firstChar) . phi) is set
abs (ar ((X -firstChar) . phi)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
proj2 phi is non empty finite set
(proj2 phi) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 phi
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(TermSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
I is Relation-like Function-like Function-yielding V164() (X,S) set
(X,S,I,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,I) is Relation-like Function-like Function-yielding V164() (X,S) (X,S,I) set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
I +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
(X,S,I,(X,S,I),((X -firstChar) . phi)) is non empty Relation-like (abs (ar ((X -firstChar) . phi))) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,(X -firstChar) . phi)
(abs (ar ((X -firstChar) . phi))) -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
(X,S,I) is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
(X,S,I) (*) (SubTerms phi) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,I,(X,S,I),((X -firstChar) . phi)) . ((X,S,I) (*) (SubTerms phi)) is set
I . ((X -firstChar) . phi) is Relation-like Function-like set
(I . ((X -firstChar) . phi)) . ((X,S,I) (*) (SubTerms phi)) is set
(S) . ((X,S,I) (*) (SubTerms phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b₁ is 0wff } is set
ar (X) is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X . (X) is set
abs (ar (X)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar (X))) - 2 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
{(X)} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf X)
{(X)} is non empty trivial finite 1 -element set
(X) .--> (S) is trivial Relation-like AllSymbolsOf X -defined {(X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(X)},{(S)}:]
[:{(X)},{(S)}:] is non empty Relation-like finite set
bool [:{(X)},{(S)}:] is non empty finite V25() set
dom ((X) .--> (S)) is trivial finite Element of bool {(X)}
bool {(X)} is non empty finite V25() set
{(X)} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf X)
{(X)} is non empty trivial finite 1 -element set
(X) .--> (S) is trivial Relation-like AllSymbolsOf X -defined {(X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(X)},{(S)}:]
[:{(X)},{(S)}:] is non empty Relation-like finite set
bool [:{(X)},{(S)}:] is non empty finite V25() set
dom ((X) .--> (S)) is trivial finite Element of bool {(X)}
bool {(X)} is non empty finite V25() set
((X) .--> (S)) . ((X -firstChar) . phi) is Relation-like Function-like set
X is V51() V53() eligible Language-like
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
S is non empty set
phi is Relation-like Function-like Function-yielding V164() (X,S) set
(X,S,phi) is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
I is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . I is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(X,S,phi,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,phi) is Relation-like Function-like Function-yielding V164() (X,S) (X,S,phi) set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
phi +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
(X,S,phi,(X,S,phi),((X -firstChar) . I)) is non empty Relation-like (abs (ar ((X -firstChar) . I))) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,(X -firstChar) . I)
ar ((X -firstChar) . I) is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . ((X -firstChar) . I) is set
abs (ar ((X -firstChar) . I)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((X -firstChar) . I))) -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
SubTerms I is Relation-like NAT -defined (proj2 I) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . I)) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
proj2 I is non empty finite set
(proj2 I) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 I
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(TermSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(X,S,phi) (*) (SubTerms I) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,phi,(X,S,phi),((X -firstChar) . I)) . ((X,S,phi) (*) (SubTerms I)) is set
(SubTerms I) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,S,phi) . ((SubTerms I) . 1) is set
(SubTerms I) . 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,S,phi) . ((SubTerms I) . 2) is set
{ <*b₁,b₁*> where b₁ is Element of S : verum } is set
{ <*b₁,b₂*> where b₁, b₂ is Element of S : verum } is set
ar (X) is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X . (X) is set
abs (ar (X)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar (X))) - 2 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
m1 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(X,S,phi,(X,S,phi),m1) is non empty Relation-like (abs (ar m1)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,m1)
ar m1 is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X . m1 is set
abs (ar m1) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar m1)) -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
(S) . ((X,S,phi) (*) (SubTerms I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
(S) " {1} is functional V25() FinSequence-membered V166() Element of bool (2 -tuples_on S)
bool (2 -tuples_on S) is non empty set
m2 is Relation-like NAT -defined AllTermsOf X -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() FinSequence of AllTermsOf X
(X,S,phi) * m2 is Relation-like NAT -defined S -valued Function-like finite 2 -element len m2 -element FinSequence-like FinSubsequence-like V199() FinSequence of S
len m2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
m1 is Relation-like NAT -defined S -valued Function-like finite FinSequence-like FinSubsequence-like V199() FinSequence of S
q is non empty Relation-like NAT -defined S -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like V199() Element of 2 -tuples_on S
qq is Element of S
p is Element of S
<*qq,p*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like V199() set
<*qq*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() set
[1,qq] is non empty V34() set
{[1,qq]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
<*p*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() set
[1,p] is non empty V34() set
{[1,p]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
<*qq*> ^ <*p*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element 1 + 1 -element FinSequence-like FinSubsequence-like V199() set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
q . 1 is set
q . 2 is set
len m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
Seg (len m1) is finite len m1 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : ( 1 <= b₁ & b₁ <= len m1 ) } is set
dom m1 is finite Element of bool NAT
m1 . 1 is set
m1 . 2 is set
STT is Element of S
<*STT,STT*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like V199() set
<*STT*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() set
[1,STT] is non empty V34() set
{[1,STT]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
<*STT*> ^ <*STT*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element 1 + 1 -element FinSequence-like FinSubsequence-like V199() set
X is V51() V53() eligible Language-like
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S) is set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X,S) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf X, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) : verum } is set
the literal Element of LettersOf X is literal Element of LettersOf X
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
(X, the literal Element of LettersOf X) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[1, the literal Element of LettersOf X] is non empty V34() set
{[1, the literal Element of LettersOf X]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(X,(X, the literal Element of LettersOf X), the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
A is set
X is V51() V53() eligible Language-like
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S) is set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X,S) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
(X) is non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(X)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) : verum } is set
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X,(X,(X)), the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)), the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)), the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
phi is set
X is V51() V53() eligible Language-like
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S) is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X,S) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
(X) is non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(X)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) : verum } is set
psi is set
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
(X,(X,(X)),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
(X,(X,(X,(X)),phi),A) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite V167() set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . S is Element of AllSymbolsOf X
phi is Element of AllSymbolsOf X
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
(X,S) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
(X) is non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(X)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) : verum } is set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
(X,(X,(X)),A) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
(X,(X,(X,(X)),A),A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . A2 is Element of AllSymbolsOf X
A2 . 1 is set
(X,A,A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),(X,A,A1)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),(X,A,A1)) . 1 is set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(S,X) is non empty set
LettersOf S is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U3 of S is Element of the U1 of S
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " {0} is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(S,X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf S, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,(X + 1)) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
(S) is non low-compounding non relational non own Element of AllSymbolsOf S
<*(S)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf S
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(S)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
(S,(X + 1)) \ (S,X) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
(S,(X + 1)) typed\ (S,X) is functional V25() FinSequence-membered V166() Element of bool (S,(X + 1))
bool (S,(X + 1)) is non empty set
(S,(X + 1)) \ (S,X) is functional V25() FinSequence-membered V166() Element of bool (S,(X + 1))
(S,X) \/ (S,X) is non empty set
((S,X) \/ (S,X)) \/ (S,X) is non empty set
(((S,X) \/ (S,X)) \/ (S,X)) \ (S,X) is Element of bool (((S,X) \/ (S,X)) \/ (S,X))
bool (((S,X) \/ (S,X)) \/ (S,X)) is non empty set
(((S,X) \/ (S,X)) \/ (S,X)) typed\ (S,X) is Element of bool (((S,X) \/ (S,X)) \/ (S,X))
((S,X) \/ (S,X)) \ (S,X) is Element of bool ((S,X) \/ (S,X))
bool ((S,X) \/ (S,X)) is non empty set
((S,X) \/ (S,X)) typed\ (S,X) is Element of bool ((S,X) \/ (S,X))
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,S) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,S] is non empty V34() set
{[1,S]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,S),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,S),phi)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(X,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X) is non low-compounding non relational non own Element of AllSymbolsOf X
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
A is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
A + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,A) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
(X,A) is non empty set
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf X, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,A) : verum } is set
A2 is literal Element of LettersOf X
(X,A2) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
[1,A2] is non empty V34() set
{[1,A2]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,A)
(X,(X,A2),h) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,phi) + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
X is V51() V53() eligible Language-like
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S) is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X,S) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf X, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) : verum } is set
psi is set
phi is literal Element of LettersOf X
(X,phi) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[1,phi] is non empty V34() set
{[1,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
(X,(X,phi),A) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(X,S) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf X, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S) : verum } is set
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
psi is literal Element of LettersOf X
(X,psi) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[1,psi] is non empty V34() set
{[1,psi]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,S)
(X,(X,psi),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
(S,X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
(S) is non low-compounding non relational non own Element of AllSymbolsOf S
the U3 of S is Element of the U1 of S
<*(S)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf S
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(S)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
LettersOf S is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " {0} is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf S, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
(S,(X + 1)) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
(S,(X + 1)) \ (S,X) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
(S,(X + 1)) typed\ (S,X) is functional V25() FinSequence-membered V166() Element of bool (S,(X + 1))
bool (S,(X + 1)) is non empty set
(S,(X + 1)) \ (S,X) is functional V25() FinSequence-membered V166() Element of bool (S,(X + 1))
(S,X) \/ (S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
((S,X) \/ (S,X)) \/ (S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
(((S,X) \/ (S,X)) \/ (S,X)) \ (S,X) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
(((S,X) \/ (S,X)) \/ (S,X)) typed\ (S,X) is functional V25() FinSequence-membered V166() Element of bool (((S,X) \/ (S,X)) \/ (S,X))
bool (((S,X) \/ (S,X)) \/ (S,X)) is non empty set
(((S,X) \/ (S,X)) \/ (S,X)) \ (S,X) is functional V25() FinSequence-membered V166() Element of bool (((S,X) \/ (S,X)) \/ (S,X))
((S,X) \/ (S,X)) \ (S,X) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
((S,X) \/ (S,X)) typed\ (S,X) is functional V25() FinSequence-membered V166() Element of bool ((S,X) \/ (S,X))
bool ((S,X) \/ (S,X)) is non empty set
((S,X) \/ (S,X)) \ (S,X) is functional V25() FinSequence-membered V166() Element of bool ((S,X) \/ (S,X))
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(X) is non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite V167() set
phi is non literal Element of AllSymbolsOf X
(X,phi) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,phi] is non empty V34() set
{[1,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,phi),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X -firstChar) . (X,(X,phi),S) is Element of AllSymbolsOf X
(X,(X,phi),S) . 1 is set
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite V167() set
I is non literal Element of AllSymbolsOf X
(X,I) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,I] is non empty V34() set
{[1,I]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,I),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,I),S),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,S,phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,I),(X,S,phi)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(X) is non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
S is Element of AllSymbolsOf X
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (X,b₂) } is set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
I is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),S),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X,(X)),S),phi)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(X,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (X,b₂) } is set
h is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
h + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,h) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,h) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
{ ((<*(X)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,h) : verum } is set
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,h)
(X,(X,(X)),H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,h)
(X,(X,(X,(X)),H),T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S,phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),(X,S,phi)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,H,T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),(X,H,T)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,h) (X) Element of ((AllSymbolsOf X) *) \ {{}}
s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,h) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,m1,s2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,phi) + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),S),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X,(X)),S),phi)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(X,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((X,S),(X,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(max ((X,S),(X,phi))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(max ((X,S),(X,phi))) - (X,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(max ((X,S),(X,phi))) - (X,phi) is complex ext-real V40() V41() set
A1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 * A1 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(X,S) + (0 * A1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 * A2 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(X,phi) + (0 * A2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S) + A1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,phi) + A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),S),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((X,S),(X,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,(X,(X,(X,(X)),S),phi)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(max ((X,S),(X,phi))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(max ((X,S),(X,phi))) + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite V167() set
phi is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,phi) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,phi] is non empty V34() set
{[1,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,phi),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,(X,(X,phi),S)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite V167() set
phi is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,phi) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,phi] is non empty V34() set
{[1,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,phi),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,(X,S)) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (X,S) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,(X,(X,phi),S)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(X,S) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,(X,S)) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,phi),psi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,(X,S) + 1) (X,(X,psi)) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,psi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
N is Relation-like set
proj1 N is set
v1 is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))
[:(OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))):] is non empty Relation-like set
bool [:(OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))):] is non empty set
X is V51() V53() eligible Language-like
S is non empty set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
N is Relation-like Function-like Function-yielding V164() (X,S) Element of (X,S)
proj1 N is set
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
the Relation-like OwnSymbolsOf X -defined Function-like Function-yielding V164() (X,S) Element of (X,S) is Relation-like OwnSymbolsOf X -defined Function-like Function-yielding V164() (X,S) Element of (X,S)
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
N is Relation-like OwnSymbolsOf X -defined Function-like Function-yielding V164() (X,S) Element of (X,S)
dom N is Element of bool (OwnSymbolsOf X)
bool (OwnSymbolsOf X) is non empty set
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
AllSymbolsOf X is non empty non trivial non finite V167() set
phi is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
I is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
N is Element of S
(phi,I,N) is Relation-like Function-like Function-yielding V164() (X,S) set
{} .--> N is trivial Relation-like {{}} -defined S -valued Function-like one-to-one constant finite V199() set
{{}} --> N is non empty Relation-like {{}} -defined S -valued {N} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{N}:]
{N} is non empty trivial finite 1 -element set
[:{{}},{N}:] is non empty Relation-like finite set
bool [:{{}},{N}:] is non empty finite V25() set
I .--> ({} .--> N) is trivial Relation-like AllSymbolsOf X -defined {I} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{I} is non empty trivial finite 1 -element set
{I} --> ({} .--> N) is non empty Relation-like {I} -defined {({} .--> N)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{I},{({} .--> N)}:]
{({} .--> N)} is non empty trivial functional finite V25() 1 -element set
[:{I},{({} .--> N)}:] is non empty Relation-like finite set
bool [:{I},{({} .--> N)}:] is non empty finite V25() set
phi +* (I .--> ({} .--> N)) is Relation-like Function-like Function-yielding V164() set
{{}} --> N is non empty Relation-like {{}} -defined S -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},S:]
[:{{}},S:] is non empty Relation-like set
bool [:{{}},S:] is non empty set
I .--> ({{}} --> N) is trivial Relation-like AllSymbolsOf X -defined {I} -defined bool [:{{}},S:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{I} --> ({{}} --> N) is non empty Relation-like non-empty non empty-yielding {I} -defined bool [:{{}},S:] -valued {({{}} --> N)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{I},{({{}} --> N)}:]
{({{}} --> N)} is non empty trivial functional finite V25() 1 -element V166() V167() set
[:{I},{({{}} --> N)}:] is non empty Relation-like finite set
bool [:{I},{({{}} --> N)}:] is non empty finite V25() set
A2 is own ofAtomicFormula Element of AllSymbolsOf X
{I} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
dom (I .--> ({{}} --> N)) is trivial finite Element of bool {I}
bool {I} is non empty finite V25() set
bool (OwnSymbolsOf X) is non empty set
proj1 (phi,I,N) is set
dom phi is Element of bool (OwnSymbolsOf X)
h is Element of bool (OwnSymbolsOf X)
(dom phi) \/ h is Element of bool (OwnSymbolsOf X)
(OwnSymbolsOf X) \/ h is non empty set
(OwnSymbolsOf X) null h is set
(OwnSymbolsOf X) \typed/ h is Element of bool ((OwnSymbolsOf X) \/ h)
bool ((OwnSymbolsOf X) \/ h) is non empty set
t is Relation-like OwnSymbolsOf X -defined Function-like set
t | (OwnSymbolsOf X) is Relation-like OwnSymbolsOf X -defined OwnSymbolsOf X -defined Function-like set
t null (OwnSymbolsOf X) is Relation-like (OwnSymbolsOf X) \/ (proj1 t) -defined (OwnSymbolsOf X) \/ (proj2 t) -valued Function-like set
proj1 t is set
(OwnSymbolsOf X) \/ (proj1 t) is non empty set
proj2 t is set
(OwnSymbolsOf X) \/ (proj2 t) is non empty set
t \typed/ (OwnSymbolsOf X) is Element of bool (t \/ (OwnSymbolsOf X))
t \/ (OwnSymbolsOf X) is non empty set
bool (t \/ (OwnSymbolsOf X)) is non empty set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
I is non empty set
I * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of I
I \/ BOOLEAN is non empty set
PFuncs ((I *),(I \/ BOOLEAN)) is non empty functional M26(I * ,I \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((I *),(I \/ BOOLEAN))
(S,I) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((I *),(I \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) : b₁ is (S,I) } is set
(S,X,I) is Relation-like [:(S,I),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
[:(S,I),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
PFuncs ([:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,I),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
v1 is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,I) Element of (S,I)
(S,I,X,v1) is Relation-like ((AllSymbolsOf S) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf S) *) \ {{}}, BOOLEAN )
curry (S,X,I) is Relation-like Function-like set
(curry (S,X,I)) . v1 is set
(S,I,X,v1) . phi is set
[v1,phi] is non empty V34() Element of [:(S,I),(((AllSymbolsOf S) *) \ {{}}):]
[:(S,I),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
(S,X,I) . [v1,phi] is set
(S,X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
[:(S,I),(S,X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
Funcs ([:(S,I),(S,X):],BOOLEAN) is non empty functional FUNCTION_DOMAIN of [:(S,I),(S,X):], BOOLEAN
[:[:(S,I),(S,X):],BOOLEAN:] is non empty Relation-like set
bool [:[:(S,I),(S,X):],BOOLEAN:] is non empty set
A1 is non empty Relation-like [:(S,I),(S,X):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(S,I),(S,X):],BOOLEAN:]
dom A1 is non empty Relation-like non empty-yielding (S,I) -defined (S,X) -valued Element of bool [:(S,I),(S,X):]
bool [:(S,I),(S,X):] is non empty set
dom (S,X,I) is Relation-like (S,I) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,I),(((AllSymbolsOf S) *) \ {{}}):]
bool [:(S,I),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
dom (S,I,X,v1) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
(S,X,I) . (v1,phi) is set
[v1,phi] is non empty V34() set
(S,X,I) . [v1,phi] is set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(S,X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (S,phi) } is set
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
[:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
[:(S,phi),(S,X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
I is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
(S,I) is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
TermSymbolsOf S is non empty set
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
[1,I] is non empty V34() set
{[1,I]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,I),N) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,1 + (S,N)) (S,(S,N)) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (S,N) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
v1 is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,phi) Element of (S,phi)
(S) is non literal non low-compounding non relational non own Element of AllSymbolsOf S
(S) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (S,b₂) } is set
t is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:]
dom t is Relation-like (S,phi) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):]
bool [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
(S,phi,v1,t,(S,(S,I),N)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
m1 is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf S
(S,I) ^ m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
((S,I) ^ m1) /^ 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,(S,I),N) . 1 is set
(S,(S,I),N) /^ 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
i2 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
s2 is Element of phi
(S,phi,v1,i2,s2) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,phi) Element of (S,phi)
{} .--> s2 is trivial Relation-like {{}} -defined phi -valued Function-like one-to-one constant finite V199() set
{{}} --> s2 is non empty Relation-like {{}} -defined phi -valued {s2} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{s2}:]
{s2} is non empty trivial finite 1 -element set
[:{{}},{s2}:] is non empty Relation-like finite set
bool [:{{}},{s2}:] is non empty finite V25() set
i2 .--> ({} .--> s2) is trivial Relation-like AllSymbolsOf S -defined {i2} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{i2} is non empty trivial finite 1 -element set
{i2} --> ({} .--> s2) is non empty Relation-like {i2} -defined {({} .--> s2)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{i2},{({} .--> s2)}:]
{({} .--> s2)} is non empty trivial functional finite V25() 1 -element set
[:{i2},{({} .--> s2)}:] is non empty Relation-like finite set
bool [:{i2},{({} .--> s2)}:] is non empty finite V25() set
v1 +* (i2 .--> ({} .--> s2)) is Relation-like Function-like Function-yielding V164() set
t . ((S,phi,v1,i2,s2),((S,(S,I),N) /^ 1)) is set
[(S,phi,v1,i2,s2),((S,(S,I),N) /^ 1)] is non empty V34() set
t . [(S,phi,v1,i2,s2),((S,(S,I),N) /^ 1)] is set
m2 is Element of phi
(S,phi,v1,I,m2) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,phi) Element of (S,phi)
{} .--> m2 is trivial Relation-like {{}} -defined phi -valued Function-like one-to-one constant finite V199() set
{{}} --> m2 is non empty Relation-like {{}} -defined phi -valued {m2} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{m2}:]
{m2} is non empty trivial finite 1 -element set
[:{{}},{m2}:] is non empty Relation-like finite set
bool [:{{}},{m2}:] is non empty finite V25() set
I .--> ({} .--> m2) is trivial Relation-like AllSymbolsOf S -defined {I} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{I} is non empty trivial finite 1 -element set
{I} --> ({} .--> m2) is non empty Relation-like {I} -defined {({} .--> m2)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{I},{({} .--> m2)}:]
{({} .--> m2)} is non empty trivial functional finite V25() 1 -element set
[:{I},{({} .--> m2)}:] is non empty Relation-like finite set
bool [:{I},{({} .--> m2)}:] is non empty finite V25() set
v1 +* (I .--> ({} .--> m2)) is Relation-like Function-like Function-yielding V164() set
t . ((S,phi,v1,I,m2),N) is set
[(S,phi,v1,I,m2),N] is non empty V34() set
t . [(S,phi,v1,I,m2),N] is set
s2 is Element of phi
(S,phi,v1,I,s2) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,phi) Element of (S,phi)
{} .--> s2 is trivial Relation-like {{}} -defined phi -valued Function-like one-to-one constant finite V199() set
{{}} --> s2 is non empty Relation-like {{}} -defined phi -valued {s2} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{s2}:]
{s2} is non empty trivial finite 1 -element set
[:{{}},{s2}:] is non empty Relation-like finite set
bool [:{{}},{s2}:] is non empty finite V25() set
I .--> ({} .--> s2) is trivial Relation-like AllSymbolsOf S -defined {I} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{I} --> ({} .--> s2) is non empty Relation-like {I} -defined {({} .--> s2)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{I},{({} .--> s2)}:]
{({} .--> s2)} is non empty trivial functional finite V25() 1 -element set
[:{I},{({} .--> s2)}:] is non empty Relation-like finite set
bool [:{I},{({} .--> s2)}:] is non empty finite V25() set
v1 +* (I .--> ({} .--> s2)) is Relation-like Function-like Function-yielding V164() set
t . ((S,phi,v1,I,s2),N) is set
[(S,phi,v1,I,s2),N] is non empty V34() set
t . [(S,phi,v1,I,s2),N] is set
T is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf S
T . 1 is set
T /^ 1 is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf S
m2 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
i2 is Element of phi
(S,phi,v1,m2,i2) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,phi) Element of (S,phi)
{} .--> i2 is trivial Relation-like {{}} -defined phi -valued Function-like one-to-one constant finite V199() set
{{}} --> i2 is non empty Relation-like {{}} -defined phi -valued {i2} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{i2}:]
{i2} is non empty trivial finite 1 -element set
[:{{}},{i2}:] is non empty Relation-like finite set
bool [:{{}},{i2}:] is non empty finite V25() set
m2 .--> ({} .--> i2) is trivial Relation-like AllSymbolsOf S -defined {m2} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{m2} is non empty trivial finite 1 -element set
{m2} --> ({} .--> i2) is non empty Relation-like {m2} -defined {({} .--> i2)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{m2},{({} .--> i2)}:]
{({} .--> i2)} is non empty trivial functional finite V25() 1 -element set
[:{m2},{({} .--> i2)}:] is non empty Relation-like finite set
bool [:{m2},{({} .--> i2)}:] is non empty finite V25() set
v1 +* (m2 .--> ({} .--> i2)) is Relation-like Function-like Function-yielding V164() set
t . ((S,phi,v1,m2,i2),(T /^ 1)) is set
[(S,phi,v1,m2,i2),(T /^ 1)] is non empty V34() set
t . [(S,phi,v1,m2,i2),(T /^ 1)] is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
phi is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,phi) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,phi] is non empty V34() set
{[1,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,phi),I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,1 + (X,I)) (X,(X,I)) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (X,I) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
N is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
(X,S,N,(X,(X,phi),I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,S),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
(X,I) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
[:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
(X,S) is non empty Relation-like NAT -defined PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
(X,(X,I)) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
(X,((X,I) + 1)) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,(X,I)) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,((X,I) + 1),S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,(X,I),S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,(X,I)) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(X)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,(X,I)) : verum } is set
(X,(X,I)) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf X, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,(X,I)) : verum } is set
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,(X,I) + 1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
q is literal Element of LettersOf X
(X,q) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
[1,q] is non empty V34() set
{[1,q]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,(X,I))
(X,(X,q),m1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
[N,H] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
[:(X,S),(X,(X,I)):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
[:(X,S),(X,(X,I)):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):]
(X,S,(X,(X,I),S)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom (X,S,(X,(X,I),S)) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
(X,S,(X,(X,I),S)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom (X,S,(X,(X,I),S)) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
s2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S) . s2 is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S) . m1 is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,S,((X,S) . m1)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,((X,S) . m1)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,((X,S) . m1)) +* (X,S,((X,S) . m1)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
((X,S,((X,S) . m1)) +* (X,S,((X,S) . m1))) +* ((X,S) . m1) is Relation-like Function-like set
[:(X,S),(X,(X,I)):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):]
Funcs ([:(X,S),(X,(X,I)):],BOOLEAN) is non empty functional FUNCTION_DOMAIN of [:(X,S),(X,(X,I)):], BOOLEAN
[:[:(X,S),(X,(X,I)):],BOOLEAN:] is non empty Relation-like set
bool [:[:(X,S),(X,(X,I)):],BOOLEAN:] is non empty set
proj1 ((X,S) . m1) is set
tq is non empty Relation-like [:(X,S),(X,(X,I)):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(X,S),(X,(X,I)):],BOOLEAN:]
dom tq is non empty Relation-like non empty-yielding (X,S) -defined (X,(X,I)) -valued Element of bool [:(X,S),(X,(X,I)):]
bool [:(X,S),(X,(X,I)):] is non empty set
tq is non empty Relation-like [:(X,S),(X,(X,I)):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(X,S),(X,(X,I)):],BOOLEAN:]
dom tq is non empty Relation-like non empty-yielding (X,S) -defined (X,(X,I)) -valued Element of bool [:(X,S),(X,(X,I)):]
bool [:(X,S),(X,(X,I)):] is non empty set
(X,S,N,H) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,((X,I) + 1),N) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf X) *) \ {{}}, BOOLEAN )
curry (X,((X,I) + 1),S) is Relation-like Function-like set
(curry (X,((X,I) + 1),S)) . N is set
(X,S,((X,I) + 1),N) . H is set
(X,((X,I) + 1),S) . [N,H] is set
((X,S) . s2) . [N,H] is set
((X,S,((X,S) . m1)) +* (X,S,((X,S) . m1))) . [N,H] is set
(X,S,((X,S) . m1)) +* (X,S,(X,(X,I),S)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
((X,S,((X,S) . m1)) +* (X,S,(X,(X,I),S))) . [N,H] is set
(X,S,((X,S) . m1)) . [N,H] is set
H₁((X,(X,I),S)) . (N,H) is set
[N,H] is non empty V34() set
(X,S,(X,(X,I),S)) . [N,H] is set
(X,S,N,(X,(X,I),S),H) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
g1 is Element of S
(X,S,N,phi,g1) is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
{} .--> g1 is trivial Relation-like {{}} -defined S -valued Function-like one-to-one constant finite V199() set
{{}} --> g1 is non empty Relation-like {{}} -defined S -valued {g1} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{g1}:]
{g1} is non empty trivial finite 1 -element set
[:{{}},{g1}:] is non empty Relation-like finite set
bool [:{{}},{g1}:] is non empty finite V25() set
phi .--> ({} .--> g1) is trivial Relation-like AllSymbolsOf X -defined {phi} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{phi} is non empty trivial finite 1 -element set
{phi} --> ({} .--> g1) is non empty Relation-like {phi} -defined {({} .--> g1)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{phi},{({} .--> g1)}:]
{({} .--> g1)} is non empty trivial functional finite V25() 1 -element set
[:{phi},{({} .--> g1)}:] is non empty Relation-like finite set
bool [:{phi},{({} .--> g1)}:] is non empty finite V25() set
N +* (phi .--> ({} .--> g1)) is Relation-like Function-like Function-yielding V164() set
(X,(X,I),S) . ((X,S,N,phi,g1),t) is set
[(X,S,N,phi,g1),t] is non empty V34() set
(X,(X,I),S) . [(X,S,N,phi,g1),t] is set
(X,S,(X,S,N,phi,g1),t) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,(X,I),(X,S,N,phi,g1)) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
curry (X,(X,I),S) is Relation-like Function-like set
(curry (X,(X,I),S)) . (X,S,N,phi,g1) is set
(X,S,(X,I),(X,S,N,phi,g1)) . t is set
g1 is Element of S
(X,S,N,phi,g1) is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
{} .--> g1 is trivial Relation-like {{}} -defined S -valued Function-like one-to-one constant finite V199() set
{{}} --> g1 is non empty Relation-like {{}} -defined S -valued {g1} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{g1}:]
{g1} is non empty trivial finite 1 -element set
[:{{}},{g1}:] is non empty Relation-like finite set
bool [:{{}},{g1}:] is non empty finite V25() set
phi .--> ({} .--> g1) is trivial Relation-like AllSymbolsOf X -defined {phi} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{phi} is non empty trivial finite 1 -element set
{phi} --> ({} .--> g1) is non empty Relation-like {phi} -defined {({} .--> g1)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{phi},{({} .--> g1)}:]
{({} .--> g1)} is non empty trivial functional finite V25() 1 -element set
[:{phi},{({} .--> g1)}:] is non empty Relation-like finite set
bool [:{phi},{({} .--> g1)}:] is non empty finite V25() set
N +* (phi .--> ({} .--> g1)) is Relation-like Function-like Function-yielding V164() set
(X,S,(X,S,N,phi,g1),t) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,(X,I),S) . ((X,S,N,phi,g1),t) is set
[(X,S,N,phi,g1),t] is non empty V34() set
(X,(X,I),S) . [(X,S,N,phi,g1),t] is set
(X,S,(X,I),(X,S,N,phi,g1)) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
curry (X,(X,I),S) is Relation-like Function-like set
(curry (X,(X,I),S)) . (X,S,N,phi,g1) is set
(X,S,(X,I),(X,S,N,phi,g1)) . t is set
g1 is Element of S
(X,S,N,phi,g1) is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
{} .--> g1 is trivial Relation-like {{}} -defined S -valued Function-like one-to-one constant finite V199() set
{{}} --> g1 is non empty Relation-like {{}} -defined S -valued {g1} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{g1}:]
{g1} is non empty trivial finite 1 -element set
[:{{}},{g1}:] is non empty Relation-like finite set
bool [:{{}},{g1}:] is non empty finite V25() set
phi .--> ({} .--> g1) is trivial Relation-like AllSymbolsOf X -defined {phi} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{phi} is non empty trivial finite 1 -element set
{phi} --> ({} .--> g1) is non empty Relation-like {phi} -defined {({} .--> g1)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{phi},{({} .--> g1)}:]
{({} .--> g1)} is non empty trivial functional finite V25() 1 -element set
[:{phi},{({} .--> g1)}:] is non empty Relation-like finite set
bool [:{phi},{({} .--> g1)}:] is non empty finite V25() set
N +* (phi .--> ({} .--> g1)) is Relation-like Function-like Function-yielding V164() set
(X,S,(X,S,N,phi,g1),I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
g2 is Element of S
(X,S,N,phi,g2) is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
{} .--> g2 is trivial Relation-like {{}} -defined S -valued Function-like one-to-one constant finite V199() set
{{}} --> g2 is non empty Relation-like {{}} -defined S -valued {g2} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{g2}:]
{g2} is non empty trivial finite 1 -element set
[:{{}},{g2}:] is non empty Relation-like finite set
bool [:{{}},{g2}:] is non empty finite V25() set
phi .--> ({} .--> g2) is trivial Relation-like AllSymbolsOf X -defined {phi} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{phi} --> ({} .--> g2) is non empty Relation-like {phi} -defined {({} .--> g2)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{phi},{({} .--> g2)}:]
{({} .--> g2)} is non empty trivial functional finite V25() 1 -element set
[:{phi},{({} .--> g2)}:] is non empty Relation-like finite set
bool [:{phi},{({} .--> g2)}:] is non empty finite V25() set
N +* (phi .--> ({} .--> g2)) is Relation-like Function-like Function-yielding V164() set
(X,(X,I),S) . ((X,S,N,phi,g2),t) is set
[(X,S,N,phi,g2),t] is non empty V34() set
(X,(X,I),S) . [(X,S,N,phi,g2),t] is set
dx is Element of S
(X,S,N,phi,dx) is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
{} .--> dx is trivial Relation-like {{}} -defined S -valued Function-like one-to-one constant finite V199() set
{{}} --> dx is non empty Relation-like {{}} -defined S -valued {dx} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{dx}:]
{dx} is non empty trivial finite 1 -element set
[:{{}},{dx}:] is non empty Relation-like finite set
bool [:{{}},{dx}:] is non empty finite V25() set
phi .--> ({} .--> dx) is trivial Relation-like AllSymbolsOf X -defined {phi} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{phi} --> ({} .--> dx) is non empty Relation-like {phi} -defined {({} .--> dx)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{phi},{({} .--> dx)}:]
{({} .--> dx)} is non empty trivial functional finite V25() 1 -element set
[:{phi},{({} .--> dx)}:] is non empty Relation-like finite set
bool [:{phi},{({} .--> dx)}:] is non empty finite V25() set
N +* (phi .--> ({} .--> dx)) is Relation-like Function-like Function-yielding V164() set
(X,S,(X,S,N,phi,dx),t) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(S,X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
(S) is non literal non low-compounding non relational non own Element of AllSymbolsOf S
(S,(S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
I is non empty set
I * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of I
I \/ BOOLEAN is non empty set
PFuncs ((I *),(I \/ BOOLEAN)) is non empty functional M26(I * ,I \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((I *),(I \/ BOOLEAN))
(S,I) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined PFuncs ((I *),(I \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) : b₁ is (S,I) } is set
[:(S,I),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
[:[:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
[:(S,I),(S,X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN)))) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((I *),(I \/ BOOLEAN))))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),N) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),N),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
v1 is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,I) Element of (S,I)
(S) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (S,b₂) } is set
H is Relation-like [:(S,I),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(S,I),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN:]
dom H is Relation-like (S,I) -defined ((AllSymbolsOf S) *) \ {{}} -valued Element of bool [:(S,I),(((AllSymbolsOf S) *) \ {{}}):]
bool [:(S,I),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V167() set
(S,I,H,v1,(S,(S,(S,(S)),N),phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
H . (v1,N) is set
[v1,N] is non empty V34() set
H . [v1,N] is set
H . (v1,phi) is set
[v1,phi] is non empty V34() set
H . [v1,phi] is set
[v1,N] is non empty V34() Element of [:(S,I),(((AllSymbolsOf S) *) \ {{}}):]
[:(S,I),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
i2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[v1,i2] is non empty V34() Element of [:(S,I),(((AllSymbolsOf S) *) \ {{}}):]
H . (v1,i2) is set
[v1,i2] is non empty V34() set
H . [v1,i2] is set
m2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
H . (v1,m2) is set
[v1,m2] is non empty V34() set
H . [v1,m2] is set
(S,(S,(S)),i2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),i2),m2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,i2,m2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),(S,i2,m2)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,N,phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),(S,N,phi)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),phi),I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X, max ((X,phi),(X,I))) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((X,phi),(X,I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
N is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
(X,S,N,(X,(X,(X,(X)),phi),I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,N,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,N,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,S),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
[:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial Relation-like non finite V167() set
bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:] is non empty non trivial non finite V167() set
(X,S) is non empty Relation-like NAT -defined PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
(max ((X,phi),(X,I))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(max ((X,phi),(X,I))) - (X,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(max ((X,phi),(X,I))) - (X,I) is complex ext-real V40() V41() set
m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 * m1 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(X,phi) + (0 * m1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
s2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 * s2 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(X,I) + (0 * s2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,phi) + m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,I) + s2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
i2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X, max ((X,phi),(X,I))) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),i2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
m2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X, max ((X,phi),(X,I))) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),i2),m2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X, max ((X,i2),(X,m2))) (X,(max ((X,phi),(X,I))) + 1) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,i2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,m2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((X,i2),(X,m2)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,(max ((X,phi),(X,I)))) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
(X,((max ((X,phi),(X,I))) + 1)) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,((max ((X,phi),(X,I))) + 1),S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,(max ((X,phi),(X,I))),S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,(max ((X,phi),(X,I)))) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
{ ((<*(X)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,(max ((X,phi),(X,I)))) : verum } is set
(X,S,(max ((X,phi),(X,I))),N) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf X) *) \ {{}}, BOOLEAN )
curry (X,(max ((X,phi),(X,I))),S) is Relation-like Function-like set
(curry (X,(max ((X,phi),(X,I))),S)) . N is set
(X,S,(max ((X,phi),(X,I))),N) . i2 is set
(X,(max ((X,phi),(X,I))),S) . (N,phi) is set
[N,phi] is non empty V34() set
(X,(max ((X,phi),(X,I))),S) . [N,phi] is set
(X,S,N,m2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,(max ((X,phi),(X,I))),N) . m2 is set
(X,(max ((X,phi),(X,I))),S) . (N,I) is set
[N,I] is non empty V34() set
(X,(max ((X,phi),(X,I))),S) . [N,I] is set
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,(max ((X,phi),(X,I))) + 1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
g2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,(max ((X,phi),(X,I))))
(X,(X,(X)),g2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
dx is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,(max ((X,phi),(X,I))))
(X,(X,(X,(X)),g2),dx) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
[N,m1] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
[:(X,S),(X,(max ((X,phi),(X,I)))):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
(X,S,(X,(max ((X,phi),(X,I))),S)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
dom (X,S,(X,(max ((X,phi),(X,I))),S)) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
qq is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S) . qq is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
q is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S) . q is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(X,S,((X,S) . q)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,((X,S) . q)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
(X,S,((X,S) . q)) +* (X,S,((X,S) . q)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
((X,S,((X,S) . q)) +* (X,S,((X,S) . q))) +* ((X,S) . q) is Relation-like Function-like set
[:(X,S),(X,(max ((X,phi),(X,I)))):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):]
Funcs ([:(X,S),(X,(max ((X,phi),(X,I)))):],BOOLEAN) is non empty functional FUNCTION_DOMAIN of [:(X,S),(X,(max ((X,phi),(X,I)))):], BOOLEAN
[:[:(X,S),(X,(max ((X,phi),(X,I)))):],BOOLEAN:] is non empty Relation-like set
bool [:[:(X,S),(X,(max ((X,phi),(X,I)))):],BOOLEAN:] is non empty set
proj1 ((X,S) . q) is set
o is non empty Relation-like [:(X,S),(X,(max ((X,phi),(X,I)))):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(X,S),(X,(max ((X,phi),(X,I)))):],BOOLEAN:]
dom o is non empty Relation-like non empty-yielding (X,S) -defined (X,(max ((X,phi),(X,I)))) -valued Element of bool [:(X,S),(X,(max ((X,phi),(X,I)))):]
bool [:(X,S),(X,(max ((X,phi),(X,I)))):] is non empty set
o is non empty Relation-like [:(X,S),(X,(max ((X,phi),(X,I)))):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(X,S),(X,(max ((X,phi),(X,I)))):],BOOLEAN:]
dom o is non empty Relation-like non empty-yielding (X,S) -defined (X,(max ((X,phi),(X,I)))) -valued Element of bool [:(X,S),(X,(max ((X,phi),(X,I)))):]
bool [:(X,S),(X,(max ((X,phi),(X,I)))):] is non empty set
(X,S,N,m1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,((max ((X,phi),(X,I))) + 1),N) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
curry (X,((max ((X,phi),(X,I))) + 1),S) is Relation-like Function-like set
(curry (X,((max ((X,phi),(X,I))) + 1),S)) . N is set
(X,S,((max ((X,phi),(X,I))) + 1),N) . m1 is set
(X,((max ((X,phi),(X,I))) + 1),S) . [N,m1] is set
((X,S) . qq) . [N,m1] is set
((X,S,((X,S) . q)) +* (X,S,((X,S) . q))) . [N,m1] is set
(X,S,((X,S) . q)) +* (X,S,(X,(max ((X,phi),(X,I))),S)) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of bool [:[:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN:]
((X,S,((X,S) . q)) +* (X,S,(X,(max ((X,phi),(X,I))),S))) . [N,m1] is set
H₂((X,(max ((X,phi),(X,I))),S)) . (N,m1) is set
[N,m1] is non empty V34() set
(X,S,(X,(max ((X,phi),(X,I))),S)) . [N,m1] is set
(X,S,(X,(max ((X,phi),(X,I))),S),N,m1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),S),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,S) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(X,(X,(X)),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),phi),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X, max ((X,phi),(X,phi))) (X,S + 1) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((X,phi),(X,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(X,(X,(X)),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),S),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X, max ((X,S),(X,S))) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((X,S),(X,S)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(X) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
RelSymbolsOf X is set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
INT \ NAT is Element of bool INT
bool INT is non empty non trivial non finite V167() set
INT typed\ NAT is Element of bool INT
the adicity of X " (INT \ NAT) is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
{(X)} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(RelSymbolsOf X) \ (OwnSymbolsOf X) is Element of bool (RelSymbolsOf X)
bool (RelSymbolsOf X) is non empty set
(RelSymbolsOf X) typed\ (OwnSymbolsOf X) is Element of bool (RelSymbolsOf X)
N is Element of AllSymbolsOf X
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,S) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,S] is non empty V34() set
{[1,S]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,(X,S),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,1 + (X,phi)) (X,(X,phi)) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
1 + (X,phi) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,(X,(X,S),phi)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(X,phi) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),phi),I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X, max ((X,phi),(X,I))) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((X,phi),(X,I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,(X,(X,(X,(X)),phi),I)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
1 + (max ((X,phi),(X,I))) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
LettersOf S is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U3 of S is Element of the U1 of S
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " {0} is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
(S,X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf S, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
(S) is non literal non low-compounding non relational non own Element of AllSymbolsOf S
<*(S)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf S
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(S)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b₁ is (X,S) } is set
v1 is V51() V53() eligible Language-like
AllSymbolsOf v1 is non empty non trivial non finite V167() set
the U1 of v1 is set
AllSymbolsOf v1 is non empty non trivial non finite V167() set
(AllSymbolsOf v1) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf v1
((AllSymbolsOf v1) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf v1) *)
bool ((AllSymbolsOf v1) *) is non empty non trivial non finite V167() set
((AllSymbolsOf v1) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf v1) *)
OwnSymbolsOf v1 is non empty Element of bool (AllSymbolsOf v1)
bool (AllSymbolsOf v1) is non empty non trivial non finite V167() set
the U2 of v1 is Element of the U1 of v1
the U3 of v1 is Element of the U1 of v1
{ the U2 of v1, the U3 of v1} is non empty finite set
the U1 of v1 \ { the U2 of v1, the U3 of v1} is Element of bool the U1 of v1
bool the U1 of v1 is non empty set
the U1 of v1 typed\ { the U2 of v1, the U3 of v1} is Element of bool the U1 of v1
psi is non empty set
psi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of psi
psi \/ BOOLEAN is non empty set
PFuncs ((psi *),(psi \/ BOOLEAN)) is non empty functional M26(psi * ,psi \/ BOOLEAN)
Funcs ((OwnSymbolsOf v1),(PFuncs ((psi *),(psi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf v1, PFuncs ((psi *),(psi \/ BOOLEAN))
(v1,psi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf v1),(PFuncs ((psi *),(psi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf v1),(PFuncs ((psi *),(psi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf v1 -defined PFuncs ((psi *),(psi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf v1),(PFuncs ((psi *),(psi \/ BOOLEAN)))) : b₁ is (v1,psi) } is set
h is V51() V53() eligible Language-like
AllSymbolsOf h is non empty non trivial non finite V167() set
the U1 of h is set
(AllSymbolsOf h) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf h
((AllSymbolsOf h) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf h) *)
bool ((AllSymbolsOf h) *) is non empty non trivial non finite V167() set
((AllSymbolsOf h) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf h) *)
OwnSymbolsOf h is non empty Element of bool (AllSymbolsOf h)
bool (AllSymbolsOf h) is non empty non trivial non finite V167() set
the U2 of h is Element of the U1 of h
the U3 of h is Element of the U1 of h
{ the U2 of h, the U3 of h} is non empty finite set
the U1 of h \ { the U2 of h, the U3 of h} is Element of bool the U1 of h
bool the U1 of h is non empty set
the U1 of h typed\ { the U2 of h, the U3 of h} is Element of bool the U1 of h
t is non empty set
t * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of t
t \/ BOOLEAN is non empty set
PFuncs ((t *),(t \/ BOOLEAN)) is non empty functional M26(t * ,t \/ BOOLEAN)
Funcs ((OwnSymbolsOf h),(PFuncs ((t *),(t \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf h, PFuncs ((t *),(t \/ BOOLEAN))
(h,t) is non empty functional Element of bool (Funcs ((OwnSymbolsOf h),(PFuncs ((t *),(t \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf h),(PFuncs ((t *),(t \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf h -defined PFuncs ((t *),(t \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf h),(PFuncs ((t *),(t \/ BOOLEAN)))) : b₁ is (h,t) } is set
s2 is V51() V53() eligible Language-like
AllSymbolsOf s2 is non empty non trivial non finite V167() set
the U1 of s2 is set
(AllSymbolsOf s2) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf s2
((AllSymbolsOf s2) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf s2) *)
bool ((AllSymbolsOf s2) *) is non empty non trivial non finite V167() set
((AllSymbolsOf s2) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf s2) *)
OwnSymbolsOf s2 is non empty Element of bool (AllSymbolsOf s2)
bool (AllSymbolsOf s2) is non empty non trivial non finite V167() set
the U2 of s2 is Element of the U1 of s2
the U3 of s2 is Element of the U1 of s2
{ the U2 of s2, the U3 of s2} is non empty finite set
the U1 of s2 \ { the U2 of s2, the U3 of s2} is Element of bool the U1 of s2
bool the U1 of s2 is non empty set
the U1 of s2 typed\ { the U2 of s2, the U3 of s2} is Element of bool the U1 of s2
i2 is non empty set
i2 * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of i2
i2 \/ BOOLEAN is non empty set
PFuncs ((i2 *),(i2 \/ BOOLEAN)) is non empty functional M26(i2 * ,i2 \/ BOOLEAN)
Funcs ((OwnSymbolsOf s2),(PFuncs ((i2 *),(i2 \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf s2, PFuncs ((i2 *),(i2 \/ BOOLEAN))
(s2,i2) is non empty functional Element of bool (Funcs ((OwnSymbolsOf s2),(PFuncs ((i2 *),(i2 \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf s2),(PFuncs ((i2 *),(i2 \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf s2 -defined PFuncs ((i2 *),(i2 \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf s2),(PFuncs ((i2 *),(i2 \/ BOOLEAN)))) : b₁ is (s2,i2) } is set
N is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
phi is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,phi) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,phi] is non empty V34() set
{[1,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,phi),I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,1 + (X,I)) (X,(X,I)) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (X,I) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S,N,(X,(X,phi),I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
A1 is Relation-like OwnSymbolsOf v1 -defined Function-like total Function-yielding V164() (v1,psi) Element of (v1,psi)
phi is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf v1
A2 is Element of psi
(v1,psi,A1,phi,A2) is Relation-like OwnSymbolsOf v1 -defined Function-like total Function-yielding V164() (v1,psi) Element of (v1,psi)
{} .--> A2 is trivial Relation-like {{}} -defined psi -valued Function-like one-to-one constant finite V199() set
{{}} --> A2 is non empty Relation-like {{}} -defined psi -valued {A2} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{A2}:]
{A2} is non empty trivial finite 1 -element set
[:{{}},{A2}:] is non empty Relation-like finite set
bool [:{{}},{A2}:] is non empty finite V25() set
phi .--> ({} .--> A2) is trivial Relation-like AllSymbolsOf v1 -defined {phi} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{phi} is non empty trivial finite 1 -element set
{phi} --> ({} .--> A2) is non empty Relation-like {phi} -defined {({} .--> A2)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{phi},{({} .--> A2)}:]
{({} .--> A2)} is non empty trivial functional finite V25() 1 -element set
[:{phi},{({} .--> A2)}:] is non empty Relation-like finite set
bool [:{phi},{({} .--> A2)}:] is non empty finite V25() set
A1 +* (phi .--> ({} .--> A2)) is Relation-like Function-like Function-yielding V164() set
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (v1) Element of ((AllSymbolsOf v1) *) \ {{}}
(v1,psi,(v1,psi,A1,phi,A2),A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(v1,phi) is non empty trivial Relation-like NAT -defined TermSymbolsOf v1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf v1) *) \ {{}}
TermSymbolsOf v1 is non empty set
{ the U3 of v1} is non empty trivial finite 1 -element set
the U1 of v1 \ { the U3 of v1} is non empty Element of bool the U1 of v1
the U1 of v1 typed\ { the U3 of v1} is Element of bool the U1 of v1
the adicity of v1 is non empty Relation-like the U1 of v1 \ { the U3 of v1} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of v1 \ { the U3 of v1}),INT:]
[:( the U1 of v1 \ { the U3 of v1}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of v1 \ { the U3 of v1}),INT:] is non empty non trivial non finite V167() set
the adicity of v1 " NAT is Element of bool ( the U1 of v1 \ { the U3 of v1})
bool ( the U1 of v1 \ { the U3 of v1}) is non empty set
[1,phi] is non empty V34() set
{[1,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(v1,(v1,phi),A) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (v1,1 + (v1,A)) (v1,(v1,A)) (v1) (v1) Element of ((AllSymbolsOf v1) *) \ {{}}
(v1,A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (v1,A) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(v1,psi,A1,(v1,(v1,phi),A)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
m1 is Relation-like OwnSymbolsOf h -defined Function-like total Function-yielding V164() (h,t) Element of (h,t)
(h) is non literal non low-compounding non relational non own Element of AllSymbolsOf h
AllSymbolsOf h is non empty non trivial non finite V167() set
(h,(h)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf h) *) \ {{}}
[1,(h)] is non empty V34() set
{[1,(h)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (h) Element of ((AllSymbolsOf h) *) \ {{}}
(h,(h,(h)),H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (h) Element of ((AllSymbolsOf h) *) \ {{}}
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (h) Element of ((AllSymbolsOf h) *) \ {{}}
(h,(h,(h,(h)),H),T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (h, max ((h,H),(h,T))) (h) (h) Element of ((AllSymbolsOf h) *) \ {{}}
(h,H) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(h,T) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((h,H),(h,T)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(h,t,m1,(h,(h,(h,(h)),H),T)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(h,t,m1,H) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(h,t,m1,T) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
q is Relation-like OwnSymbolsOf s2 -defined Function-like total Function-yielding V164() (s2,i2) Element of (s2,i2)
m2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (s2) Element of ((AllSymbolsOf s2) *) \ {{}}
(s2,i2,q,m2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (s2) Element of ((AllSymbolsOf s2) *) \ {{}}
(s2,i2,q,m1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(s2) is non literal non low-compounding non relational non own Element of AllSymbolsOf s2
AllSymbolsOf s2 is non empty non trivial non finite V167() set
(s2,(s2)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf s2) *) \ {{}}
[1,(s2)] is non empty V34() set
{[1,(s2)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(s2,(s2,(s2)),m2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (s2) Element of ((AllSymbolsOf s2) *) \ {{}}
(s2,(s2,(s2,(s2)),m2),m1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (s2, max ((s2,m2),(s2,m1))) (s2) (s2) Element of ((AllSymbolsOf s2) *) \ {{}}
(s2,m2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(s2,m1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((s2,m2),(s2,m1)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(s2,i2,q,(s2,(s2,(s2,(s2)),m2),m1)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
S is V51() V53() eligible Language-like
AllTermsOf S is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365((((AllSymbolsOf S) *) \ {{}}))
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V167() set
S -termsOfMaxDepth is Relation-like Function-like set
proj2 (S -termsOfMaxDepth) is set
union (proj2 (S -termsOfMaxDepth)) is set
S -termsOfMaxDepth is non empty Relation-like NAT -defined K365((((AllSymbolsOf S) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K365((((AllSymbolsOf S) *) \ {{}})):]
[:NAT,K365((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial non finite V167() set
(S -termsOfMaxDepth) . X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365((((AllSymbolsOf S) *) \ {{}}))
phi is non empty set
Funcs ((AllTermsOf S),phi) is non empty functional FUNCTION_DOMAIN of AllTermsOf S,phi
I is Element of phi
N is Relation-like Function-like Function-yielding V164() (S,phi) set
(S,phi,I,N) is non empty Relation-like NAT -defined Funcs ((AllTermsOf S),phi) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf S),phi)):]
[:NAT,(Funcs ((AllTermsOf S),phi)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(Funcs ((AllTermsOf S),phi)):] is non empty non trivial non finite V167() set
(S,phi,I,N) . (X + 1) is Relation-like AllTermsOf S -defined phi -valued Function-like total quasi_total Element of Funcs ((AllTermsOf S),phi)
((S,phi,I,N) . (X + 1)) | ((S -termsOfMaxDepth) . X) is Relation-like AllTermsOf S -defined (S -termsOfMaxDepth) . X -defined AllTermsOf S -defined phi -valued Function-like Element of bool [:(AllTermsOf S),phi:]
[:(AllTermsOf S),phi:] is non empty Relation-like set
bool [:(AllTermsOf S),phi:] is non empty set
(S,phi,N) is non empty Relation-like AllTermsOf S -defined phi -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),phi:]
(S,phi,N) | ((S -termsOfMaxDepth) . X) is Relation-like AllTermsOf S -defined (S -termsOfMaxDepth) . X -defined AllTermsOf S -defined phi -valued Function-like Element of bool [:(AllTermsOf S),phi:]
psi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S,phi,I,N) . psi is Relation-like AllTermsOf S -defined phi -valued Function-like total quasi_total Element of Funcs ((AllTermsOf S),phi)
bool (AllTermsOf S) is non empty set
v1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S -termsOfMaxDepth) . v1 is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365((((AllSymbolsOf S) *) \ {{}}))
(S -termsOfMaxDepth) . psi is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365((((AllSymbolsOf S) *) \ {{}}))
h is non empty Relation-like AllTermsOf S -defined phi -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),phi:]
t is functional V25() FinSequence-membered V166() Element of bool (AllTermsOf S)
h | t is Relation-like AllTermsOf S -defined t -defined AllTermsOf S -defined phi -valued Function-like total Element of bool [:(AllTermsOf S),phi:]
(S,phi,N) | t is Relation-like AllTermsOf S -defined t -defined AllTermsOf S -defined phi -valued Function-like total Element of bool [:(AllTermsOf S),phi:]
dom (h | t) is functional V25() FinSequence-membered V166() Element of bool t
bool t is non empty set
dom ((S,phi,N) | t) is functional V25() FinSequence-membered V166() Element of bool t
s2 is set
dom h is non empty functional V25() FinSequence-membered V166() V167() Element of bool (AllTermsOf S)
m2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of t
(h | t) . m2 is set
h . m2 is set
((h | t) . m2) \+\ (h . m2) is set
((h | t) . m2) \ (h . m2) is set
((h | t) . m2) typed\ (h . m2) is Element of bool ((h | t) . m2)
bool ((h | t) . m2) is non empty set
((h | t) . m2) \ (h . m2) is Element of bool ((h | t) . m2)
(h . m2) \ ((h | t) . m2) is set
(h . m2) typed\ ((h | t) . m2) is Element of bool (h . m2)
bool (h . m2) is non empty set
(h . m2) \ ((h | t) . m2) is Element of bool (h . m2)
(((h | t) . m2) \ (h . m2)) \/ ((h . m2) \ ((h | t) . m2)) is set
((S,phi,N) | t) . m2 is set
(S,phi,N) . m2 is set
(((S,phi,N) | t) . m2) \+\ ((S,phi,N) . m2) is set
(((S,phi,N) | t) . m2) \ ((S,phi,N) . m2) is set
(((S,phi,N) | t) . m2) typed\ ((S,phi,N) . m2) is Element of bool (((S,phi,N) | t) . m2)
bool (((S,phi,N) | t) . m2) is non empty set
(((S,phi,N) | t) . m2) \ ((S,phi,N) . m2) is Element of bool (((S,phi,N) | t) . m2)
((S,phi,N) . m2) \ (((S,phi,N) | t) . m2) is set
((S,phi,N) . m2) typed\ (((S,phi,N) | t) . m2) is Element of bool ((S,phi,N) . m2)
bool ((S,phi,N) . m2) is non empty set
((S,phi,N) . m2) \ (((S,phi,N) | t) . m2) is Element of bool ((S,phi,N) . m2)
((((S,phi,N) | t) . m2) \ ((S,phi,N) . m2)) \/ (((S,phi,N) . m2) \ (((S,phi,N) | t) . m2)) is set
(h | t) . s2 is set
i2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of AllTermsOf S
h . i2 is Element of phi
((S,phi,N) | t) . s2 is set
(S,phi,N) . s2 is set
(S,phi,N,i2) is Element of phi
X is V51() V53() eligible Language-like
TermSymbolsOf X is non empty set
the U1 of X is set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
S is non empty set
phi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . phi is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
SubTerms phi is Relation-like NAT -defined (proj2 phi) * -valued AllTermsOf X -valued Function-like finite abs (ar phi) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
proj2 phi is non empty finite set
(proj2 phi) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 phi
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
ar phi is complex ext-real V40() V41() Element of INT
ar ((X -firstChar) . phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of X . ((X -firstChar) . phi) is set
abs (ar phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
I is Relation-like Function-like Function-yielding V164() (X,S) set
(X,S,I) is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
(X,S,I) . phi is set
(X,S,I,((X -firstChar) . phi)) is non empty Relation-like (abs (ar ((X -firstChar) . phi))) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,(X -firstChar) . phi)
abs (ar ((X -firstChar) . phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar ((X -firstChar) . phi))) -tuples_on S is non empty functional V25() FinSequence-membered FinSequenceSet of S
S \/ BOOLEAN is non empty set
(X,S,I) (*) (SubTerms phi) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,I,((X -firstChar) . phi)) . ((X,S,I) (*) (SubTerms phi)) is set
the Element of S is Element of S
(X,S, the Element of S,I) is non empty Relation-like NAT -defined Funcs ((AllTermsOf X),S) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf X),S)):]
Funcs ((AllTermsOf X),S) is non empty functional FUNCTION_DOMAIN of AllTermsOf X,S
[:NAT,(Funcs ((AllTermsOf X),S)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(Funcs ((AllTermsOf X),S)):] is non empty non trivial non finite V167() set
Depth phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X -termsOfMaxDepth is non empty Relation-like NAT -defined K365((((AllSymbolsOf X) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):]
[:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial non finite V167() set
(Depth phi) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
0 * 1 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(Depth phi) + (0 * 1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
H is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
H + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
bool (AllTermsOf X) is non empty set
(X -termsOfMaxDepth) . H is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
T is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X -termsOfMaxDepth) . T is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
m1 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal Depth phi -termal Element of ((AllSymbolsOf X) *) \ {{}}
q is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of AllTermsOf X
(X,S,I,q) is Element of S
(X,S, the Element of S,I) . T is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
i2 is functional V25() FinSequence-membered V166() Element of bool (AllTermsOf X)
s2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal H + 1 -termal Element of ((AllSymbolsOf X) *) \ {{}}
SubTerms s2 is Relation-like NAT -defined (X -termsOfMaxDepth) . H -valued (proj2 s2) * -valued AllTermsOf X -valued Function-like finite abs (ar s2) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
K365(((AllSymbolsOf X) *)) is non empty non trivial non finite V167() Element of bool (bool ((AllSymbolsOf X) *))
bool (bool ((AllSymbolsOf X) *)) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is non empty Relation-like NAT -defined K365(((AllSymbolsOf X) *)) -valued Function-like total quasi_total Element of bool [:NAT,K365(((AllSymbolsOf X) *)):]
[:NAT,K365(((AllSymbolsOf X) *)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365(((AllSymbolsOf X) *)):] is non empty non trivial non finite V167() set
(X -termsOfMaxDepth) . H is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365(((AllSymbolsOf X) *))
proj2 s2 is non empty finite set
(proj2 s2) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 s2
ar s2 is complex ext-real V40() V41() Element of INT
(X -firstChar) . s2 is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
ar ((X -firstChar) . s2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of X . ((X -firstChar) . s2) is set
abs (ar s2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S,I) | i2 is Relation-like AllTermsOf X -defined i2 -defined AllTermsOf X -defined S -valued Function-like total Element of bool [:(AllTermsOf X),S:]
dom ((X,S,I) | i2) is functional V25() FinSequence-membered V166() Element of bool i2
bool i2 is non empty set
p is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
p | i2 is Relation-like AllTermsOf X -defined i2 -defined AllTermsOf X -defined S -valued Function-like total Element of bool [:(AllTermsOf X),S:]
dom (p | i2) is functional V25() FinSequence-membered V166() Element of bool i2
rng (SubTerms phi) is functional finite V25() FinSequence-membered Element of bool ((proj2 phi) *)
bool ((proj2 phi) *) is non empty non trivial non finite V167() set
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X -termsOfMaxDepth) . H
((X,S, the Element of S,I) . T) . m1 is set
((Depth phi) + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,S, the Element of S,I) . (((Depth phi) + 1) + 1) is Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of Funcs ((AllTermsOf X),S)
((X,S, the Element of S,I) . (((Depth phi) + 1) + 1)) . m1 is set
((X,S, the Element of S,I) . T) (*) (SubTerms phi) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,I,((X -firstChar) . phi)) . (((X,S, the Element of S,I) . T) (*) (SubTerms phi)) is set
((X,S, the Element of S,I) . T) | i2 is Relation-like AllTermsOf X -defined i2 -defined AllTermsOf X -defined S -valued Function-like total Element of bool [:(AllTermsOf X),S:]
(((X,S, the Element of S,I) . T) | i2) (*) (SubTerms phi) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,I,((X -firstChar) . phi)) . ((((X,S, the Element of S,I) . T) | i2) (*) (SubTerms phi)) is set
((X,S,I) | i2) (*) (SubTerms phi) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,I,((X -firstChar) . phi)) . (((X,S,I) | i2) (*) (SubTerms phi)) is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X -firstChar) . S is Element of AllSymbolsOf X
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
(X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (X,b₂) } is set
(X,((X -firstChar) . S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,((X -firstChar) . S)] is non empty V34() set
{[1,((X -firstChar) . S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
[S,{}] is non empty V34() set
A1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
A1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,A1) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,A1) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf X, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,A1) : verum } is set
A2 is literal Element of LettersOf X
(X,A2) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
[1,A2] is non empty V34() set
{[1,A2]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,A1)
(X,(X,A2),h) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
S . 1 is set
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,A1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
[H,{}] is non empty V34() set
T is non empty V34() set
(X,(X,((X -firstChar) . S)),H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
proj1 {} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(AllSymbolsOf X) \/ (proj1 {}) is non empty non trivial non finite V167() set
proj2 {} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V167() V192() V198() V199() set
(AllSymbolsOf X) \/ (proj2 {}) is non empty non trivial non finite V167() set
len {} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
{} null (AllSymbolsOf X) is empty trivial Relation-like non-empty empty-yielding NAT -defined (AllSymbolsOf X) \/ (proj1 {}) -defined {{}} -valued AllSymbolsOf X -valued (AllSymbolsOf X) \/ (proj2 {}) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element len {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
{} \typed/ (AllSymbolsOf X) is Element of bool ({} \/ (AllSymbolsOf X))
{} \/ (AllSymbolsOf X) is non empty non trivial non finite V167() set
bool ({} \/ (AllSymbolsOf X)) is non empty non trivial non finite V167() set
m1 is empty trivial Relation-like non-empty empty-yielding NAT -defined (AllSymbolsOf X) \/ (proj1 {}) -defined {{}} -valued AllSymbolsOf X -valued (AllSymbolsOf X) \/ (proj2 {}) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element len {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
[H,m1] is non empty V34() set
(X,(X,((X -firstChar) . S)),H) ^ m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,(X,((X -firstChar) . S)),H) null m1 is Relation-like NAT -defined m1 \/ (proj1 (X,(X,((X -firstChar) . S)),H)) -defined m1 \/ (proj2 (X,(X,((X -firstChar) . S)),H)) -valued Function-like finite len (X,(X,((X -firstChar) . S)),H) -element FinSequence-like FinSubsequence-like V199() set
proj1 (X,(X,((X -firstChar) . S)),H) is non empty finite set
m1 \/ (proj1 (X,(X,((X -firstChar) . S)),H)) is non empty finite set
proj2 (X,(X,((X -firstChar) . S)),H) is non empty finite set
m1 \/ (proj2 (X,(X,((X -firstChar) . S)),H)) is non empty finite set
len (X,(X,((X -firstChar) . S)),H) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,(X,((X -firstChar) . S)),H) \typed/ m1 is Relation-like NAT -defined finite Element of bool ((X,(X,((X -firstChar) . S)),H) \/ m1)
(X,(X,((X -firstChar) . S)),H) \/ m1 is non empty Relation-like NAT -defined finite set
bool ((X,(X,((X -firstChar) . S)),H) \/ m1) is non empty finite V25() set
m1 ^ (X,(X,((X -firstChar) . S)),H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,A1) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,A1) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(X)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,A1) : verum } is set
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,A1)
(X,(X,(X)),A2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,A1)
(X,(X,(X,(X)),A2),h) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
S . 1 is set
(X,A2,h) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),(X,A2,h)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),(X,A2,h)) . 1 is set
[:(((AllSymbolsOf X) *) \ {{}}),(X,A1):] is non empty non trivial Relation-like non finite V167() set
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,A1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
[t,h] is non empty V34() Element of [:(((AllSymbolsOf X) *) \ {{}}),(X,A1):]
T is non empty V34() Element of [:(((AllSymbolsOf X) *) \ {{}}),(X,A1):]
(X,(X,((X -firstChar) . S)),t) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,A1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,A1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
[t,m1] is non empty V34() set
(X,(X,((X -firstChar) . S)),t) ^ m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
[t,m1] is non empty V34() Element of [:(((AllSymbolsOf X) *) \ {{}}),(((AllSymbolsOf X) *) \ {{}}):]
[:(((AllSymbolsOf X) *) \ {{}}),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
(X,(X,(X,((X -firstChar) . S)),t),m1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
A1 is non empty V34() set
A1 is set
A2 is set
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
H is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
[t,H] is non empty V34() set
(X,(X,((X -firstChar) . S)),t) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,((X -firstChar) . S)),t) ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
m1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
[T,m1] is non empty V34() set
(X,(X,((X -firstChar) . S)),T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,((X -firstChar) . S)),T) ^ m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
H is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
[t,H] is non empty V34() set
(X,(X,((X -firstChar) . S)),t) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,((X -firstChar) . S)),t) ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
m1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
[T,m1] is non empty V34() set
(X,(X,((X -firstChar) . S)),T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,((X -firstChar) . S)),T) ^ m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
i2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
[s2,i2] is non empty V34() set
(X,(X,((X -firstChar) . S)),s2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,((X -firstChar) . S)),s2) ^ i2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
m1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
[T,m1] is non empty V34() set
(X,(X,((X -firstChar) . S)),T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,((X -firstChar) . S)),T) ^ m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
t ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,((X -firstChar) . S)) ^ (t ^ H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
T ^ m1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,((X -firstChar) . S)) ^ (T ^ m1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
s2 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
t ^ s2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
i2 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
T ^ i2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is set
AllSymbolsOf X is non empty non trivial non finite V167() set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X,S) `1 is set
(X -firstChar) . S is Element of AllSymbolsOf X
(X,((X -firstChar) . S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,((X -firstChar) . S)] is non empty V34() set
{[1,((X -firstChar) . S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
psi is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
[v1,psi] is non empty V34() set
(X,(X,((X -firstChar) . S)),v1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,((X -firstChar) . S)),v1) ^ psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
((X,S) `1) \+\ v1 is set
((X,S) `1) \ v1 is set
((X,S) `1) typed\ v1 is Element of bool ((X,S) `1)
bool ((X,S) `1) is non empty set
((X,S) `1) \ v1 is Element of bool ((X,S) `1)
v1 \ ((X,S) `1) is Relation-like finite set
v1 typed\ ((X,S) `1) is Relation-like NAT -defined Function-like finite V199() Element of bool v1
bool v1 is non empty finite V25() set
v1 \ ((X,S) `1) is Relation-like NAT -defined Function-like finite V199() Element of bool v1
(((X,S) `1) \ v1) \/ (v1 \ ((X,S) `1)) is set
[S,{}] is non empty V34() set
((X,S) `1) \+\ S is set
((X,S) `1) \ S is set
((X,S) `1) typed\ S is Element of bool ((X,S) `1)
bool ((X,S) `1) is non empty set
((X,S) `1) \ S is Element of bool ((X,S) `1)
S \ ((X,S) `1) is Relation-like finite set
S typed\ ((X,S) `1) is Relation-like NAT -defined Function-like finite V199() Element of bool S
bool S is non empty finite V25() set
S \ ((X,S) `1) is Relation-like NAT -defined Function-like finite V199() Element of bool S
(((X,S) `1) \ S) \/ (S \ ((X,S) `1)) is set
(X,S) `2 is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
(X -firstChar) . S is Element of AllSymbolsOf X
(X,((X -firstChar) . S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,((X -firstChar) . S)] is non empty V34() set
{[1,((X -firstChar) . S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
psi is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
[v1,psi] is non empty V34() set
(X,(X,((X -firstChar) . S)),v1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,((X -firstChar) . S)),v1) ^ psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
((X,S) `2) \+\ psi is set
((X,S) `2) \ psi is set
((X,S) `2) typed\ psi is Element of bool ((X,S) `2)
bool ((X,S) `2) is non empty set
((X,S) `2) \ psi is Element of bool ((X,S) `2)
psi \ ((X,S) `2) is Relation-like finite set
psi typed\ ((X,S) `2) is Relation-like NAT -defined Function-like finite V199() Element of bool psi
bool psi is non empty finite V25() set
psi \ ((X,S) `2) is Relation-like NAT -defined Function-like finite V199() Element of bool psi
(((X,S) `2) \ psi) \/ (psi \ ((X,S) `2)) is set
[S,{}] is non empty V34() set
((X,S) `2) \+\ {} is set
((X,S) `2) \ {} is set
((X,S) `2) typed\ {} is Element of bool ((X,S) `2)
bool ((X,S) `2) is non empty set
((X,S) `2) \ {} is Element of bool ((X,S) `2)
{} \ ((X,S) `2) is Relation-like finite set
{} typed\ ((X,S) `2) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural non proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool {}
bool {} is non empty finite V25() set
{} \ ((X,S) `2) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural non proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool {}
(((X,S) `2) \ {}) \/ ({} \ ((X,S) `2)) is set
{} null (AllSymbolsOf X) is empty trivial Relation-like non-empty empty-yielding NAT -defined (AllSymbolsOf X) \/ (proj1 {}) -defined {{}} -valued AllSymbolsOf X -valued (AllSymbolsOf X) \/ (proj2 {}) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element len {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
proj1 {} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(AllSymbolsOf X) \/ (proj1 {}) is non empty non trivial non finite V167() set
proj2 {} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V167() V192() V198() V199() set
(AllSymbolsOf X) \/ (proj2 {}) is non empty non trivial non finite V167() set
len {} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
{} \typed/ (AllSymbolsOf X) is Element of bool ({} \/ (AllSymbolsOf X))
{} \/ (AllSymbolsOf X) is non empty non trivial non finite V167() set
bool ({} \/ (AllSymbolsOf X)) is non empty non trivial non finite V167() set
v1 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,S) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
(X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (X,b₂) } is set
(X,S) \ (X) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,S) typed\ (X) is functional V25() FinSequence-membered V166() Element of bool (X,S)
bool (X,S) is non empty set
(X,S) \ (X) is functional V25() FinSequence-membered V166() Element of bool (X,S)
N is set
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,S) (X) Element of ((AllSymbolsOf X) *) \ {{}}
N is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b₁ is 0wff } is set
(X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (X,b₂) } is set
(AtomicFormulasOf X) \ (X) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
(AtomicFormulasOf X) typed\ (X) is functional V25() FinSequence-membered V166() Element of bool (AtomicFormulasOf X)
bool (AtomicFormulasOf X) is non empty set
(AtomicFormulasOf X) \ (X) is functional V25() FinSequence-membered V166() Element of bool (AtomicFormulasOf X)
(X,0) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,0) \ (X) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V167() V192() V198() V199() Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,0) typed\ (X) is functional V25() FinSequence-membered V166() Element of bool (X,0)
bool (X,0) is non empty set
(X,0) \ (X) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V167() V192() V198() V199() Element of bool (X,0)
S is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
I is V51() V53() eligible Language-like
AllSymbolsOf I is non empty non trivial non finite V167() set
the U1 of I is set
(AllSymbolsOf I) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf I
((AllSymbolsOf I) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf I) *)
bool ((AllSymbolsOf I) *) is non empty non trivial non finite V167() set
((AllSymbolsOf I) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf I) *)
psi is V51() V53() eligible Language-like
AllSymbolsOf psi is non empty non trivial non finite V167() set
the U1 of psi is set
(AllSymbolsOf psi) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf psi
((AllSymbolsOf psi) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf psi) *)
bool ((AllSymbolsOf psi) *) is non empty non trivial non finite V167() set
((AllSymbolsOf psi) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf psi) *)
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,S) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,S] is non empty V34() set
{[1,S]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,S),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,1 + (X,phi)) (X,(X,phi)) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (X,phi) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,(X,(X,S),phi)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(I) is non literal non low-compounding non relational non own Element of AllSymbolsOf I
AllSymbolsOf I is non empty non trivial non finite V167() set
the U3 of I is Element of the U1 of I
(I,(I)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf I) *) \ {{}}
[1,(I)] is non empty V34() set
{[1,(I)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (I) Element of ((AllSymbolsOf I) *) \ {{}}
(I,(I,(I)),N) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (I) Element of ((AllSymbolsOf I) *) \ {{}}
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (I) Element of ((AllSymbolsOf I) *) \ {{}}
(I,(I,(I,(I)),N),v1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (I, max ((I,N),(I,v1))) (I) (I) Element of ((AllSymbolsOf I) *) \ {{}}
(I,N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(I,v1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((I,N),(I,v1)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(I,(I,(I,(I,(I)),N),v1)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(psi) is non literal non low-compounding non relational non own Element of AllSymbolsOf psi
AllSymbolsOf psi is non empty non trivial non finite V167() set
the U3 of psi is Element of the U1 of psi
(psi,(psi)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf psi) *) \ {{}}
[1,(psi)] is non empty V34() set
{[1,(psi)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (psi) Element of ((AllSymbolsOf psi) *) \ {{}}
(psi,(psi,(psi)),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (psi) Element of ((AllSymbolsOf psi) *) \ {{}}
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (psi) Element of ((AllSymbolsOf psi) *) \ {{}}
(psi,(psi,(psi,(psi)),phi),A) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (psi, max ((psi,phi),(psi,A))) (psi) (psi) Element of ((AllSymbolsOf psi) *) \ {{}}
(psi,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(psi,A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((psi,phi),(psi,A)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(psi,(psi,(psi,(psi,(psi)),phi),A)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
X is set
<*X*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() set
[1,X] is non empty V34() set
{[1,X]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
S -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
[:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V167() set
(AllSymbolsOf S) -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(AllSymbolsOf S) -pr1 is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total V201( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf S),(AllSymbolsOf S)) is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
MultPlace ((AllSymbolsOf S) -pr1) is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
phi is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S -firstChar) . I is Element of AllSymbolsOf S
(S,I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,I) is set
(S,I) `1 is set
(S,I) is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of (AllSymbolsOf S) *
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
(S,I) `2 is set
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
<*X*> ^ N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(<*X*> ^ N) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,((S -firstChar) . I)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[1,((S -firstChar) . I)] is non empty V34() set
{[1,((S -firstChar) . I)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
A2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
[A1,A2] is non empty V34() set
(S,(S,((S -firstChar) . I)),A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,((S -firstChar) . I)),A1) ^ A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
((S,I) `1) \+\ A1 is set
((S,I) `1) \ A1 is set
((S,I) `1) typed\ A1 is Element of bool ((S,I) `1)
bool ((S,I) `1) is non empty set
((S,I) `1) \ A1 is Element of bool ((S,I) `1)
A1 \ ((S,I) `1) is Relation-like finite set
A1 typed\ ((S,I) `1) is Relation-like NAT -defined Function-like finite V199() Element of bool A1
bool A1 is non empty finite V25() set
A1 \ ((S,I) `1) is Relation-like NAT -defined Function-like finite V199() Element of bool A1
(((S,I) `1) \ A1) \/ (A1 \ ((S,I) `1)) is set
((S,I) `2) \+\ A2 is set
((S,I) `2) \ A2 is set
((S,I) `2) typed\ A2 is Element of bool ((S,I) `2)
bool ((S,I) `2) is non empty set
((S,I) `2) \ A2 is Element of bool ((S,I) `2)
A2 \ ((S,I) `2) is Relation-like finite set
A2 typed\ ((S,I) `2) is Relation-like NAT -defined Function-like finite V199() Element of bool A2
bool A2 is non empty finite V25() set
A2 \ ((S,I) `2) is Relation-like NAT -defined Function-like finite V199() Element of bool A2
(((S,I) `2) \ A2) \/ (A2 \ ((S,I) `2)) is set
I . 1 is set
N ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
<*X*> ^ (N ^ phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(<*X*> ^ (N ^ phi)) . 1 is set
proj2 phi is finite set
proj2 I is non empty finite set
[N,phi] is non empty V34() set
(S,(S,((S -firstChar) . I)),N) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,((S -firstChar) . I)),N) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
X is V51() V53() eligible Language-like
S is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}} is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(X,(X,(X)), the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)), the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}), the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X, max ((X, the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}),(X, the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}))) (X,0 + 1) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X, the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((X, the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}),(X, the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}})) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
v1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
v1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
0 * v1 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
1 + (0 * v1) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,S) (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of (AllSymbolsOf X) *
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
(X,S) is set
(X,S) `2 is set
(X,S) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(X,S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) `1 is set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b₁ is (X,b₂) } is set
(X -firstChar) . S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
A2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,A2) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,A2) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf X, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,A2) : verum } is set
t is literal Element of LettersOf X
(X,t) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
[1,t] is non empty V34() set
{[1,t]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,A2)
(X,(X,t),H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,A2) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,t),T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X,A2 + 1) (X,1 + (X,T)) (X,(X,T)) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,T) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (X,T) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,(X,t),T) ^ {} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,(X,t),T) null {} is Relation-like NAT -defined {} \/ (proj1 (X,(X,t),T)) -defined {} \/ (proj2 (X,(X,t),T)) -valued Function-like finite len (X,(X,t),T) -element FinSequence-like FinSubsequence-like V199() set
proj1 (X,(X,t),T) is non empty finite set
{} \/ (proj1 (X,(X,t),T)) is non empty finite set
proj2 (X,(X,t),T) is non empty finite set
{} \/ (proj2 (X,(X,t),T)) is non empty finite set
len (X,(X,t),T) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,(X,t),T) \typed/ {} is Relation-like NAT -defined finite Element of bool ((X,(X,t),T) \/ {})
(X,(X,t),T) \/ {} is non empty Relation-like NAT -defined finite set
bool ((X,(X,t),T) \/ {}) is non empty finite V25() set
{} ^ (X,(X,t),T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
m1 is set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,phi) is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of (AllSymbolsOf S) *
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
(S,phi) is set
(S,phi) `2 is set
(S,X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
(S) is non literal non low-compounding non relational non own Element of AllSymbolsOf S
the U3 of S is Element of the U1 of S
(S,X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) \ {{}})
<*(S)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf S
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(S)*> ^ b<sub>1</sub>) ^ b<sub>2</sub>) where b<sub>1</sub>, b<sub>2</sub> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X) : verum } is set
(S,(S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X)
(S,(S,(S)),psi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (S,X)
(S,(S,(S,(S)),psi),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,X) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,A) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,X) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,A1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,(S,(S)),A) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),A),A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S, max ((S,A),(S,A1))) (S,X + 1) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
max ((S,A),(S,A1)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of (AllSymbolsOf X) *
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
(X,S) is set
(X,S) `2 is set
(X,S) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,phi) (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is set
(X,S) `2 is set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is set
(X,S) `1 is set
S null is set
[S,{}] is non empty V34() set
[S,{}] `1 is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . S is non relational Element of AllSymbolsOf X
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
((X -firstChar) . S) \+\ (X) is set
((X -firstChar) . S) \ (X) is set
((X -firstChar) . S) typed\ (X) is Element of bool ((X -firstChar) . S)
bool ((X -firstChar) . S) is non empty set
((X -firstChar) . S) \ (X) is Element of bool ((X -firstChar) . S)
(X) \ ((X -firstChar) . S) is set
(X) typed\ ((X -firstChar) . S) is Element of bool (X)
bool (X) is non empty set
(X) \ ((X -firstChar) . S) is Element of bool (X)
(((X -firstChar) . S) \ (X)) \/ ((X) \ ((X -firstChar) . S)) is set
(X,S) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
v1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
v1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,v1) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
(X,v1) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
<*(X)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() FinSequence of AllSymbolsOf X
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
{ ((<*(X)*> ^ b<sub>1</sub>) ^ b<sub>2</sub>) where b<sub>1</sub>, b<sub>2</sub> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,v1) : verum } is set
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,v1)
(X,(X,(X)),psi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,v1)
(X,(X,(X,(X)),psi),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
S . 1 is set
(X,psi,phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),(X,psi,phi)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X)),(X,psi,phi)) . 1 is set
A is set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is set
(S,phi) `1 is set
(S,phi) is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of (AllSymbolsOf S) *
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
(S,phi) `2 is set
(S) is non literal non low-compounding non relational non own Element of AllSymbolsOf S
the U3 of S is Element of the U1 of S
S -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
[:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V167() set
(AllSymbolsOf S) -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(AllSymbolsOf S) -pr1 is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total V201( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf S),(AllSymbolsOf S)) is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
MultPlace ((AllSymbolsOf S) -pr1) is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,X + 1) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S -firstChar) . I is non relational Element of AllSymbolsOf S
(S,I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,I) is set
(S,I) `1 is set
(S,(S,I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,I) `2 is set
(S,(S,I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((S,(S,I)),(S,(S,I))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,I) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
((S -firstChar) . I) \+\ (S) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
((S -firstChar) . I) \ (S) is set
((S -firstChar) . I) typed\ (S) is Element of bool ((S -firstChar) . I)
bool ((S -firstChar) . I) is non empty set
((S -firstChar) . I) \ (S) is Element of bool ((S -firstChar) . I)
(S) \ ((S -firstChar) . I) is set
(S) typed\ ((S -firstChar) . I) is Element of bool (S)
bool (S) is non empty set
(S) \ ((S -firstChar) . I) is Element of bool (S)
(((S -firstChar) . I) \ (S)) \/ ((S) \ ((S -firstChar) . I)) is set
(S,(S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,(S,(S,I))) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),h) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,(S,(S,I))) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),h),t) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S, max ((S,h),(S,t))) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,h) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,t) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((S,h),(S,t)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(max ((S,(S,I)),(S,(S,I)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
((max ((S,(S,I)),(S,(S,I)))) + 1) - 1 is complex ext-real V40() V41() set
(X + 1) - 1 is complex ext-real V40() V41() set
- (S,(S,I)) is complex ext-real non positive V40() V41() set
(max ((S,(S,I)),(S,(S,I)))) + (- (S,(S,I))) is complex ext-real V40() V41() set
X + (- (S,(S,I))) is complex ext-real V40() V41() set
- (S,(S,I)) is complex ext-real non positive V40() V41() set
(max ((S,(S,I)),(S,(S,I)))) + (- (S,(S,I))) is complex ext-real V40() V41() set
X + (- (S,(S,I))) is complex ext-real V40() V41() set
(max ((S,(S,I)),(S,(S,I)))) - (S,(S,I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X - (S,(S,I)) is complex ext-real V40() V41() set
(max ((S,(S,I)),(S,(S,I)))) - (S,(S,I)) is complex ext-real V40() V41() set
X - (S,(S,I)) is complex ext-real V40() V41() set
H is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 * H is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(S,(S,I)) + (0 * H) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
T is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 * T is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(S,(S,I)) + (0 * T) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S,(S,I)) + H is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,(S,I)) + T is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,X + 1) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is set
(S,phi) `1 is set
(S,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
[:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V167() set
(AllSymbolsOf S) -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(AllSymbolsOf S) -pr1 is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total V201( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf S),(AllSymbolsOf S)) is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
MultPlace ((AllSymbolsOf S) -pr1) is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(S -firstChar) . phi is Element of AllSymbolsOf S
(S) is non literal non low-compounding non relational non own Element of AllSymbolsOf S
AllSymbolsOf S is non empty non trivial non finite V167() set
the U3 of S is Element of the U1 of S
(S,(S,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
AtomicFormulaSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
TheNorSymbOf S is set
{(TheNorSymbOf S)} is non empty trivial finite 1 -element set
(AllSymbolsOf S) \ {(TheNorSymbOf S)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
(AllSymbolsOf S) typed\ {(TheNorSymbOf S)} is Element of bool (AllSymbolsOf S)
0 * X is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
0 + (0 * X) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
A1 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (S, 0 ) (S) Element of ((AllSymbolsOf S) *) \ {{}}
A1 null A1 is Relation-like NAT -defined A1 \/ (proj1 A1) -defined A1 \/ (proj2 A1) -valued Function-like finite len A1 -element FinSequence-like FinSubsequence-like V199() set
proj1 A1 is non empty finite set
A1 \/ (proj1 A1) is non empty finite set
proj2 A1 is non empty finite set
A1 \/ (proj2 A1) is non empty finite set
len A1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
A1 \typed/ A1 is Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued finite Element of bool (A1 \/ A1)
A1 \/ A1 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued finite set
bool (A1 \/ A1) is non empty finite V25() set
0 + X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S,A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,A1) is set
(S,A1) `1 is set
A1 null is set
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,X + 1) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,A1) is set
(S,A1) `1 is set
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,X + 1) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,A1) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued AllSymbolsOf S -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of (AllSymbolsOf S) *
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
(S,A1) is set
(S,A1) `2 is set
(S,((S -firstChar) . phi)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[1,((S -firstChar) . phi)] is non empty V34() set
{[1,((S -firstChar) . phi)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
A is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S,(S,(S,phi))) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,((S -firstChar) . phi)),A) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,((S -firstChar) . phi)),A) ^ (S,A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,(S,((S -firstChar) . phi)),A) null (S,A1) is Relation-like NAT -defined (S,A1) \/ (proj1 (S,(S,((S -firstChar) . phi)),A)) -defined (S,A1) \/ (proj2 (S,(S,((S -firstChar) . phi)),A)) -valued Function-like finite len (S,(S,((S -firstChar) . phi)),A) -element FinSequence-like FinSubsequence-like V199() set
proj1 (S,(S,((S -firstChar) . phi)),A) is non empty finite set
(S,A1) \/ (proj1 (S,(S,((S -firstChar) . phi)),A)) is non empty finite set
proj2 (S,(S,((S -firstChar) . phi)),A) is non empty finite set
(S,A1) \/ (proj2 (S,(S,((S -firstChar) . phi)),A)) is non empty finite set
len (S,(S,((S -firstChar) . phi)),A) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(S,(S,((S -firstChar) . phi)),A) \typed/ (S,A1) is Relation-like NAT -defined finite Element of bool ((S,(S,((S -firstChar) . phi)),A) \/ (S,A1))
(S,(S,((S -firstChar) . phi)),A) \/ (S,A1) is non empty Relation-like NAT -defined finite set
bool ((S,(S,((S -firstChar) . phi)),A) \/ (S,A1)) is non empty finite V25() set
(S,A1) ^ (S,(S,((S -firstChar) . phi)),A) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(S,(S,phi)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
- (S,(S,phi)) is complex ext-real non positive V40() V41() set
(S,(S,phi)) + (- (S,(S,phi))) is complex ext-real V40() V41() set
X + (- (S,(S,phi))) is complex ext-real V40() V41() set
X - (S,(S,phi)) is complex ext-real V40() V41() set
h is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 * h is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(S,(S,phi)) + (0 * h) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S,(S,phi)) + h is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
S is V51() V53() eligible Language-like
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S,X + 1) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is set
(S,phi) `2 is set
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
(S,X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite V167() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
Funcs ((S,X),BOOLEAN) is non empty functional FUNCTION_DOMAIN of (S,X), BOOLEAN
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((phi *),(phi \/ BOOLEAN))
(S,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf S -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b<sub>1</sub> is (S,phi) } is set
v1 is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,phi) Element of (S,phi)
(S,phi,X,v1) is Relation-like ((AllSymbolsOf S) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf S) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf S) *) \ {{}}, BOOLEAN )
(S,X,phi) is Relation-like [:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN)
[:(S,phi),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN)))) -defined (AllSymbolsOf S) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):]
[:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf S),(PFuncs ((phi *),(phi \/ BOOLEAN))))),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
PFuncs ([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(S,phi),(((AllSymbolsOf S) *) \ {{}}):], BOOLEAN )
curry (S,X,phi) is Relation-like Function-like set
(curry (S,X,phi)) . v1 is set
[:(S,phi),(Funcs ((S,X),BOOLEAN)):] is non empty Relation-like set
bool [:(S,phi),(Funcs ((S,X),BOOLEAN)):] is non empty set
psi is non empty Relation-like (S,phi) -defined Funcs ((S,X),BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:(S,phi),(Funcs ((S,X),BOOLEAN)):]
psi . v1 is Relation-like (S,X) -defined BOOLEAN -valued Function-like total quasi_total Element of Funcs ((S,X),BOOLEAN)
X is V51() V53() eligible Language-like
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
the U2 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b<sub>1</sub> is (X,S) } is set
phi is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}
N is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
(X,S,N,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,N,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,N) is Relation-like Function-like Function-yielding V164() (X,S) (X,S,N) set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
N +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X -firstChar) . phi is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(X,S,N,(X,S,N),((X -firstChar) . phi)) is non empty Relation-like (abs (ar ((X -firstChar) . phi))) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,(X -firstChar) . phi)
ar ((X -firstChar) . phi) is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . ((X -firstChar) . phi) is set
abs (ar ((X -firstChar) . phi)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((X -firstChar) . phi))) -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
SubTerms phi is Relation-like NAT -defined (proj2 phi) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . phi)) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
proj2 phi is non empty finite set
(proj2 phi) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 phi
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(TermSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(X,S,N) is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
(X,S,N) (*) (SubTerms phi) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,N,(X,S,N),((X -firstChar) . phi)) . ((X,S,N) (*) (SubTerms phi)) is set
(X,0,S) is Relation-like [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] -defined BOOLEAN -valued Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined (AllSymbolsOf X) * -valued non finite V167() Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) is non empty functional M26([:(X,S),(((AllSymbolsOf X) *) \ {{}}):], BOOLEAN )
(X,0) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AtomicFormulasOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : b<sub>1</sub> is 0wff } is set
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X,0)
(X,S,0,N) is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) is non empty functional M26(((AllSymbolsOf X) *) \ {{}}, BOOLEAN )
curry (X,0,S) is Relation-like Function-like set
(curry (X,0,S)) . N is set
Funcs ((X,0),BOOLEAN) is non empty functional FUNCTION_DOMAIN of (X,0), BOOLEAN
[:(X,0),BOOLEAN:] is non empty Relation-like set
bool [:(X,0),BOOLEAN:] is non empty set
[:(X,S),(PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)):] is non empty Relation-like set
bool [:(X,S),(PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)):] is non empty set
s2 is non empty Relation-like (X,S) -defined PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:(X,S),(PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)):]
dom s2 is non empty functional Element of bool (X,S)
bool (X,S) is non empty set
T is non empty Relation-like (X,0) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(X,0),BOOLEAN:]
dom T is non empty functional V25() FinSequence-membered V166() V167() Element of bool (X,0)
bool (X,0) is non empty set
s2 . N is Relation-like Function-like Element of PFuncs ((((AllSymbolsOf X) *) \ {{}}),BOOLEAN)
T . phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
(X,0,S) . (N,phi) is set
[N,phi] is non empty V34() set
(X,0,S) . [N,phi] is set
[N,phi] is non empty V34() Element of [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
[:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
dom (X,0,S) is Relation-like (X,S) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(X,S),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
(X,S) is non empty Relation-like NAT -defined PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):]
[:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,(PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)):] is non empty non trivial non finite V167() set
H is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(X,S) . H is Relation-like Function-like Element of PFuncs ([:(X,S),(((AllSymbolsOf X) *) \ {{}}):],BOOLEAN)
((X,S) . H) . [N,phi] is set
(X,S) is non empty Relation-like [:(X,S),(AtomicFormulasOf X):] -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:]
[:(X,S),(AtomicFormulasOf X):] is non empty Relation-like non empty-yielding Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):]
[:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite V167() set
bool [:(Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite V167() set
[:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:] is non empty Relation-like set
bool [:[:(X,S),(AtomicFormulasOf X):],BOOLEAN:] is non empty set
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() 0wff Element of AtomicFormulasOf X
(X,S) . (N,t) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
[N,t] is non empty V34() set
(X,S) . [N,t] is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b<sub>1</sub> is (X,S) } is set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
I is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S,phi,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,phi,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,S,phi) is Relation-like Function-like Function-yielding V164() (X,S) (X,S,phi) set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
(S) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
2 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
[:(2 -tuples_on S),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on S),BOOLEAN:] is non empty set
[:(S *),(S *):] is non empty non trivial Relation-like non finite V167() set
S -concatenation is non empty Relation-like [:(S *),(S *):] -defined S * -valued Function-like total quasi_total Function-yielding V164() V198() V201(S * ) Element of bool [:[:(S *),(S *):],(S *):]
[:[:(S *),(S *):],(S *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(S *),(S *):],(S *):] is non empty non trivial non finite V167() set
1 -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
id (1 -tuples_on S) is non empty Relation-like non empty-yielding 1 -tuples_on S -defined 1 -tuples_on S -valued Function-like one-to-one total quasi_total onto bijective V155() V157() V158() V162() Function-yielding V164() V198() Element of bool [:(1 -tuples_on S),(1 -tuples_on S):]
[:(1 -tuples_on S),(1 -tuples_on S):] is non empty Relation-like set
bool [:(1 -tuples_on S),(1 -tuples_on S):] is non empty set
(S -concatenation) .: (id (1 -tuples_on S)) is functional V25() FinSequence-membered Element of bool (S *)
bool (S *) is non empty non trivial non finite V167() set
chi (((S -concatenation) .: (id (1 -tuples_on S))),(2 -tuples_on S)) is non empty Relation-like 2 -tuples_on S -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on S),BOOLEAN:]
(TheEqSymbOf X) .--> (S) is trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() V199() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element set
{(TheEqSymbOf X)} --> (S) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on S),BOOLEAN:] -valued {(S)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{(TheEqSymbOf X)},{(S)}:]
{(S)} is non empty trivial functional finite 1 -element V166() V167() set
[:{(TheEqSymbOf X)},{(S)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf X)},{(S)}:] is non empty finite V25() set
phi +* ((TheEqSymbOf X) .--> (S)) is Relation-like Function-like Function-yielding V164() set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X -firstChar) . I is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(X,S,phi,(X,S,phi),((X -firstChar) . I)) is non empty Relation-like (abs (ar ((X -firstChar) . I))) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,(X -firstChar) . I)
ar ((X -firstChar) . I) is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . ((X -firstChar) . I) is set
abs (ar ((X -firstChar) . I)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((X -firstChar) . I))) -tuples_on S is non empty functional V25() FinSequence-membered V166() V167() FinSequenceSet of S
SubTerms I is Relation-like NAT -defined (proj2 I) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . I)) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
proj2 I is non empty finite set
(proj2 I) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 I
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(TermSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(X,S,phi) is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
(X,S,phi) (*) (SubTerms I) is Relation-like NAT -defined S -valued Function-like finite V199() set
(X,S,phi,(X,S,phi),((X -firstChar) . I)) . ((X,S,phi) (*) (SubTerms I)) is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(X) is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
X is set
X * is non empty functional V25() FinSequence-membered FinSequenceSet of X
S is V51() V53() eligible Language-like
AllTermsOf S is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365((((AllSymbolsOf S) *) \ {{}}))
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V167() set
S -termsOfMaxDepth is Relation-like Function-like set
proj2 (S -termsOfMaxDepth) is set
union (proj2 (S -termsOfMaxDepth)) is set
phi is non empty set
S -termsOfMaxDepth is non empty Relation-like NAT -defined K365((((AllSymbolsOf S) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K365((((AllSymbolsOf S) *) \ {{}})):]
[:NAT,K365((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial non finite V167() set
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
AllSymbolsOf S is non empty non trivial non finite V167() set
LettersOf S is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " {0} is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
S -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
[:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V167() set
(AllSymbolsOf S) -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(AllSymbolsOf S) -pr1 is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total V201( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf S),(AllSymbolsOf S)) is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
MultPlace ((AllSymbolsOf S) -pr1) is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
S -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
((AllSymbolsOf S) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf S) *
[:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
(AllSymbolsOf S) -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
{} .--> {} is trivial Relation-like {{}} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite set
bool [:{{}},{{}}:] is non empty finite V25() set
(AllSymbolsOf S) -concatenation is non empty Relation-like [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() V198() V201((AllSymbolsOf S) * ) Element of bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):]
[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
[:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
MultPlace ((AllSymbolsOf S) -concatenation) is non empty Relation-like (((AllSymbolsOf S) *) *) \ {{}} -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):]
(((AllSymbolsOf S) *) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf S) *) *)
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V167() set
(((AllSymbolsOf S) *) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool (((AllSymbolsOf S) *) *)
[:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V167() set
bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial non finite V167() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf S) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
A2 is Relation-like Function-like Function-yielding V164() (S,phi) set
A2 | X is Relation-like X -defined Function-like Function-yielding V164() set
h is Relation-like Function-like Function-yielding V164() (S,phi) set
h | X is Relation-like X -defined Function-like Function-yielding V164() set
(S,phi,A2) is non empty Relation-like AllTermsOf S -defined phi -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),phi:]
[:(AllTermsOf S),phi:] is non empty Relation-like set
bool [:(AllTermsOf S),phi:] is non empty set
(S,phi,A2) | (X *) is Relation-like X * -defined AllTermsOf S -defined phi -valued Function-like Element of bool [:(AllTermsOf S),phi:]
(S,phi,h) is non empty Relation-like AllTermsOf S -defined phi -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),phi:]
(S,phi,h) | (X *) is Relation-like X * -defined AllTermsOf S -defined phi -valued Function-like Element of bool [:(AllTermsOf S),phi:]
dom (S,phi,A2) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (AllTermsOf S)
bool (AllTermsOf S) is non empty set
dom (S,phi,h) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (AllTermsOf S)
(S -termsOfMaxDepth) . 0 is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365((((AllSymbolsOf S) *) \ {{}}))
(X *) /\ ((S -termsOfMaxDepth) . 0) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
(X *) typed/\ ((S -termsOfMaxDepth) . 0) is functional V25() FinSequence-membered Element of bool (X *)
bool (X *) is non empty set
(X *) /\ ((S -termsOfMaxDepth) . 0) is set
(X *) /\typed ((S -termsOfMaxDepth) . 0) is functional V25() FinSequence-membered V166() Element of bool ((S -termsOfMaxDepth) . 0)
bool ((S -termsOfMaxDepth) . 0) is non empty set
(S,phi,A2) | ((X *) /\ ((S -termsOfMaxDepth) . 0)) is Relation-like AllTermsOf S -defined (X *) /\ ((S -termsOfMaxDepth) . 0) -defined AllTermsOf S -defined phi -valued Function-like Element of bool [:(AllTermsOf S),phi:]
(S,phi,h) | ((X *) /\ ((S -termsOfMaxDepth) . 0)) is Relation-like AllTermsOf S -defined (X *) /\ ((S -termsOfMaxDepth) . 0) -defined AllTermsOf S -defined phi -valued Function-like Element of bool [:(AllTermsOf S),phi:]
i2 is functional V25() FinSequence-membered V166() Element of bool (AllTermsOf S)
(S,phi,A2) | i2 is Relation-like AllTermsOf S -defined i2 -defined AllTermsOf S -defined phi -valued Function-like total Element of bool [:(AllTermsOf S),phi:]
dom ((S,phi,A2) | i2) is functional V25() FinSequence-membered V166() Element of bool i2
bool i2 is non empty set
(S,phi,h) | i2 is Relation-like AllTermsOf S -defined i2 -defined AllTermsOf S -defined phi -valued Function-like total Element of bool [:(AllTermsOf S),phi:]
dom ((S,phi,h) | i2) is functional V25() FinSequence-membered V166() Element of bool i2
m2 is set
dom ((S,phi,A2) | ((X *) /\ ((S -termsOfMaxDepth) . 0))) is functional V25() FinSequence-membered V166() Element of bool ((X *) /\ ((S -termsOfMaxDepth) . 0))
bool ((X *) /\ ((S -termsOfMaxDepth) . 0)) is non empty set
m1 is non empty functional V25() FinSequence-membered V166() V167() Element of bool (AllTermsOf S)
TermSymbolsOf S is non empty set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
qq is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
(S -firstChar) . qq is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
SubTerms qq is empty trivial Relation-like non-empty empty-yielding NAT -defined (proj2 qq) * -valued AllTermsOf S -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element abs (ar qq) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of (AllTermsOf S) *
proj2 qq is non empty trivial finite 1 -element set
(proj2 qq) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 qq
AllTermsOf S is non empty functional V25() FinSequence-membered AllSymbolsOf S -prefix S -prefix Element of bool ((AllSymbolsOf S) *)
ar qq is complex ext-real V40() V41() Element of INT
ar ((S -firstChar) . qq) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of INT
the adicity of S . ((S -firstChar) . qq) is set
abs (ar qq) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(AllTermsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf S) *) *)
qqq is non empty set
qqq * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of qqq
tq is non empty Relation-like NAT -defined qqq -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of qqq *
tq . 1 is set
{(tq . 1)} is non empty trivial finite 1 -element set
{(tq . 1)} \ qqq is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool {(tq . 1)}
bool {(tq . 1)} is non empty finite V25() set
{(tq . 1)} typed\ qqq is trivial finite Element of bool {(tq . 1)}
g1 is Element of qqq
(A2 | X) . g1 is Relation-like Function-like set
A2 . g1 is Relation-like Function-like set
((A2 | X) . g1) \+\ (A2 . g1) is Relation-like set
((A2 | X) . g1) \ (A2 . g1) is Relation-like set
((A2 | X) . g1) typed\ (A2 . g1) is Relation-like Function-like Element of bool ((A2 | X) . g1)
bool ((A2 | X) . g1) is non empty set
((A2 | X) . g1) \ (A2 . g1) is Relation-like Function-like Element of bool ((A2 | X) . g1)
(A2 . g1) \ ((A2 | X) . g1) is Relation-like set
(A2 . g1) typed\ ((A2 | X) . g1) is Relation-like Function-like Element of bool (A2 . g1)
bool (A2 . g1) is non empty set
(A2 . g1) \ ((A2 | X) . g1) is Relation-like Function-like Element of bool (A2 . g1)
(((A2 | X) . g1) \ (A2 . g1)) \/ ((A2 . g1) \ ((A2 | X) . g1)) is Relation-like set
(h | X) . g1 is Relation-like Function-like set
h . g1 is Relation-like Function-like set
((h | X) . g1) \+\ (h . g1) is Relation-like set
((h | X) . g1) \ (h . g1) is Relation-like set
((h | X) . g1) typed\ (h . g1) is Relation-like Function-like Element of bool ((h | X) . g1)
bool ((h | X) . g1) is non empty set
((h | X) . g1) \ (h . g1) is Relation-like Function-like Element of bool ((h | X) . g1)
(h . g1) \ ((h | X) . g1) is Relation-like set
(h . g1) typed\ ((h | X) . g1) is Relation-like Function-like Element of bool (h . g1)
bool (h . g1) is non empty set
(h . g1) \ ((h | X) . g1) is Relation-like Function-like Element of bool (h . g1)
(((h | X) . g1) \ (h . g1)) \/ ((h . g1) \ ((h | X) . g1)) is Relation-like set
(S,phi,A2) | m1 is Relation-like AllTermsOf S -defined m1 -defined AllTermsOf S -defined phi -valued Function-like total Element of bool [:(AllTermsOf S),phi:]
q is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of m1
((S,phi,A2) | m1) . q is set
(S,phi,A2) . q is Element of phi
(((S,phi,A2) | m1) . q) \+\ ((S,phi,A2) . q) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(((S,phi,A2) | m1) . q) \ ((S,phi,A2) . q) is set
(((S,phi,A2) | m1) . q) typed\ ((S,phi,A2) . q) is Element of bool (((S,phi,A2) | m1) . q)
bool (((S,phi,A2) | m1) . q) is non empty set
(((S,phi,A2) | m1) . q) \ ((S,phi,A2) . q) is Element of bool (((S,phi,A2) | m1) . q)
((S,phi,A2) . q) \ (((S,phi,A2) | m1) . q) is set
((S,phi,A2) . q) typed\ (((S,phi,A2) | m1) . q) is Element of bool ((S,phi,A2) . q)
bool ((S,phi,A2) . q) is non empty set
((S,phi,A2) . q) \ (((S,phi,A2) | m1) . q) is Element of bool ((S,phi,A2) . q)
((((S,phi,A2) | m1) . q) \ ((S,phi,A2) . q)) \/ (((S,phi,A2) . q) \ (((S,phi,A2) | m1) . q)) is set
(S,phi,h) | m1 is Relation-like AllTermsOf S -defined m1 -defined AllTermsOf S -defined phi -valued Function-like total Element of bool [:(AllTermsOf S),phi:]
((S,phi,h) | m1) . q is set
(S,phi,h) . q is Element of phi
(((S,phi,h) | m1) . q) \+\ ((S,phi,h) . q) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(((S,phi,h) | m1) . q) \ ((S,phi,h) . q) is set
(((S,phi,h) | m1) . q) typed\ ((S,phi,h) . q) is Element of bool (((S,phi,h) | m1) . q)
bool (((S,phi,h) | m1) . q) is non empty set
(((S,phi,h) | m1) . q) \ ((S,phi,h) . q) is Element of bool (((S,phi,h) | m1) . q)
((S,phi,h) . q) \ (((S,phi,h) | m1) . q) is set
((S,phi,h) . q) typed\ (((S,phi,h) | m1) . q) is Element of bool ((S,phi,h) . q)
bool ((S,phi,h) . q) is non empty set
((S,phi,h) . q) \ (((S,phi,h) | m1) . q) is Element of bool ((S,phi,h) . q)
((((S,phi,h) | m1) . q) \ ((S,phi,h) . q)) \/ (((S,phi,h) . q) \ (((S,phi,h) | m1) . q)) is set
(A2 | X) . ((S -firstChar) . qq) is Relation-like Function-like set
(S,phi,A2,((S -firstChar) . qq)) is non empty Relation-like (abs (ar ((S -firstChar) . qq))) -tuples_on phi -defined phi \/ BOOLEAN -valued Function-like total quasi_total (S,phi,(S -firstChar) . qq)
abs (ar ((S -firstChar) . qq)) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(abs (ar ((S -firstChar) . qq))) -tuples_on phi is non empty functional V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
(h | X) . ((S -firstChar) . qq) is Relation-like Function-like set
(S,phi,h,((S -firstChar) . qq)) is non empty Relation-like (abs (ar ((S -firstChar) . qq))) -tuples_on phi -defined phi \/ BOOLEAN -valued Function-like total quasi_total (S,phi,(S -firstChar) . qq)
((S,phi,A2) | ((X *) /\ ((S -termsOfMaxDepth) . 0))) . m2 is set
(S,phi,A2) . m2 is set
((S,phi,h) | ((X *) /\ ((S -termsOfMaxDepth) . 0))) . m2 is set
(S,phi,h) . m2 is set
(S,phi,A2) (*) (SubTerms qq) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued phi -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element len (SubTerms qq) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
len (SubTerms qq) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(S,phi,A2,((S -firstChar) . qq)) . ((S,phi,A2) (*) (SubTerms qq)) is set
(S,phi,h) (*) (SubTerms qq) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued phi -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element len (SubTerms qq) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(S,phi,h,((S -firstChar) . qq)) . ((S,phi,h) (*) (SubTerms qq)) is set
s2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S -termsOfMaxDepth) . s2 is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365((((AllSymbolsOf S) *) \ {{}}))
(X *) /\ ((S -termsOfMaxDepth) . s2) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
(X *) typed/\ ((S -termsOfMaxDepth) . s2) is functional V25() FinSequence-membered Element of bool (X *)
(X *) /\ ((S -termsOfMaxDepth) . s2) is set
(X *) /\typed ((S -termsOfMaxDepth) . s2) is functional V25() FinSequence-membered V166() Element of bool ((S -termsOfMaxDepth) . s2)
bool ((S -termsOfMaxDepth) . s2) is non empty set
(S,phi,A2) | ((X *) /\ ((S -termsOfMaxDepth) . s2)) is Relation-like AllTermsOf S -defined (X *) /\ ((S -termsOfMaxDepth) . s2) -defined AllTermsOf S -defined phi -valued Function-like Element of bool [:(AllTermsOf S),phi:]
(S,phi,h) | ((X *) /\ ((S -termsOfMaxDepth) . s2)) is Relation-like AllTermsOf S -defined (X *) /\ ((S -termsOfMaxDepth) . s2) -defined AllTermsOf S -defined phi -valued Function-like Element of bool [:(AllTermsOf S),phi:]
s2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(S -termsOfMaxDepth) . (s2 + 1) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365((((AllSymbolsOf S) *) \ {{}}))
(X *) /\ ((S -termsOfMaxDepth) . (s2 + 1)) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
(X *) typed/\ ((S -termsOfMaxDepth) . (s2 + 1)) is functional V25() FinSequence-membered Element of bool (X *)
(X *) /\ ((S -termsOfMaxDepth) . (s2 + 1)) is set
(X *) /\typed ((S -termsOfMaxDepth) . (s2 + 1)) is functional V25() FinSequence-membered V166() Element of bool ((S -termsOfMaxDepth) . (s2 + 1))
bool ((S -termsOfMaxDepth) . (s2 + 1)) is non empty set
(S,phi,A2) | ((X *) /\ ((S -termsOfMaxDepth) . (s2 + 1))) is Relation-like AllTermsOf S -defined (X *) /\ ((S -termsOfMaxDepth) . (s2 + 1)) -defined AllTermsOf S -defined phi -valued Function-like Element of bool [:(AllTermsOf S),phi:]
(S,phi,h) | ((X *) /\ ((S -termsOfMaxDepth) . (s2 + 1))) is Relation-like AllTermsOf S -defined (X *) /\ ((S -termsOfMaxDepth) . (s2 + 1)) -defined AllTermsOf S -defined phi -valued Function-like Element of bool [:(AllTermsOf S),phi:]
q is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S -termsOfMaxDepth) . q is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365((((AllSymbolsOf S) *) \ {{}}))
m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S -termsOfMaxDepth) . m1 is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365((((AllSymbolsOf S) *) \ {{}}))
p is functional V25() FinSequence-membered V166() Element of bool (AllTermsOf S)
(S,phi,A2) | p is Relation-like AllTermsOf S -defined p -defined AllTermsOf S -defined phi -valued Function-like total Element of bool [:(AllTermsOf S),phi:]
dom ((S,phi,A2) | p) is functional V25() FinSequence-membered V166() Element of bool p
bool p is non empty set
(S,phi,h) | p is Relation-like AllTermsOf S -defined p -defined AllTermsOf S -defined phi -valued Function-like total Element of bool [:(AllTermsOf S),phi:]
dom ((S,phi,h) | p) is functional V25() FinSequence-membered V166() Element of bool p
qq is functional V25() FinSequence-membered V166() Element of bool (AllTermsOf S)
(S,phi,A2) | qq is Relation-like AllTermsOf S -defined qq -defined AllTermsOf S -defined phi -valued Function-like total Element of bool [:(AllTermsOf S),phi:]
dom ((S,phi,A2) | qq) is functional V25() FinSequence-membered V166() Element of bool qq
bool qq is non empty set
(S,phi,h) | qq is Relation-like AllTermsOf S -defined qq -defined AllTermsOf S -defined phi -valued Function-like total Element of bool [:(AllTermsOf S),phi:]
dom ((S,phi,h) | qq) is functional V25() FinSequence-membered V166() Element of bool qq
STT is set
dom ((S,phi,A2) | ((X *) /\ ((S -termsOfMaxDepth) . (s2 + 1)))) is functional V25() FinSequence-membered V166() Element of bool ((X *) /\ ((S -termsOfMaxDepth) . (s2 + 1)))
bool ((X *) /\ ((S -termsOfMaxDepth) . (s2 + 1))) is non empty set
m1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
TermSymbolsOf S is non empty set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
tq is non empty set
tq * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of tq
g1 is non empty functional V25() FinSequence-membered V166() V167() Element of bool (AllTermsOf S)
qqq is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal m1 + 1 -termal Element of ((AllSymbolsOf S) *) \ {{}}
(S -firstChar) . qqq is non relational termal own ofAtomicFormula Element of AllSymbolsOf S
ar ((S -firstChar) . qqq) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of S . ((S -firstChar) . qqq) is set
abs (ar ((S -firstChar) . qqq)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
g2 is non empty Relation-like NAT -defined tq -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of tq *
g2 . 1 is set
{(g2 . 1)} is non empty trivial finite 1 -element set
{(g2 . 1)} \ tq is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool {(g2 . 1)}
bool {(g2 . 1)} is non empty finite V25() set
{(g2 . 1)} typed\ tq is trivial finite Element of bool {(g2 . 1)}
bool X is non empty set
rng qqq is non empty finite Element of bool (TermSymbolsOf S)
bool (TermSymbolsOf S) is non empty set
r is Element of bool X
r * is non empty functional V25() FinSequence-membered Element of bool (X *)
(rng qqq) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool ((TermSymbolsOf S) *)
(TermSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of TermSymbolsOf S
bool ((TermSymbolsOf S) *) is non empty non trivial non finite V167() set
newords is non empty functional V25() FinSequence-membered Element of bool (X *)
SubTerms qqq is Relation-like NAT -defined (S -termsOfMaxDepth) . m1 -valued (proj2 qqq) * -valued AllTermsOf S -valued Function-like finite abs (ar qqq) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf S) *
K365(((AllSymbolsOf S) *)) is non empty non trivial non finite V167() Element of bool (bool ((AllSymbolsOf S) *))
bool (bool ((AllSymbolsOf S) *)) is non empty non trivial non finite V167() set
S -termsOfMaxDepth is non empty Relation-like NAT -defined K365(((AllSymbolsOf S) *)) -valued Function-like total quasi_total Element of bool [:NAT,K365(((AllSymbolsOf S) *)):]
[:NAT,K365(((AllSymbolsOf S) *)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365(((AllSymbolsOf S) *)):] is non empty non trivial non finite V167() set
(S -termsOfMaxDepth) . m1 is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365(((AllSymbolsOf S) *))
proj2 qqq is non empty finite set
(proj2 qqq) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 qqq
AllTermsOf S is non empty functional V25() FinSequence-membered AllSymbolsOf S -prefix S -prefix Element of bool ((AllSymbolsOf S) *)
ar qqq is complex ext-real V40() V41() Element of INT
abs (ar qqq) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(AllTermsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf S) *) *)
oo is Element of tq
(A2 | X) . oo is Relation-like Function-like set
A2 . oo is Relation-like Function-like set
((A2 | X) . oo) \+\ (A2 . oo) is Relation-like set
((A2 | X) . oo) \ (A2 . oo) is Relation-like set
((A2 | X) . oo) typed\ (A2 . oo) is Relation-like Function-like Element of bool ((A2 | X) . oo)
bool ((A2 | X) . oo) is non empty set
((A2 | X) . oo) \ (A2 . oo) is Relation-like Function-like Element of bool ((A2 | X) . oo)
(A2 . oo) \ ((A2 | X) . oo) is Relation-like set
(A2 . oo) typed\ ((A2 | X) . oo) is Relation-like Function-like Element of bool (A2 . oo)
bool (A2 . oo) is non empty set
(A2 . oo) \ ((A2 | X) . oo) is Relation-like Function-like Element of bool (A2 . oo)
(((A2 | X) . oo) \ (A2 . oo)) \/ ((A2 . oo) \ ((A2 | X) . oo)) is Relation-like set
(h | X) . oo is Relation-like Function-like set
h . oo is Relation-like Function-like set
((h | X) . oo) \+\ (h . oo) is Relation-like set
((h | X) . oo) \ (h . oo) is Relation-like set
((h | X) . oo) typed\ (h . oo) is Relation-like Function-like Element of bool ((h | X) . oo)
bool ((h | X) . oo) is non empty set
((h | X) . oo) \ (h . oo) is Relation-like Function-like Element of bool ((h | X) . oo)
(h . oo) \ ((h | X) . oo) is Relation-like set
(h . oo) typed\ ((h | X) . oo) is Relation-like Function-like Element of bool (h . oo)
bool (h . oo) is non empty set
(h . oo) \ ((h | X) . oo) is Relation-like Function-like Element of bool (h . oo)
(((h | X) . oo) \ (h . oo)) \/ ((h . oo) \ ((h | X) . oo)) is Relation-like set
(S,phi,A2) | g1 is Relation-like AllTermsOf S -defined g1 -defined AllTermsOf S -defined phi -valued Function-like total Element of bool [:(AllTermsOf S),phi:]
dx is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of g1
((S,phi,A2) | g1) . dx is set
(S,phi,A2) . dx is Element of phi
(((S,phi,A2) | g1) . dx) \+\ ((S,phi,A2) . dx) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(((S,phi,A2) | g1) . dx) \ ((S,phi,A2) . dx) is set
(((S,phi,A2) | g1) . dx) typed\ ((S,phi,A2) . dx) is Element of bool (((S,phi,A2) | g1) . dx)
bool (((S,phi,A2) | g1) . dx) is non empty set
(((S,phi,A2) | g1) . dx) \ ((S,phi,A2) . dx) is Element of bool (((S,phi,A2) | g1) . dx)
((S,phi,A2) . dx) \ (((S,phi,A2) | g1) . dx) is set
((S,phi,A2) . dx) typed\ (((S,phi,A2) | g1) . dx) is Element of bool ((S,phi,A2) . dx)
bool ((S,phi,A2) . dx) is non empty set
((S,phi,A2) . dx) \ (((S,phi,A2) | g1) . dx) is Element of bool ((S,phi,A2) . dx)
((((S,phi,A2) | g1) . dx) \ ((S,phi,A2) . dx)) \/ (((S,phi,A2) . dx) \ (((S,phi,A2) | g1) . dx)) is set
(S,phi,h) | g1 is Relation-like AllTermsOf S -defined g1 -defined AllTermsOf S -defined phi -valued Function-like total Element of bool [:(AllTermsOf S),phi:]
((S,phi,h) | g1) . dx is set
(S,phi,h) . dx is Element of phi
(((S,phi,h) | g1) . dx) \+\ ((S,phi,h) . dx) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(((S,phi,h) | g1) . dx) \ ((S,phi,h) . dx) is set
(((S,phi,h) | g1) . dx) typed\ ((S,phi,h) . dx) is Element of bool (((S,phi,h) | g1) . dx)
bool (((S,phi,h) | g1) . dx) is non empty set
(((S,phi,h) | g1) . dx) \ ((S,phi,h) . dx) is Element of bool (((S,phi,h) | g1) . dx)
((S,phi,h) . dx) \ (((S,phi,h) | g1) . dx) is set
((S,phi,h) . dx) typed\ (((S,phi,h) | g1) . dx) is Element of bool ((S,phi,h) . dx)
bool ((S,phi,h) . dx) is non empty set
((S,phi,h) . dx) \ (((S,phi,h) | g1) . dx) is Element of bool ((S,phi,h) . dx)
((((S,phi,h) | g1) . dx) \ ((S,phi,h) . dx)) \/ (((S,phi,h) . dx) \ (((S,phi,h) | g1) . dx)) is set
((S,phi,A2) | ((X *) /\ ((S -termsOfMaxDepth) . (s2 + 1)))) . STT is set
(S,phi,A2) . STT is set
((S,phi,h) | ((X *) /\ ((S -termsOfMaxDepth) . (s2 + 1)))) . STT is set
(S,phi,h) . STT is set
ST is Relation-like NAT -defined newords -valued Function-like finite abs (ar ((S -firstChar) . qqq)) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() set
rng ST is functional finite V25() FinSequence-membered Element of bool newords
bool newords is non empty set
((S,phi,A2) | ((X *) /\ ((S -termsOfMaxDepth) . s2))) (*) ST is Relation-like NAT -defined phi -valued Function-like finite V199() set
(S,phi,A2) (*) ST is Relation-like NAT -defined phi -valued Function-like finite V199() set
((S,phi,h) | ((X *) /\ ((S -termsOfMaxDepth) . s2))) (*) ST is Relation-like NAT -defined phi -valued Function-like finite V199() set
(S,phi,h) (*) ST is Relation-like NAT -defined phi -valued Function-like finite V199() set
(S,phi,A2,((S -firstChar) . qqq)) is non empty Relation-like (abs (ar ((S -firstChar) . qqq))) -tuples_on phi -defined phi \/ BOOLEAN -valued Function-like total quasi_total (S,phi,(S -firstChar) . qqq)
(abs (ar ((S -firstChar) . qqq))) -tuples_on phi is non empty functional V25() FinSequence-membered FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
(S,phi,A2,((S -firstChar) . qqq)) . (((S,phi,A2) | ((X *) /\ ((S -termsOfMaxDepth) . s2))) (*) ST) is set
(S,phi,A2) . qqq is set
dom ((S,phi,A2) | (X *)) is functional V25() FinSequence-membered Element of bool (X *)
(X *) /\ (AllTermsOf S) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
(X *) typed/\ (AllTermsOf S) is functional V25() FinSequence-membered Element of bool (X *)
(X *) /\ (AllTermsOf S) is set
(X *) /\typed (AllTermsOf S) is functional V25() FinSequence-membered V166() Element of bool (AllTermsOf S)
dom ((S,phi,h) | (X *)) is functional V25() FinSequence-membered Element of bool (X *)
m2 is set
TermSymbolsOf S is non empty set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
q is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of ((AllSymbolsOf S) *) \ {{}}
Depth q is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
p is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal Depth q -termal Element of ((AllSymbolsOf S) *) \ {{}}
(S -termsOfMaxDepth) . (Depth q) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf S -prefix S -prefix Element of K365((((AllSymbolsOf S) *) \ {{}}))
(X *) /\ ((S -termsOfMaxDepth) . (Depth q)) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
(X *) typed/\ ((S -termsOfMaxDepth) . (Depth q)) is functional V25() FinSequence-membered Element of bool (X *)
(X *) /\ ((S -termsOfMaxDepth) . (Depth q)) is set
(X *) /\typed ((S -termsOfMaxDepth) . (Depth q)) is functional V25() FinSequence-membered V166() Element of bool ((S -termsOfMaxDepth) . (Depth q))
bool ((S -termsOfMaxDepth) . (Depth q)) is non empty set
STT is non empty set
(S,phi,A2) | STT is Relation-like AllTermsOf S -defined STT -defined AllTermsOf S -defined phi -valued Function-like Element of bool [:(AllTermsOf S),phi:]
(S,phi,h) | STT is Relation-like AllTermsOf S -defined STT -defined AllTermsOf S -defined phi -valued Function-like Element of bool [:(AllTermsOf S),phi:]
tq is Relation-like NAT -defined X -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of X *
((S,phi,A2) | (X *)) . tq is set
(S,phi,A2) . tq is set
(((S,phi,A2) | (X *)) . tq) \+\ ((S,phi,A2) . tq) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(((S,phi,A2) | (X *)) . tq) \ ((S,phi,A2) . tq) is set
(((S,phi,A2) | (X *)) . tq) typed\ ((S,phi,A2) . tq) is Element of bool (((S,phi,A2) | (X *)) . tq)
bool (((S,phi,A2) | (X *)) . tq) is non empty set
(((S,phi,A2) | (X *)) . tq) \ ((S,phi,A2) . tq) is Element of bool (((S,phi,A2) | (X *)) . tq)
((S,phi,A2) . tq) \ (((S,phi,A2) | (X *)) . tq) is set
((S,phi,A2) . tq) typed\ (((S,phi,A2) | (X *)) . tq) is Element of bool ((S,phi,A2) . tq)
bool ((S,phi,A2) . tq) is non empty set
((S,phi,A2) . tq) \ (((S,phi,A2) | (X *)) . tq) is Element of bool ((S,phi,A2) . tq)
((((S,phi,A2) | (X *)) . tq) \ ((S,phi,A2) . tq)) \/ (((S,phi,A2) . tq) \ (((S,phi,A2) | (X *)) . tq)) is set
((S,phi,h) | (X *)) . tq is set
(S,phi,h) . tq is set
(((S,phi,h) | (X *)) . tq) \+\ ((S,phi,h) . tq) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(((S,phi,h) | (X *)) . tq) \ ((S,phi,h) . tq) is set
(((S,phi,h) | (X *)) . tq) typed\ ((S,phi,h) . tq) is Element of bool (((S,phi,h) | (X *)) . tq)
bool (((S,phi,h) | (X *)) . tq) is non empty set
(((S,phi,h) | (X *)) . tq) \ ((S,phi,h) . tq) is Element of bool (((S,phi,h) | (X *)) . tq)
((S,phi,h) . tq) \ (((S,phi,h) | (X *)) . tq) is set
((S,phi,h) . tq) typed\ (((S,phi,h) | (X *)) . tq) is Element of bool ((S,phi,h) . tq)
bool ((S,phi,h) . tq) is non empty set
((S,phi,h) . tq) \ (((S,phi,h) | (X *)) . tq) is Element of bool ((S,phi,h) . tq)
((((S,phi,h) | (X *)) . tq) \ ((S,phi,h) . tq)) \/ (((S,phi,h) . tq) \ (((S,phi,h) | (X *)) . tq)) is set
qqq is Element of STT
((S,phi,A2) | STT) . qqq is set
(S,phi,A2) . qqq is set
(((S,phi,A2) | STT) . qqq) \+\ ((S,phi,A2) . qqq) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(((S,phi,A2) | STT) . qqq) \ ((S,phi,A2) . qqq) is set
(((S,phi,A2) | STT) . qqq) typed\ ((S,phi,A2) . qqq) is Element of bool (((S,phi,A2) | STT) . qqq)
bool (((S,phi,A2) | STT) . qqq) is non empty set
(((S,phi,A2) | STT) . qqq) \ ((S,phi,A2) . qqq) is Element of bool (((S,phi,A2) | STT) . qqq)
((S,phi,A2) . qqq) \ (((S,phi,A2) | STT) . qqq) is set
((S,phi,A2) . qqq) typed\ (((S,phi,A2) | STT) . qqq) is Element of bool ((S,phi,A2) . qqq)
bool ((S,phi,A2) . qqq) is non empty set
((S,phi,A2) . qqq) \ (((S,phi,A2) | STT) . qqq) is Element of bool ((S,phi,A2) . qqq)
((((S,phi,A2) | STT) . qqq) \ ((S,phi,A2) . qqq)) \/ (((S,phi,A2) . qqq) \ (((S,phi,A2) | STT) . qqq)) is set
((S,phi,h) | STT) . qqq is set
(S,phi,h) . qqq is set
(((S,phi,h) | STT) . qqq) \+\ ((S,phi,h) . qqq) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(((S,phi,h) | STT) . qqq) \ ((S,phi,h) . qqq) is set
(((S,phi,h) | STT) . qqq) typed\ ((S,phi,h) . qqq) is Element of bool (((S,phi,h) | STT) . qqq)
bool (((S,phi,h) | STT) . qqq) is non empty set
(((S,phi,h) | STT) . qqq) \ ((S,phi,h) . qqq) is Element of bool (((S,phi,h) | STT) . qqq)
((S,phi,h) . qqq) \ (((S,phi,h) | STT) . qqq) is set
((S,phi,h) . qqq) typed\ (((S,phi,h) | STT) . qqq) is Element of bool ((S,phi,h) . qqq)
bool ((S,phi,h) . qqq) is non empty set
((S,phi,h) . qqq) \ (((S,phi,h) | STT) . qqq) is Element of bool ((S,phi,h) . qqq)
((((S,phi,h) | STT) . qqq) \ ((S,phi,h) . qqq)) \/ (((S,phi,h) . qqq) \ (((S,phi,h) | STT) . qqq)) is set
((S,phi,A2) | (X *)) . m2 is set
(S,phi,A2) . m2 is set
((S,phi,h) | (X *)) . m2 is set
(S,phi,h) . m2 is set
((S,phi,A2) | STT) . m2 is set
((S,phi,h) | STT) . m2 is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
S is non empty set
phi is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
proj2 phi is finite set
I is Element of S
N is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
v1 is Relation-like Function-like Function-yielding V164() (X,S) set
(v1,N,I) is Relation-like Function-like Function-yielding V164() (X,S) set
{} .--> I is trivial Relation-like {{}} -defined S -valued Function-like one-to-one constant finite V199() set
{{}} --> I is non empty Relation-like {{}} -defined S -valued {I} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{I}:]
{I} is non empty trivial finite 1 -element set
[:{{}},{I}:] is non empty Relation-like finite set
bool [:{{}},{I}:] is non empty finite V25() set
N .--> ({} .--> I) is trivial Relation-like AllSymbolsOf X -defined {N} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{N} is non empty trivial finite 1 -element set
{N} --> ({} .--> I) is non empty Relation-like {N} -defined {({} .--> I)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{N},{({} .--> I)}:]
{({} .--> I)} is non empty trivial functional finite V25() 1 -element set
[:{N},{({} .--> I)}:] is non empty Relation-like finite set
bool [:{N},{({} .--> I)}:] is non empty finite V25() set
v1 +* (N .--> ({} .--> I)) is Relation-like Function-like Function-yielding V164() set
(X,S,(v1,N,I)) is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
[:(AllTermsOf X),S:] is non empty Relation-like set
bool [:(AllTermsOf X),S:] is non empty set
(X,S,(v1,N,I)) . phi is set
(X,S,v1) is non empty Relation-like AllTermsOf X -defined S -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),S:]
(X,S,v1) . phi is set
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b<sub>1</sub> is (X,S) } is set
phi null {} is Relation-like NAT -defined {} \/ (proj1 phi) -defined {} \/ (proj2 phi) -valued Function-like finite len phi -element FinSequence-like FinSubsequence-like V199() set
proj1 phi is finite set
{} \/ (proj1 phi) is finite set
{} \/ (proj2 phi) is finite set
len phi is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
phi \typed/ {} is Relation-like NAT -defined finite Element of bool (phi \/ {})
phi \/ {} is Relation-like NAT -defined finite set
bool (phi \/ {}) is non empty finite V25() set
phi ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
{} ^ phi is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(proj2 phi) * is non empty functional V25() FinSequence-membered FinSequenceSet of proj2 phi
(X,S,(v1,N,I)) | ((proj2 phi) *) is Relation-like AllTermsOf X -defined (proj2 phi) * -defined AllTermsOf X -defined S -valued Function-like Element of bool [:(AllTermsOf X),S:]
A2 is Relation-like NAT -defined proj2 phi -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of (proj2 phi) *
((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2 is set
(X,S,(v1,N,I)) . A2 is set
(((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2) \+\ ((X,S,(v1,N,I)) . A2) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2) \ ((X,S,(v1,N,I)) . A2) is set
(((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2) typed\ ((X,S,(v1,N,I)) . A2) is Element of bool (((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2)
bool (((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2) is non empty set
(((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2) \ ((X,S,(v1,N,I)) . A2) is Element of bool (((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2)
((X,S,(v1,N,I)) . A2) \ (((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2) is set
((X,S,(v1,N,I)) . A2) typed\ (((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2) is Element of bool ((X,S,(v1,N,I)) . A2)
bool ((X,S,(v1,N,I)) . A2) is non empty set
((X,S,(v1,N,I)) . A2) \ (((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2) is Element of bool ((X,S,(v1,N,I)) . A2)
((((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2) \ ((X,S,(v1,N,I)) . A2)) \/ (((X,S,(v1,N,I)) . A2) \ (((X,S,(v1,N,I)) | ((proj2 phi) *)) . A2)) is set
(X,S,v1) | ((proj2 phi) *) is Relation-like AllTermsOf X -defined (proj2 phi) * -defined AllTermsOf X -defined S -valued Function-like Element of bool [:(AllTermsOf X),S:]
((X,S,v1) | ((proj2 phi) *)) . A2 is set
(X,S,v1) . A2 is set
(((X,S,v1) | ((proj2 phi) *)) . A2) \+\ ((X,S,v1) . A2) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
(((X,S,v1) | ((proj2 phi) *)) . A2) \ ((X,S,v1) . A2) is set
(((X,S,v1) | ((proj2 phi) *)) . A2) typed\ ((X,S,v1) . A2) is Element of bool (((X,S,v1) | ((proj2 phi) *)) . A2)
bool (((X,S,v1) | ((proj2 phi) *)) . A2) is non empty set
(((X,S,v1) | ((proj2 phi) *)) . A2) \ ((X,S,v1) . A2) is Element of bool (((X,S,v1) | ((proj2 phi) *)) . A2)
((X,S,v1) . A2) \ (((X,S,v1) | ((proj2 phi) *)) . A2) is set
((X,S,v1) . A2) typed\ (((X,S,v1) | ((proj2 phi) *)) . A2) is Element of bool ((X,S,v1) . A2)
bool ((X,S,v1) . A2) is non empty set
((X,S,v1) . A2) \ (((X,S,v1) | ((proj2 phi) *)) . A2) is Element of bool ((X,S,v1) . A2)
((((X,S,v1) | ((proj2 phi) *)) . A2) \ ((X,S,v1) . A2)) \/ (((X,S,v1) . A2) \ (((X,S,v1) | ((proj2 phi) *)) . A2)) is set
((X,S,(v1,N,I)) | ((proj2 phi) *)) . phi is set
((X,S,v1) | ((proj2 phi) *)) . phi is set
{N} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
dom (N .--> ({} .--> I)) is trivial finite Element of bool {N}
bool {N} is non empty finite V25() set
(v1,N,I) | (proj2 phi) is Relation-like proj2 phi -defined Function-like finite Function-yielding V164() V199() set
v1 | (proj2 phi) is Relation-like proj2 phi -defined Function-like finite Function-yielding V164() V199() set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
X is finite set
LettersOf S is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U3 of S is Element of the U1 of S
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of S " {0} is Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
bool X is non empty finite V25() set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(((AllSymbolsOf S) *) \ {{}}) /\ X is functional finite V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(((AllSymbolsOf S) *) \ {{}}) typed/\ X is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
(((AllSymbolsOf S) *) \ {{}}) /\ X is finite set
(((AllSymbolsOf S) *) \ {{}}) /\typed X is finite Element of bool X
N is functional finite V25() FinSequence-membered Element of bool X
SymbolsOf N is finite set
N \/ {{}} is non empty functional finite V25() set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of N \/ {{}} : b<sub>1</sub> in N } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of N \/ {{}} : b<sub>1</sub> in N } is set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of N : b<sub>1</sub> in N } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of N : b<sub>1</sub> in N } is set
bool (LettersOf S) is non empty non trivial non finite V167() set
v1 is finite set
(LettersOf S) \ v1 is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
(LettersOf S) typed\ v1 is Element of bool (LettersOf S)
(LettersOf S) \ v1 is non empty non trivial non finite V167() Element of bool (LettersOf S)
psi is non empty non trivial non finite V167() Element of bool (LettersOf S)
the Element of psi is Element of psi
A is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
proj2 S is non empty finite set
(proj2 S) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(proj2 S) typed/\ (LettersOf X) is finite Element of bool (proj2 S)
bool (proj2 S) is non empty finite V25() set
(proj2 S) /\ (LettersOf X) is finite set
(proj2 S) /\typed (LettersOf X) is Element of bool (LettersOf X)
bool (LettersOf X) is non empty non trivial non finite V167() set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
{} .--> {} is trivial Relation-like {{}} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite set
bool [:{{}},{{}}:] is non empty finite V25() set
(AllSymbolsOf X) -concatenation is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() V201((AllSymbolsOf X) * ) Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
MultPlace ((AllSymbolsOf X) -concatenation) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf X) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -concatenation is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() V201((AllSymbolsOf X) * ) Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
MultPlace ((AllSymbolsOf X) -concatenation) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf X) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
X -termsOfMaxDepth is non empty Relation-like NAT -defined K365((((AllSymbolsOf X) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):]
[:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial non finite V167() set
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
proj2 A2 is non empty finite set
(proj2 A2) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(proj2 A2) typed/\ (LettersOf X) is finite Element of bool (proj2 A2)
bool (proj2 A2) is non empty finite V25() set
(proj2 A2) /\ (LettersOf X) is finite set
(proj2 A2) /\typed (LettersOf X) is Element of bool (LettersOf X)
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
h is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . h is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
t is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X,t) is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
[1,t] is non empty V34() set
{[1,t]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
SubTerms h is empty trivial Relation-like non-empty empty-yielding NAT -defined (proj2 h) * -valued AllTermsOf X -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element abs (ar h) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of (AllTermsOf X) *
proj2 h is non empty trivial finite 1 -element set
(proj2 h) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 h
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
ar h is complex ext-real V40() V41() Element of INT
ar ((X -firstChar) . h) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of INT
the adicity of X . ((X -firstChar) . h) is set
abs (ar h) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
(X -multiCat) . (SubTerms h) is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of (AllSymbolsOf X) *
(X,t) ^ ((X -multiCat) . (SubTerms h)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,t) ^ {} is non empty Relation-like NAT -defined Function-like finite 1 + {} -element FinSequence-like FinSubsequence-like V199() set
1 + {} is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(X,t) null {} is Relation-like NAT -defined {} \/ (proj1 (X,t)) -defined Seg (1 + {}) -defined {} \/ (proj2 (X,t)) -valued Function-like finite len (X,t) -element total FinSequence-like FinSubsequence-like V199() set
proj1 (X,t) is non empty trivial finite 1 -element set
{} \/ (proj1 (X,t)) is non empty finite set
Seg (1 + {}) is non empty finite 1 + {} -element Element of bool NAT
{ b<sub>1</sub> where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> <= 1 + {} ) } is set
proj2 (X,t) is non empty trivial finite 1 -element set
{} \/ (proj2 (X,t)) is non empty finite set
len (X,t) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(X,t) \typed/ {} is Relation-like NAT -defined finite Element of bool ((X,t) \/ {})
(X,t) \/ {} is non empty Relation-like NAT -defined finite set
bool ((X,t) \/ {}) is non empty finite V25() set
{} ^ (X,t) is non empty Relation-like NAT -defined Function-like finite {} + 1 -element {} + 1 -element FinSequence-like FinSubsequence-like V199() set
{} + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
{} + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng h is non empty trivial finite 1 -element Element of bool (TermSymbolsOf X)
bool (TermSymbolsOf X) is non empty set
(rng h) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(rng h) typed/\ (LettersOf X) is trivial finite Element of bool (rng h)
bool (rng h) is non empty finite V25() set
(rng h) /\ (LettersOf X) is finite set
(rng h) /\typed (LettersOf X) is Element of bool (LettersOf X)
H is literal Element of LettersOf X
{H} is non empty trivial finite 1 -element Element of bool (LettersOf X)
{H} null (LettersOf X) is set
(LettersOf X) /\ {H} is finite Element of bool (LettersOf X)
(LettersOf X) typed/\ {H} is Element of bool (LettersOf X)
(LettersOf X) /\ {H} is finite set
(LettersOf X) /\typed {H} is trivial finite Element of bool {H}
bool {H} is non empty finite V25() set
{H} \typed/ (LettersOf X) is Element of bool ({H} \/ (LettersOf X))
{H} \/ (LettersOf X) is non empty non trivial non finite V167() set
bool ({H} \/ (LettersOf X)) is non empty non trivial non finite V167() set
A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
A2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
proj2 t is non empty finite set
(proj2 t) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(proj2 t) typed/\ (LettersOf X) is finite Element of bool (proj2 t)
bool (proj2 t) is non empty finite V25() set
(proj2 t) /\ (LettersOf X) is finite set
(proj2 t) /\typed (LettersOf X) is Element of bool (LettersOf X)
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
H is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal A2 + 1 -termal Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . H is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
ar ((X -firstChar) . H) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of X . ((X -firstChar) . H) is set
abs (ar ((X -firstChar) . H)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
T is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
m1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
m1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
h is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
h + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite V167() set
SubTerms H is Relation-like NAT -defined (proj2 H) * -valued AllTermsOf X -valued Function-like finite abs (ar H) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
proj2 H is non empty finite set
(proj2 H) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 H
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
ar H is complex ext-real V40() V41() Element of INT
abs (ar H) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
(m1 + 1) + 0 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
m1 is non empty Relation-like non empty-yielding NAT -defined AllTermsOf X -valued Function-like finite m1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
m1 . (m1 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
{(m1 . (m1 + 1))} is non empty trivial functional finite V25() 1 -element set
{(m1 . (m1 + 1))} \ (AllTermsOf X) is trivial functional finite V25() Element of bool {(m1 . (m1 + 1))}
bool {(m1 . (m1 + 1))} is non empty finite V25() set
{(m1 . (m1 + 1))} typed\ (AllTermsOf X) is trivial functional finite V25() Element of bool {(m1 . (m1 + 1))}
A1 is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of A1
Seg m1 is finite m1 -element Element of bool NAT
{ b<sub>1</sub> where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> <= m1 ) } is set
m1 | (Seg m1) is Relation-like NAT -defined Seg m1 -defined NAT -defined Seg m1 -defined AllTermsOf X -valued Function-like finite m1 -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() set
<*(m1 . (m1 + 1))*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() set
[1,(m1 . (m1 + 1))] is non empty V34() set
{[1,(m1 . (m1 + 1))]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*> is non empty Relation-like NAT -defined Function-like finite m1 + 1 -element m1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() set
m1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
((m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*>) \+\ m1 is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
((m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*>) \ m1 is Relation-like NAT -defined finite set
((m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*>) typed\ m1 is Relation-like NAT -defined Function-like finite V199() Element of bool ((m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*>)
bool ((m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*>) is non empty finite V25() set
((m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*>) \ m1 is Relation-like NAT -defined Function-like finite V199() Element of bool ((m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*>)
m1 \ ((m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*>) is Relation-like NAT -defined AllTermsOf X -valued finite set
m1 typed\ ((m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*>) is Relation-like NAT -defined AllTermsOf X -valued Function-like finite Function-yielding V164() V198() V199() Element of bool m1
bool m1 is non empty finite V25() set
m1 \ ((m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*>) is Relation-like NAT -defined AllTermsOf X -valued Function-like finite Function-yielding V164() V198() V199() Element of bool m1
(((m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*>) \ m1) \/ (m1 \ ((m1 | (Seg m1)) ^ <*(m1 . (m1 + 1))*>)) is Relation-like NAT -defined finite set
p is Relation-like NAT -defined A1 -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() V199() set
qq is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
<*qq*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() set
[1,qq] is non empty V34() set
{[1,qq]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
p ^ <*qq*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X -multiCat) . m1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X -multiCat) . p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
((X -multiCat) . p) ^ qq is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,((X -firstChar) . H)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,((X -firstChar) . H)] is non empty V34() set
{[1,((X -firstChar) . H)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(X,((X -firstChar) . H)) ^ (((X -multiCat) . p) ^ qq) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
rng H is non empty finite Element of bool (TermSymbolsOf X)
bool (TermSymbolsOf X) is non empty set
proj2 (X,((X -firstChar) . H)) is non empty trivial finite 1 -element set
proj2 (((X -multiCat) . p) ^ qq) is finite set
(proj2 (X,((X -firstChar) . H))) \/ (proj2 (((X -multiCat) . p) ^ qq)) is non empty finite set
{((X -firstChar) . H)} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf X)
{((X -firstChar) . H)} \/ (proj2 (((X -multiCat) . p) ^ qq)) is non empty finite set
proj2 ((X -multiCat) . p) is finite set
rng qq is finite Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(proj2 ((X -multiCat) . p)) \/ (rng qq) is finite set
{((X -firstChar) . H)} \/ ((proj2 ((X -multiCat) . p)) \/ (rng qq)) is non empty finite set
{((X -firstChar) . H)} \/ (proj2 ((X -multiCat) . p)) is non empty finite set
(rng qq) \/ ({((X -firstChar) . H)} \/ (proj2 ((X -multiCat) . p))) is non empty finite set
(rng qq) null ({((X -firstChar) . H)} \/ (proj2 ((X -multiCat) . p))) is set
(rng qq) \typed/ ({((X -firstChar) . H)} \/ (proj2 ((X -multiCat) . p))) is finite Element of bool ((rng qq) \/ ({((X -firstChar) . H)} \/ (proj2 ((X -multiCat) . p))))
bool ((rng qq) \/ ({((X -firstChar) . H)} \/ (proj2 ((X -multiCat) . p)))) is non empty finite V25() set
proj2 q is finite set
(proj2 q) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(proj2 q) typed/\ (LettersOf X) is finite Element of bool (proj2 q)
bool (proj2 q) is non empty finite V25() set
(proj2 q) /\ (LettersOf X) is finite set
(proj2 q) /\typed (LettersOf X) is Element of bool (LettersOf X)
(rng H) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(rng H) typed/\ (LettersOf X) is finite Element of bool (rng H)
bool (rng H) is non empty finite V25() set
(rng H) /\ (LettersOf X) is finite set
(rng H) /\typed (LettersOf X) is Element of bool (LettersOf X)
(X -termsOfMaxDepth) . h is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
m2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal h + 1 -termal Element of ((AllSymbolsOf X) *) \ {{}}
SubTerms m2 is Relation-like NAT -defined (X -termsOfMaxDepth) . h -valued (proj2 m2) * -valued AllTermsOf X -valued Function-like finite abs (ar m2) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
K365(((AllSymbolsOf X) *)) is non empty non trivial non finite V167() Element of bool (bool ((AllSymbolsOf X) *))
bool (bool ((AllSymbolsOf X) *)) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is non empty Relation-like NAT -defined K365(((AllSymbolsOf X) *)) -valued Function-like total quasi_total Element of bool [:NAT,K365(((AllSymbolsOf X) *)):]
[:NAT,K365(((AllSymbolsOf X) *)):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365(((AllSymbolsOf X) *)):] is non empty non trivial non finite V167() set
(X -termsOfMaxDepth) . h is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365(((AllSymbolsOf X) *))
proj2 m2 is non empty finite set
(proj2 m2) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 m2
ar m2 is complex ext-real V40() V41() Element of INT
(X -firstChar) . m2 is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
ar ((X -firstChar) . m2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of X . ((X -firstChar) . m2) is set
abs (ar m2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
STT is non empty Relation-like non empty-yielding NAT -defined (X -termsOfMaxDepth) . h -valued Function-like finite (m1 + 1) + 0 -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() set
STT . (m1 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
{(STT . (m1 + 1))} is non empty trivial functional finite V25() 1 -element set
{(STT . (m1 + 1))} \ ((X -termsOfMaxDepth) . h) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool {(STT . (m1 + 1))}
bool {(STT . (m1 + 1))} is non empty finite V25() set
{(STT . (m1 + 1))} typed\ ((X -termsOfMaxDepth) . h) is trivial functional finite V25() Element of bool {(STT . (m1 + 1))}
qqq is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X -termsOfMaxDepth) . h
tq is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal A2 -termal Element of ((AllSymbolsOf X) *) \ {{}}
rng tq is non empty finite Element of bool (TermSymbolsOf X)
(rng tq) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(rng tq) typed/\ (LettersOf X) is finite Element of bool (rng tq)
bool (rng tq) is non empty finite V25() set
(rng tq) /\ (LettersOf X) is finite set
(rng tq) /\typed (LettersOf X) is Element of bool (LettersOf X)
H is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal A2 + 1 -termal Element of ((AllSymbolsOf X) *) \ {{}}
H is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal A2 + 1 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
A2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of ((AllSymbolsOf X) *) \ {{}}
Depth A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is V51() V53() eligible Language-like
TermSymbolsOf X is non empty set
the U1 of X is set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of ((AllSymbolsOf X) *) \ {{}}
rng S is non empty finite Element of bool (TermSymbolsOf X)
bool (TermSymbolsOf X) is non empty set
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
(rng S) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(rng S) typed/\ (LettersOf X) is finite Element of bool (rng S)
bool (rng S) is non empty finite V25() set
(rng S) /\ (LettersOf X) is finite set
(rng S) /\typed (LettersOf X) is Element of bool (LettersOf X)
bool (LettersOf X) is non empty non trivial non finite V167() set
phi is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
proj2 S is non empty finite set
(proj2 S) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(proj2 S) typed/\ (LettersOf X) is finite Element of bool (proj2 S)
bool (proj2 S) is non empty finite V25() set
(proj2 S) /\ (LettersOf X) is finite set
(proj2 S) /\typed (LettersOf X) is Element of bool (LettersOf X)
bool (LettersOf X) is non empty non trivial non finite V167() set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total V201( AllSymbolsOf X) Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
AllTermsOf X is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of K365((((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
K365((((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
{} .--> {} is trivial Relation-like {{}} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite set
bool [:{{}},{{}}:] is non empty finite V25() set
(AllSymbolsOf X) -concatenation is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() V201((AllSymbolsOf X) * ) Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
MultPlace ((AllSymbolsOf X) -concatenation) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf X) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
(AllSymbolsOf X) -concatenation is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() V201((AllSymbolsOf X) * ) Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
MultPlace ((AllSymbolsOf X) -concatenation) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V164() V198() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite V167() set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite V167() set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite V167() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf X) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
X -termsOfMaxDepth is non empty Relation-like NAT -defined K365((((AllSymbolsOf X) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):]
[:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial Relation-like non finite V167() set
bool [:NAT,K365((((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial non finite V167() set
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
proj2 A2 is non empty finite set
(proj2 A2) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(proj2 A2) typed/\ (LettersOf X) is finite Element of bool (proj2 A2)
bool (proj2 A2) is non empty finite V25() set
(proj2 A2) /\ (LettersOf X) is finite set
(proj2 A2) /\typed (LettersOf X) is Element of bool (LettersOf X)
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
h is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() 0wff (X, 0 ) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . h is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
t is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
ar t is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X . t is set
abs (ar t) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
H is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
T is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
T + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(T + 1) + 0 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite V167() set
SubTerms h is Relation-like NAT -defined (proj2 h) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . h)) -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
ar ((X -firstChar) . h) is non empty complex ext-real non positive negative V40() V41() Element of INT
the adicity of X . ((X -firstChar) . h) is set
abs (ar ((X -firstChar) . h)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
proj2 h is non empty finite set
(proj2 h) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of proj2 h
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
(TermSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V25() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
(AllTermsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() Element of bool (((AllSymbolsOf X) *) *)
m1 is non empty Relation-like non empty-yielding NAT -defined AllTermsOf X -valued Function-like finite (T + 1) + 0 -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() Element of (AllTermsOf X) *
Seg T is finite T -element Element of bool NAT
{ b<sub>1</sub> where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> <= T ) } is set
m1 | (Seg T) is Relation-like Seg T -defined NAT -defined Seg T -defined AllTermsOf X -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() set
m1 . (T + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
{(m1 . (T + 1))} is non empty trivial functional finite V25() 1 -element set
{(m1 . (T + 1))} \ (AllTermsOf X) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool {(m1 . (T + 1))}
bool {(m1 . (T + 1))} is non empty finite V25() set
{(m1 . (T + 1))} typed\ (AllTermsOf X) is trivial functional finite V25() Element of bool {(m1 . (T + 1))}
i2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of AllTermsOf X
<*i2*> is non empty trivial Relation-like non empty-yielding NAT -defined AllTermsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() FinSequence of AllTermsOf X
[1,i2] is non empty V34() set
{[1,i2]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(m1 | (Seg T)) ^ <*i2*> is non empty Relation-like non empty-yielding NAT -defined AllTermsOf X -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() set
((m1 | (Seg T)) ^ <*i2*>) \+\ m1 is Relation-like finite set
((m1 | (Seg T)) ^ <*i2*>) \ m1 is Relation-like NAT -defined AllTermsOf X -valued finite set
((m1 | (Seg T)) ^ <*i2*>) typed\ m1 is Relation-like NAT -defined AllTermsOf X -valued Function-like finite Function-yielding V164() V198() V199() Element of bool ((m1 | (Seg T)) ^ <*i2*>)
bool ((m1 | (Seg T)) ^ <*i2*>) is non empty finite V25() set
((m1 | (Seg T)) ^ <*i2*>) \ m1 is Relation-like NAT -defined AllTermsOf X -valued Function-like finite Function-yielding V164() V198() V199() Element of bool ((m1 | (Seg T)) ^ <*i2*>)
m1 \ ((m1 | (Seg T)) ^ <*i2*>) is Relation-like NAT -defined AllTermsOf X -valued finite set
m1 typed\ ((m1 | (Seg T)) ^ <*i2*>) is Relation-like NAT -defined AllTermsOf X -valued Function-like finite Function-yielding V164() V198() V199() Element of bool m1
bool m1 is non empty finite V25() set
m1 \ ((m1 | (Seg T)) ^ <*i2*>) is Relation-like NAT -defined AllTermsOf X -valued Function-like finite Function-yielding V164() V198() V199() Element of bool m1
(((m1 | (Seg T)) ^ <*i2*>) \ m1) \/ (m1 \ ((m1 | (Seg T)) ^ <*i2*>)) is Relation-like NAT -defined AllTermsOf X -valued finite set
(X,t) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,t] is non empty V34() set
{[1,t]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(X -multiCat) . m1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,t) ^ ((X -multiCat) . m1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
s2 is Relation-like NAT -defined (AllSymbolsOf X) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() V198() V199() set
(X -multiCat) . s2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
m1 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() set
((X -multiCat) . s2) ^ m1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
(X,t) ^ (((X -multiCat) . s2) ^ m1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
rng h is non empty finite Element of bool (AtomicFormulaSymbolsOf X)
bool (AtomicFormulaSymbolsOf X) is non empty set
proj2 (X,t) is non empty trivial finite 1 -element set
((X -multiCat) . s2) ^ i2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
proj2 (((X -multiCat) . s2) ^ i2) is non empty finite set
(proj2 (X,t)) \/ (proj2 (((X -multiCat) . s2) ^ i2)) is non empty finite set
proj2 ((X -multiCat) . s2) is finite set
proj2 i2 is non empty finite set
(proj2 ((X -multiCat) . s2)) \/ (proj2 i2) is non empty finite set
(proj2 (X,t)) \/ ((proj2 ((X -multiCat) . s2)) \/ (proj2 i2)) is non empty finite set
(proj2 (X,t)) \/ (proj2 ((X -multiCat) . s2)) is non empty finite set
(proj2 i2) \/ ((proj2 (X,t)) \/ (proj2 ((X -multiCat) . s2))) is non empty finite set
m2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() termal Element of ((AllSymbolsOf X) *) \ {{}}
rng m2 is non empty finite Element of bool (TermSymbolsOf X)
bool (TermSymbolsOf X) is non empty set
(rng m2) null ((proj2 (X,t)) \/ (proj2 ((X -multiCat) . s2))) is set
(rng m2) \typed/ ((proj2 (X,t)) \/ (proj2 ((X -multiCat) . s2))) is finite Element of bool ((rng m2) \/ ((proj2 (X,t)) \/ (proj2 ((X -multiCat) . s2))))
(rng m2) \/ ((proj2 (X,t)) \/ (proj2 ((X -multiCat) . s2))) is non empty finite set
bool ((rng m2) \/ ((proj2 (X,t)) \/ (proj2 ((X -multiCat) . s2)))) is non empty finite V25() set
(rng m2) /\ (LettersOf X) is non empty finite Element of bool (AllSymbolsOf X)
(rng m2) typed/\ (LettersOf X) is finite Element of bool (rng m2)
bool (rng m2) is non empty finite V25() set
(rng m2) /\ (LettersOf X) is non empty finite set
(rng m2) /\typed (LettersOf X) is Element of bool (LettersOf X)
(rng h) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(rng h) typed/\ (LettersOf X) is finite Element of bool (rng h)
bool (rng h) is non empty finite V25() set
(rng h) /\ (LettersOf X) is finite set
(rng h) /\typed (LettersOf X) is Element of bool (LettersOf X)
A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
A2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
proj2 h is non empty finite set
(proj2 h) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(proj2 h) typed/\ (LettersOf X) is finite Element of bool (proj2 h)
bool (proj2 h) is non empty finite V25() set
(proj2 h) /\ (LettersOf X) is finite set
(proj2 h) /\typed (LettersOf X) is Element of bool (LettersOf X)
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,A2 + 1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,H) is set
(X,H) `1 is set
(X -firstChar) . H is non relational Element of AllSymbolsOf X
(X,((X -firstChar) . H)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,((X -firstChar) . H)] is non empty V34() set
{[1,((X -firstChar) . H)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,A2) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,((X -firstChar) . H)),T) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff Element of ((AllSymbolsOf X) *) \ {{}}
(X,t) is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like V199() Element of (AllSymbolsOf X) *
(X,t) is set
(X,t) `2 is set
(X,(X,((X -firstChar) . H)),T) ^ (X,t) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() set
proj2 H is non empty finite set
proj2 (X,(X,((X -firstChar) . H)),T) is non empty finite set
rng (X,t) is finite Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(proj2 (X,(X,((X -firstChar) . H)),T)) \/ (rng (X,t)) is non empty finite set
proj2 T is non empty finite set
proj2 (X,((X -firstChar) . H)) is non empty trivial finite 1 -element set
(proj2 T) \/ (proj2 (X,((X -firstChar) . H))) is non empty finite set
((proj2 T) \/ (proj2 (X,((X -firstChar) . H)))) \/ (rng (X,t)) is non empty finite set
(proj2 (X,((X -firstChar) . H))) \/ (rng (X,t)) is non empty finite set
(proj2 T) \/ ((proj2 (X,((X -firstChar) . H))) \/ (rng (X,t))) is non empty finite set
(proj2 T) null ((proj2 (X,((X -firstChar) . H))) \/ (rng (X,t))) is set
(proj2 T) \typed/ ((proj2 (X,((X -firstChar) . H))) \/ (rng (X,t))) is finite Element of bool ((proj2 T) \/ ((proj2 (X,((X -firstChar) . H))) \/ (rng (X,t))))
bool ((proj2 T) \/ ((proj2 (X,((X -firstChar) . H))) \/ (rng (X,t)))) is non empty finite V25() set
(proj2 T) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(proj2 T) typed/\ (LettersOf X) is finite Element of bool (proj2 T)
bool (proj2 T) is non empty finite V25() set
(proj2 T) /\ (LettersOf X) is finite set
(proj2 T) /\typed (LettersOf X) is Element of bool (LettersOf X)
(proj2 H) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(proj2 H) typed/\ (LettersOf X) is finite Element of bool (proj2 H)
bool (proj2 H) is non empty finite V25() set
(proj2 H) /\ (LettersOf X) is finite set
(proj2 H) /\typed (LettersOf X) is Element of bool (LettersOf X)
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,A2 + 1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
t is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X,A2 + 1) (X) Element of ((AllSymbolsOf X) *) \ {{}}
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,A2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
proj2 S is non empty finite set
LettersOf X is non empty non trivial non finite V167() Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(proj2 S) /\ (LettersOf X) is finite Element of bool (AllSymbolsOf X)
(proj2 S) typed/\ (LettersOf X) is finite Element of bool (proj2 S)
bool (proj2 S) is non empty finite V25() set
(proj2 S) /\ (LettersOf X) is finite set
(proj2 S) /\typed (LettersOf X) is Element of bool (LettersOf X)
bool (LettersOf X) is non empty non trivial non finite V167() set
phi is set
X is set
bool X is non empty set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
phi is Element of bool X
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
phi /\ (((AllSymbolsOf S) *) \ {{}}) is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
phi typed/\ (((AllSymbolsOf S) *) \ {{}}) is Element of bool phi
bool phi is non empty set
phi /\ (((AllSymbolsOf S) *) \ {{}}) is set
phi /\typed (((AllSymbolsOf S) *) \ {{}}) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V167() set
X /\ (((AllSymbolsOf S) *) \ {{}}) is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
X typed/\ (((AllSymbolsOf S) *) \ {{}}) is Element of bool X
X /\ (((AllSymbolsOf S) *) \ {{}}) is set
X /\typed (((AllSymbolsOf S) *) \ {{}}) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) \ {{}})
psi is functional set
bool psi is non empty set
phi is functional Element of bool psi
SymbolsOf phi is set
phi \/ {{}} is non empty functional set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of phi \/ {{}} : b<sub>1</sub> in phi } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of phi \/ {{}} : b<sub>1</sub> in phi } is set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of phi : b<sub>1</sub> in phi } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of phi : b<sub>1</sub> in phi } is set
SymbolsOf psi is set
psi \/ {{}} is non empty functional set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of psi \/ {{}} : b<sub>1</sub> in psi } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of psi \/ {{}} : b<sub>1</sub> in psi } is set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of psi : b<sub>1</sub> in psi } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of psi : b<sub>1</sub> in psi } is set
A is Element of AllSymbolsOf S
phi is V51() V53() eligible Language-like
AllSymbolsOf phi is non empty non trivial non finite V167() set
the U1 of phi is set
S is set
X is set
X null S is set
X \typed/ S is Element of bool (X \/ S)
X \/ S is set
bool (X \/ S) is non empty set
X /\ S is set
X typed/\ S is Element of bool X
bool X is non empty set
X /\typed S is Element of bool S
bool S is non empty set
I is Element of AllSymbolsOf phi
X is finite set
phi is V51() V53() eligible Language-like
AllSymbolsOf phi is non empty non trivial non finite V167() set
the U1 of phi is set
S is set
S \/ X is set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite V167() set
((AllSymbolsOf phi) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite V167() set
(((AllSymbolsOf phi) *) \ {{}}) /\ S is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
(((AllSymbolsOf phi) *) \ {{}}) typed/\ S is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
(((AllSymbolsOf phi) *) \ {{}}) /\ S is set
(((AllSymbolsOf phi) *) \ {{}}) /\typed S is Element of bool S
bool S is non empty set
(((AllSymbolsOf phi) *) \ {{}}) /\ X is functional finite V25() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
(((AllSymbolsOf phi) *) \ {{}}) typed/\ X is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
(((AllSymbolsOf phi) *) \ {{}}) /\ X is finite set
(((AllSymbolsOf phi) *) \ {{}}) /\typed X is finite Element of bool X
bool X is non empty finite V25() set
v1 is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
psi is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
v1 \/ psi is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
phi is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
(((AllSymbolsOf phi) *) \ {{}}) /\ (S \/ X) is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
(((AllSymbolsOf phi) *) \ {{}}) typed/\ (S \/ X) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf phi) *) \ {{}})
(((AllSymbolsOf phi) *) \ {{}}) /\ (S \/ X) is set
(((AllSymbolsOf phi) *) \ {{}}) /\typed (S \/ X) is Element of bool (S \/ X)
bool (S \/ X) is non empty set
A is (X,phi) Element of AllSymbolsOf phi
SymbolsOf v1 is set
v1 \/ {{}} is non empty functional V25() set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of v1 \/ {{}} : b<sub>1</sub> in v1 } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of v1 \/ {{}} : b<sub>1</sub> in v1 } is set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of v1 : b<sub>1</sub> in v1 } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of v1 : b<sub>1</sub> in v1 } is set
SymbolsOf psi is set
psi \/ {{}} is non empty functional V25() set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of psi \/ {{}} : b<sub>1</sub> in psi } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of psi \/ {{}} : b<sub>1</sub> in psi } is set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of psi : b<sub>1</sub> in psi } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of psi : b<sub>1</sub> in psi } is set
(SymbolsOf v1) \/ (SymbolsOf psi) is set
SymbolsOf phi is set
phi \/ {{}} is non empty functional V25() set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of phi \/ {{}} : b<sub>1</sub> in phi } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of phi \/ {{}} : b<sub>1</sub> in phi } is set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of phi : b<sub>1</sub> in phi } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of phi : b<sub>1</sub> in phi } is set
X is V51() V53() eligible Language-like
S is non empty set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
phi is Relation-like Function-like Function-yielding V164() (X,S) set
proj1 phi is set
(OwnSymbolsOf X) \ (proj1 phi) is Element of bool (AllSymbolsOf X)
(OwnSymbolsOf X) typed\ (proj1 phi) is Element of bool (OwnSymbolsOf X)
bool (OwnSymbolsOf X) is non empty set
(OwnSymbolsOf X) \ (proj1 phi) is Element of bool (OwnSymbolsOf X)
I is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
S is non empty set
phi is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
I is Relation-like Function-like Function-yielding V164() (X,S) set
(X,S,I,phi) is non empty Relation-like (abs (ar phi)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,phi)
ar phi is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite V167() set
the adicity of X . phi is set
abs (ar phi) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
(abs (ar phi)) -tuples_on S is non empty functional V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
(X,S,I,phi) . {} is set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
proj1 I is set
(OwnSymbolsOf X) \ (proj1 I) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool (AllSymbolsOf X)
(OwnSymbolsOf X) typed\ (proj1 I) is Element of bool (OwnSymbolsOf X)
bool (OwnSymbolsOf X) is non empty set
(OwnSymbolsOf X) \ (proj1 I) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool (OwnSymbolsOf X)
psi is non empty Relation-like (abs (ar phi)) -tuples_on S -defined S \/ BOOLEAN -valued Function-like total quasi_total (X,S,phi)
0 -tuples_on S is non empty functional V25() FinSequence-membered V167() FinSequenceSet of S
[:(0 -tuples_on S),S:] is non empty Relation-like set
bool [:(0 -tuples_on S),S:] is non empty set
[:{{}},S:] is non empty Relation-like set
bool [:{{}},S:] is non empty set
phi is non empty Relation-like {{}} -defined S -valued Function-like finite total quasi_total V199() Element of bool [:{{}},S:]
A is Relation-like Function-like finite V199() Element of {{}}
phi . A is Element of S
A1 is Element of S
(I,phi,A1) is Relation-like Function-like Function-yielding V164() (X,S) set
{} .--> A1 is trivial Relation-like {{}} -defined S -valued Function-like one-to-one constant finite V199() set
{{}} --> A1 is non empty Relation-like {{}} -defined S -valued {A1} -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},{A1}:]
{A1} is non empty trivial finite 1 -element set
[:{{}},{A1}:] is non empty Relation-like finite set
bool [:{{}},{A1}:] is non empty finite V25() set
phi .--> ({} .--> A1) is trivial Relation-like AllSymbolsOf X -defined {phi} -defined Function-like one-to-one constant finite Function-yielding V164() V199() set
{phi} is non empty trivial finite 1 -element set
{phi} --> ({} .--> A1) is non empty Relation-like {phi} -defined {({} .--> A1)} -valued Function-like constant finite total quasi_total Function-yielding V164() V199() Element of bool [:{phi},{({} .--> A1)}:]
{({} .--> A1)} is non empty trivial functional finite V25() 1 -element set
[:{phi},{({} .--> A1)}:] is non empty Relation-like finite set
bool [:{phi},{({} .--> A1)}:] is non empty finite V25() set
I +* (phi .--> ({} .--> A1)) is Relation-like Function-like Function-yielding V164() set
{{}} --> A1 is non empty Relation-like {{}} -defined S -valued Function-like constant finite total quasi_total V199() Element of bool [:{{}},S:]
dom (phi .--> ({} .--> A1)) is trivial finite Element of bool {phi}
bool {phi} is non empty finite V25() set
v1 is Element of OwnSymbolsOf X
{v1} is non empty trivial finite 1 -element Element of bool (OwnSymbolsOf X)
T is Relation-like Function-like finite V199() Element of {{}}
phi . T is Element of S
H is non empty Relation-like {{}} -defined S -valued Function-like finite total quasi_total V199() Element of bool [:{{}},S:]
H . T is Element of S
T is set
{phi} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
(phi .--> ({} .--> A1)) . T is Relation-like Function-like set
I . T is Relation-like Function-like set
(phi .--> ({} .--> A1)) +* I is Relation-like Function-like Function-yielding V164() set
X is V51() V53() eligible Language-like
S is set
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
the U3 of X is Element of the U1 of X
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(X,(X,(X)),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),phi),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X, max ((X,phi),(X,phi))) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((X,phi),(X,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
X is non empty set
X * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of X
X \/ BOOLEAN is non empty set
PFuncs ((X *),(X \/ BOOLEAN)) is non empty functional M26(X * ,X \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((X *),(X \/ BOOLEAN))
(S,X) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf S -defined PFuncs ((X *),(X \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) : b<sub>1</sub> is (S,X) } is set
I is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,X) Element of (S,X)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,X,I,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(S,phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is set
(S,phi) `1 is set
(S,X,I,(S,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(S,phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) `2 is set
(S,X,I,(S,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
(S,X,I,(S,phi)) 'or' (S,X,I,(S,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
'not' (S,X,I,(S,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
1 - (S,X,I,(S,phi)) is complex ext-real V40() V41() set
'not' (S,X,I,(S,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
1 - (S,X,I,(S,phi)) is complex ext-real V40() V41() set
('not' (S,X,I,(S,phi))) '&' ('not' (S,X,I,(S,phi))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
('not' (S,X,I,(S,phi))) * ('not' (S,X,I,(S,phi))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
'not' (('not' (S,X,I,(S,phi))) '&' ('not' (S,X,I,(S,phi)))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
1 - (('not' (S,X,I,(S,phi))) '&' ('not' (S,X,I,(S,phi)))) is complex ext-real V40() V41() set
'not' ((S,X,I,(S,phi)) 'or' (S,X,I,(S,phi))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
1 - ((S,X,I,(S,phi)) 'or' (S,X,I,(S,phi))) is complex ext-real V40() V41() set
(S,X,I,phi) \+\ ((S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi))) is finite set
(S,X,I,phi) \ ((S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi))) is finite set
(S,X,I,phi) typed\ ((S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi))) is finite Element of bool (S,X,I,phi)
bool (S,X,I,phi) is non empty finite V25() set
(S,X,I,phi) \ ((S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi))) is finite Element of bool (S,X,I,phi)
((S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi))) \ (S,X,I,phi) is finite set
((S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi))) typed\ (S,X,I,phi) is finite Element of bool ((S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi)))
bool ((S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi))) is non empty finite V25() set
((S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi))) \ (S,X,I,phi) is finite Element of bool ((S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi)))
((S,X,I,phi) \ ((S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi)))) \/ (((S,X,I,(S,phi)) 'nor' (S,X,I,(S,phi))) \ (S,X,I,phi)) is finite set
S -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
[:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V167() set
(AllSymbolsOf S) -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(AllSymbolsOf S) -pr1 is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total V201( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf S),(AllSymbolsOf S)) is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
MultPlace ((AllSymbolsOf S) -pr1) is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(S -firstChar) . phi is non relational Element of AllSymbolsOf S
(S) is non literal non low-compounding non relational non own Element of AllSymbolsOf S
AllSymbolsOf S is non empty non trivial non finite V167() set
((S -firstChar) . phi) \+\ (S) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
((S -firstChar) . phi) \ (S) is set
((S -firstChar) . phi) typed\ (S) is Element of bool ((S -firstChar) . phi)
bool ((S -firstChar) . phi) is non empty set
((S -firstChar) . phi) \ (S) is Element of bool ((S -firstChar) . phi)
(S) \ ((S -firstChar) . phi) is set
(S) typed\ ((S -firstChar) . phi) is Element of bool (S)
bool (S) is non empty set
(S) \ ((S -firstChar) . phi) is Element of bool (S)
(((S -firstChar) . phi) \ (S)) \/ ((S) \ ((S -firstChar) . phi)) is set
(S,(S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(S,(S,(S)),(S,phi)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),(S,phi)),(S,phi)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S, max ((S,(S,phi)),(S,(S,phi)))) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,(S,phi)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((S,(S,phi)),(S,(S,phi))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
H is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : ( b<sub>1</sub> is (X) & b<sub>1</sub> is (X) ) } is set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
{ H<sub>1</sub>(b<sub>1</sub>) where b<sub>1</sub> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : S<sub>1</sub>[b<sub>1</sub>] } is set
{ H<sub>1</sub>(b<sub>1</sub>) where b<sub>1</sub> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : S<sub>2</sub>[b<sub>1</sub>] } is set
X is V51() V53() eligible Language-like
(X) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : ( b<sub>1</sub> is (X) & b<sub>1</sub> is (X) ) } is set
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) (X) Element of ((AllSymbolsOf X) *) \ {{}} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
S is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : ( b<sub>1</sub> is (X) & b<sub>1</sub> is (X) ) } is set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of (X)
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : ( b<sub>1</sub> is (X) & b<sub>1</sub> is (X) ) } is set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) (X) Element of (X)
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : ( b<sub>1</sub> is (X) & b<sub>1</sub> is (X) ) } is set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) (X) Element of (X)
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : ( b<sub>1</sub> is (X) & b<sub>1</sub> is (X) ) } is set
(X) is non empty functional V25() FinSequence-membered V166() V167() AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b<sub>1</sub> where b<sub>1</sub> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}} : not for b<sub>2</sub> being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set holds b<sub>1</sub> is (X,b<sub>2</sub>) } is set
(X) \ (X) is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
(X) typed\ (X) is functional V25() FinSequence-membered V166() Element of bool (X)
bool (X) is non empty set
(X) \ (X) is functional V25() FinSequence-membered V166() Element of bool (X)
I is set
I is set
S is V51() V53() eligible Language-like
phi is V51() V53() eligible S -extending Language-like
X is non empty set
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
OwnSymbolsOf phi is non empty Element of bool (AllSymbolsOf phi)
AllSymbolsOf phi is non empty non trivial non finite V167() set
the U1 of phi is set
bool (AllSymbolsOf phi) is non empty non trivial non finite V167() set
the U2 of phi is Element of the U1 of phi
the U3 of phi is Element of the U1 of phi
{ the U2 of phi, the U3 of phi} is non empty finite set
the U1 of phi \ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
bool the U1 of phi is non empty set
the U1 of phi typed\ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of phi is non empty Relation-like the U1 of phi \ { the U3 of phi} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of phi \ { the U3 of phi}),INT:]
{ the U3 of phi} is non empty trivial finite 1 -element set
the U1 of phi \ { the U3 of phi} is non empty Element of bool the U1 of phi
the U1 of phi typed\ { the U3 of phi} is Element of bool the U1 of phi
[:( the U1 of phi \ { the U3 of phi}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of phi \ { the U3 of phi}),INT:] is non empty non trivial non finite V167() set
AtomicFormulaSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
TheNorSymbOf S is set
{(TheNorSymbOf S)} is non empty trivial finite 1 -element set
(AllSymbolsOf S) \ {(TheNorSymbOf S)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
(AllSymbolsOf S) typed\ {(TheNorSymbOf S)} is Element of bool (AllSymbolsOf S)
(phi) is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf phi
AllSymbolsOf phi is non empty non trivial non finite V167() set
AtomicFormulaSymbolsOf phi is non empty Element of bool (AllSymbolsOf phi)
TheNorSymbOf phi is set
{(TheNorSymbOf phi)} is non empty trivial finite 1 -element set
(AllSymbolsOf phi) \ {(TheNorSymbOf phi)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf phi)
bool (AllSymbolsOf phi) is non empty non trivial non finite V167() set
(AllSymbolsOf phi) typed\ {(TheNorSymbOf phi)} is Element of bool (AllSymbolsOf phi)
(S) is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf S
h is Relation-like Function-like set
t is Relation-like Function-like Function-yielding V164() (phi,X) set
(OwnSymbolsOf S) \ (OwnSymbolsOf phi) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool (AllSymbolsOf S)
(OwnSymbolsOf S) typed\ (OwnSymbolsOf phi) is Element of bool (OwnSymbolsOf S)
bool (OwnSymbolsOf S) is non empty set
(OwnSymbolsOf S) \ (OwnSymbolsOf phi) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural proper finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of bool (OwnSymbolsOf S)
dom the adicity of S is non empty Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
dom the adicity of phi is non empty Element of bool ( the U1 of phi \ { the U3 of phi})
bool ( the U1 of phi \ { the U3 of phi}) is non empty set
T is own ofAtomicFormula Element of AllSymbolsOf S
m1 is ofAtomicFormula Element of AllSymbolsOf phi
(phi) is non literal non low-compounding non relational non own Element of AllSymbolsOf phi
s2 is own ofAtomicFormula Element of AllSymbolsOf phi
ar s2 is complex ext-real V40() V41() Element of INT
the adicity of phi . s2 is set
abs (ar s2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar s2)) -tuples_on X is non empty functional V25() FinSequence-membered FinSequenceSet of X
X \/ BOOLEAN is non empty set
H is Relation-like Function-like (phi,X)
H . s2 is set
ar T is complex ext-real V40() V41() Element of INT
the adicity of S . T is set
the adicity of phi +* the adicity of S is non empty Relation-like INT -valued Function-like set
( the adicity of phi +* the adicity of S) . s2 is set
the adicity of S . s2 is set
i2 is non empty Relation-like (abs (ar s2)) -tuples_on X -defined X \/ BOOLEAN -valued Function-like total quasi_total (phi,X,s2)
abs (ar T) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar T)) -tuples_on X is non empty functional V25() FinSequence-membered FinSequenceSet of X
[:((abs (ar T)) -tuples_on X),BOOLEAN:] is non empty Relation-like set
bool [:((abs (ar T)) -tuples_on X),BOOLEAN:] is non empty set
h . T is set
i2 is non empty Relation-like (abs (ar s2)) -tuples_on X -defined X \/ BOOLEAN -valued Function-like total quasi_total (phi,X,s2)
abs (ar T) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar T)) -tuples_on X is non empty functional V25() FinSequence-membered FinSequenceSet of X
[:((abs (ar T)) -tuples_on X),X:] is non empty Relation-like set
bool [:((abs (ar T)) -tuples_on X),X:] is non empty set
h . T is set
S is V51() V53() eligible Language-like
phi is V51() V53() eligible S -extending Language-like
X is non empty set
I is Relation-like Function-like Function-yielding V164() (phi,X) set
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
I | (OwnSymbolsOf S) is Relation-like OwnSymbolsOf S -defined Function-like Function-yielding V164() set
N is Relation-like Function-like set
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
X is non empty set
X * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of X
X \/ BOOLEAN is non empty set
PFuncs ((X *),(X \/ BOOLEAN)) is non empty functional M26(X * ,X \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((X *),(X \/ BOOLEAN))
(S,X) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf S -defined PFuncs ((X *),(X \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) : b<sub>1</sub> is (S,X) } is set
phi is V51() V53() eligible S -extending Language-like
N is Relation-like Function-like Function-yielding V164() (phi,X) set
I is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,X) Element of (S,X)
N +* I is Relation-like Function-like Function-yielding V164() set
OwnSymbolsOf phi is non empty Element of bool (AllSymbolsOf phi)
AllSymbolsOf phi is non empty non trivial non finite V167() set
the U1 of phi is set
bool (AllSymbolsOf phi) is non empty non trivial non finite V167() set
the U2 of phi is Element of the U1 of phi
the U3 of phi is Element of the U1 of phi
{ the U2 of phi, the U3 of phi} is non empty finite set
the U1 of phi \ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
bool the U1 of phi is non empty set
the U1 of phi typed\ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
the adicity of S is non empty Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
{ the U3 of S} is non empty trivial finite 1 -element set
the U1 of S \ { the U3 of S} is non empty Element of bool the U1 of S
the U1 of S typed\ { the U3 of S} is Element of bool the U1 of S
[:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V167() set
the adicity of phi is non empty Relation-like the U1 of phi \ { the U3 of phi} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of phi \ { the U3 of phi}),INT:]
{ the U3 of phi} is non empty trivial finite 1 -element set
the U1 of phi \ { the U3 of phi} is non empty Element of bool the U1 of phi
the U1 of phi typed\ { the U3 of phi} is Element of bool the U1 of phi
[:( the U1 of phi \ { the U3 of phi}),INT:] is non empty non trivial Relation-like non finite V167() set
bool [:( the U1 of phi \ { the U3 of phi}),INT:] is non empty non trivial non finite V167() set
AtomicFormulaSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
TheNorSymbOf S is set
{(TheNorSymbOf S)} is non empty trivial finite 1 -element set
(AllSymbolsOf S) \ {(TheNorSymbOf S)} is non empty non trivial non finite V167() Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
(AllSymbolsOf S) typed\ {(TheNorSymbOf S)} is Element of bool (AllSymbolsOf S)
AllSymbolsOf phi is non empty non trivial non finite V167() set
h is own ofAtomicFormula Element of AllSymbolsOf phi
dom I is Element of bool (OwnSymbolsOf S)
bool (OwnSymbolsOf S) is non empty set
(N +* I) . h is Relation-like Function-like set
I . h is Relation-like Function-like set
t is own ofAtomicFormula Element of AllSymbolsOf S
dom the adicity of S is non empty Element of bool ( the U1 of S \ { the U3 of S})
bool ( the U1 of S \ { the U3 of S}) is non empty set
ar t is complex ext-real V40() V41() Element of INT
the adicity of S . t is set
abs (ar t) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar t)) -tuples_on X is non empty functional V25() FinSequence-membered FinSequenceSet of X
(S,X,I,t) is non empty Relation-like (abs (ar t)) -tuples_on X -defined X \/ BOOLEAN -valued Function-like total quasi_total (S,X,t)
ar h is complex ext-real V40() V41() Element of INT
the adicity of phi . h is set
the adicity of phi +* the adicity of S is non empty Relation-like INT -valued Function-like set
( the adicity of phi +* the adicity of S) . h is set
the adicity of S . h is set
H is non empty Relation-like (abs (ar t)) -tuples_on X -defined X \/ BOOLEAN -valued Function-like total quasi_total (S,X,t)
abs (ar h) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar h)) -tuples_on X is non empty functional V25() FinSequence-membered FinSequenceSet of X
[:((abs (ar h)) -tuples_on X),BOOLEAN:] is non empty Relation-like set
bool [:((abs (ar h)) -tuples_on X),BOOLEAN:] is non empty set
H is non empty Relation-like (abs (ar t)) -tuples_on X -defined X \/ BOOLEAN -valued Function-like total quasi_total (S,X,t)
abs (ar h) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar h)) -tuples_on X is non empty functional V25() FinSequence-membered FinSequenceSet of X
[:((abs (ar h)) -tuples_on X),X:] is non empty Relation-like set
bool [:((abs (ar h)) -tuples_on X),X:] is non empty set
h is own ofAtomicFormula Element of AllSymbolsOf phi
dom I is Element of bool (OwnSymbolsOf S)
bool (OwnSymbolsOf S) is non empty set
(N +* I) . h is Relation-like Function-like set
(phi,X,N,h) is non empty Relation-like (abs (ar h)) -tuples_on X -defined X \/ BOOLEAN -valued Function-like total quasi_total (phi,X,h)
ar h is complex ext-real V40() V41() Element of INT
the adicity of phi . h is set
abs (ar h) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar h)) -tuples_on X is non empty functional V25() FinSequence-membered FinSequenceSet of X
h is own ofAtomicFormula Element of AllSymbolsOf phi
dom I is Element of bool (OwnSymbolsOf S)
bool (OwnSymbolsOf S) is non empty set
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
X is non empty set
X * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of X
X \/ BOOLEAN is non empty set
PFuncs ((X *),(X \/ BOOLEAN)) is non empty functional M26(X * ,X \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((X *),(X \/ BOOLEAN))
(S,X) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf S -defined PFuncs ((X *),(X \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) : b<sub>1</sub> is (S,X) } is set
X is V51() V53() eligible Language-like
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b<sub>1</sub> is (X,S) } is set
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
X is non empty set
X * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of X
X \/ BOOLEAN is non empty set
PFuncs ((X *),(X \/ BOOLEAN)) is non empty functional M26(X * ,X \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((X *),(X \/ BOOLEAN))
(S,X) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf S -defined PFuncs ((X *),(X \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) : b<sub>1</sub> is (S,X) } is set
I is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,X) Element of (S,X)
phi is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
phi null I is empty trivial Relation-like non-empty empty-yielding NAT -defined I \/ (proj1 phi) -defined {{}} -valued I -valued I \/ (proj2 phi) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element len phi -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
proj1 phi is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
I \/ (proj1 phi) is Relation-like set
proj2 phi is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V167() V192() V198() V199() set
I \/ (proj2 phi) is Relation-like set
len phi is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
phi \typed/ I is Relation-like Element of bool (phi \/ I)
phi \/ I is Relation-like set
bool (phi \/ I) is non empty set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,X,I,N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
phi is V51() V53() eligible Language-like
OwnSymbolsOf phi is non empty Element of bool (AllSymbolsOf phi)
AllSymbolsOf phi is non empty non trivial non finite V167() set
the U1 of phi is set
bool (AllSymbolsOf phi) is non empty non trivial non finite V167() set
the U2 of phi is Element of the U1 of phi
the U3 of phi is Element of the U1 of phi
{ the U2 of phi, the U3 of phi} is non empty finite set
the U1 of phi \ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
bool the U1 of phi is non empty set
the U1 of phi typed\ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf phi),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf phi, PFuncs ((S *),(S \/ BOOLEAN))
(phi,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf phi),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf phi),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf phi -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf phi),(PFuncs ((S *),(S \/ BOOLEAN)))) : b<sub>1</sub> is (phi,S) } is set
X is set
bool X is non empty set
I is Relation-like OwnSymbolsOf phi -defined Function-like total Function-yielding V164() (phi,S) Element of (phi,S)
{} null I is empty trivial Relation-like non-empty empty-yielding NAT -defined I \/ (proj1 {}) -defined {{}} -valued I -valued {{}} -valued I \/ (proj2 {}) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element len {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() (S,phi,I) set
proj1 {} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
I \/ (proj1 {}) is Relation-like set
proj2 {} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V167() V192() V198() V199() set
I \/ (proj2 {}) is Relation-like set
len {} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
{} \typed/ I is Relation-like Element of bool ({} \/ I)
{} \/ I is Relation-like set
bool ({} \/ I) is non empty set
N is Element of bool X
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
X is non empty set
X * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of X
X \/ BOOLEAN is non empty set
PFuncs ((X *),(X \/ BOOLEAN)) is non empty functional M26(X * ,X \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((X *),(X \/ BOOLEAN))
(S,X) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf S -defined PFuncs ((X *),(X \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) : b<sub>1</sub> is (S,X) } is set
phi is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,X) Element of (S,X)
bool 1 is non empty finite V25() set
the finite (X,S,phi) Element of bool 1 is finite (X,S,phi) Element of bool 1
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
X is non empty set
X * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of X
X \/ BOOLEAN is non empty set
PFuncs ((X *),(X \/ BOOLEAN)) is non empty functional M26(X * ,X \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((X *),(X \/ BOOLEAN))
(S,X) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf S -defined PFuncs ((X *),(X \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) : b<sub>1</sub> is (S,X) } is set
phi is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,X) Element of (S,X)
I is (X,S,phi) set
bool I is non empty set
N is Element of bool I
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,X,phi,v1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
X is non empty set
X * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of X
X \/ BOOLEAN is non empty set
PFuncs ((X *),(X \/ BOOLEAN)) is non empty functional M26(X * ,X \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((X *),(X \/ BOOLEAN))
(S,X) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf S -defined PFuncs ((X *),(X \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) : b<sub>1</sub> is (S,X) } is set
phi is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,X) Element of (S,X)
I is (X,S,phi) set
N is (X,S,phi) set
I \/ N is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
v1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,X,phi,v1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
X is non empty set
X * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of X
X \/ BOOLEAN is non empty set
PFuncs ((X *),(X \/ BOOLEAN)) is non empty functional M26(X * ,X \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((X *),(X \/ BOOLEAN))
(S,X) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf S -defined PFuncs ((X *),(X \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) : b<sub>1</sub> is (S,X) } is set
phi is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,X) Element of (S,X)
I is (X,S,phi) set
phi null I is Relation-like I \/ (proj1 phi) -defined I \/ (proj2 phi) -valued Function-like set
proj1 phi is set
I \/ (proj1 phi) is set
proj2 phi is set
I \/ (proj2 phi) is set
phi \typed/ I is Element of bool (phi \/ I)
phi \/ I is set
bool (phi \/ I) is non empty set
N is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,X) Element of (S,X)
proj1 {} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
proj2 {} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V167() V192() V198() V199() set
len {} is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() Element of NAT
X is V51() V53() eligible Language-like
{} null X is empty trivial Relation-like non-empty empty-yielding NAT -defined X \/ (proj1 {}) -defined {{}} -valued X -valued X \/ (proj2 {}) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element len {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() set
X \/ (proj1 {}) is set
X \/ (proj2 {}) is set
{} \typed/ X is Element of bool ({} \/ X)
{} \/ X is set
bool ({} \/ X) is non empty set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b<sub>1</sub> is (X,S) } is set
phi is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
I is (S,X,phi) set
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
[I,N] is non empty V34() set
(X,S,phi,N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
S is set
bool S is non empty set
X is V51() V53() eligible Language-like
{} null X is empty trivial Relation-like non-empty empty-yielding NAT -defined X \/ (proj1 {}) -defined X \/ (proj1 {}) -defined {{}} -valued X -valued {{}} -valued X \/ (proj2 {}) -valued X \/ (proj2 {}) -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding V25() cardinal {} -element len {} -element len {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V167() V192() V198() V199() (X) set
X \/ (proj1 {}) is set
X \/ (proj2 {}) is set
{} \typed/ X is Element of bool ({} \/ X)
{} \/ X is set
bool ({} \/ X) is non empty set
phi is Element of bool S
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S is non empty set
S * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of S
S \/ BOOLEAN is non empty set
PFuncs ((S *),(S \/ BOOLEAN)) is non empty functional M26(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((S *),(S \/ BOOLEAN))
(X,S) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf X -defined PFuncs ((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((S *),(S \/ BOOLEAN)))) : b<sub>1</sub> is (X,S) } is set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
{phi} is non empty trivial functional finite V25() 1 -element FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
I is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,S) Element of (X,S)
(X,S,I,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
N is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S,I,N) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
N is (S,X,I) set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite V167() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is Element of AllSymbolsOf X
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
{phi} is non empty trivial functional finite V25() 1 -element FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
proj2 phi is non empty finite set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite V167() set
v1 is non empty functional V25() FinSequence-membered V166() V167() Element of bool (((AllSymbolsOf X) *) \ {{}})
(((AllSymbolsOf X) *) \ {{}}) /\ v1 is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
(((AllSymbolsOf X) *) \ {{}}) typed/\ v1 is functional V25() FinSequence-membered V166() Element of bool (((AllSymbolsOf X) *) \ {{}})
(((AllSymbolsOf X) *) \ {{}}) /\ v1 is set
(((AllSymbolsOf X) *) \ {{}}) /\typed v1 is functional V25() FinSequence-membered V166() Element of bool v1
bool v1 is non empty set
v1 null (((AllSymbolsOf X) *) \ {{}}) is set
v1 \typed/ (((AllSymbolsOf X) *) \ {{}}) is functional V25() V166() Element of bool (v1 \/ (((AllSymbolsOf X) *) \ {{}}))
v1 \/ (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial functional non finite V25() V166() V167() set
bool (v1 \/ (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite V167() set
SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ v1) is set
((((AllSymbolsOf X) *) \ {{}}) /\ v1) \/ {{}} is non empty functional V25() set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of ((((AllSymbolsOf X) *) \ {{}}) /\ v1) \/ {{}} : b<sub>1</sub> in (((AllSymbolsOf X) *) \ {{}}) /\ v1 } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of ((((AllSymbolsOf X) *) \ {{}}) /\ v1) \/ {{}} : b<sub>1</sub> in (((AllSymbolsOf X) *) \ {{}}) /\ v1 } is set
{ (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of (((AllSymbolsOf X) *) \ {{}}) /\ v1 : b<sub>1</sub> in (((AllSymbolsOf X) *) \ {{}}) /\ v1 } is set
union { (proj2 b<sub>1</sub>) where b<sub>1</sub> is Relation-like Function-like Element of (((AllSymbolsOf X) *) \ {{}}) /\ v1 : b<sub>1</sub> in (((AllSymbolsOf X) *) \ {{}}) /\ v1 } is set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V167() set
the U2 of S is Element of the U1 of S
the U3 of S is Element of the U1 of S
{ the U2 of S, the U3 of S} is non empty finite set
the U1 of S \ { the U2 of S, the U3 of S} is Element of bool the U1 of S
bool the U1 of S is non empty set
the U1 of S typed\ { the U2 of S, the U3 of S} is Element of bool the U1 of S
X is non empty set
X * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of X
X \/ BOOLEAN is non empty set
PFuncs ((X *),(X \/ BOOLEAN)) is non empty functional M26(X * ,X \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S, PFuncs ((X *),(X \/ BOOLEAN))
(S,X) is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN))))) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like OwnSymbolsOf S -defined PFuncs ((X *),(X \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),(PFuncs ((X *),(X \/ BOOLEAN)))) : b<sub>1</sub> is (S,X) } is set
N is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() (S,X) Element of (S,X)
(S) is non literal non low-compounding non relational non own Element of AllSymbolsOf S
AllSymbolsOf S is non empty non trivial non finite V167() set
(S,(S)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(S)] is non empty V34() set
{[1,(S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S)),phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S) Element of ((AllSymbolsOf S) *) \ {{}}
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S)),phi),I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (S, max ((S,phi),(S,I))) (S) (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((S,phi),(S,I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S,X,N,(S,(S,(S,(S)),phi),I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(S,X,N,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(S,X,N,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(S,X,N,phi) 'nor' (S,X,N,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
(S,X,N,phi) 'or' (S,X,N,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
'not' (S,X,N,phi) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
1 - (S,X,N,phi) is complex ext-real V40() V41() set
'not' (S,X,N,I) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
1 - (S,X,N,I) is complex ext-real V40() V41() set
('not' (S,X,N,phi)) '&' ('not' (S,X,N,I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
('not' (S,X,N,phi)) * ('not' (S,X,N,I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
'not' (('not' (S,X,N,phi)) '&' ('not' (S,X,N,I))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
1 - (('not' (S,X,N,phi)) '&' ('not' (S,X,N,I))) is complex ext-real V40() V41() set
'not' ((S,X,N,phi) 'or' (S,X,N,I)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
1 - ((S,X,N,phi) 'or' (S,X,N,I)) is complex ext-real V40() V41() set
(S,X,N,(S,(S,(S,(S)),phi),I)) \+\ ((S,X,N,phi) 'nor' (S,X,N,I)) is finite set
(S,X,N,(S,(S,(S,(S)),phi),I)) \ ((S,X,N,phi) 'nor' (S,X,N,I)) is finite set
(S,X,N,(S,(S,(S,(S)),phi),I)) typed\ ((S,X,N,phi) 'nor' (S,X,N,I)) is finite Element of bool (S,X,N,(S,(S,(S,(S)),phi),I))
bool (S,X,N,(S,(S,(S,(S)),phi),I)) is non empty finite V25() set
(S,X,N,(S,(S,(S,(S)),phi),I)) \ ((S,X,N,phi) 'nor' (S,X,N,I)) is finite Element of bool (S,X,N,(S,(S,(S,(S)),phi),I))
((S,X,N,phi) 'nor' (S,X,N,I)) \ (S,X,N,(S,(S,(S,(S)),phi),I)) is finite set
((S,X,N,phi) 'nor' (S,X,N,I)) typed\ (S,X,N,(S,(S,(S,(S)),phi),I)) is finite Element of bool ((S,X,N,phi) 'nor' (S,X,N,I))
bool ((S,X,N,phi) 'nor' (S,X,N,I)) is non empty finite V25() set
((S,X,N,phi) 'nor' (S,X,N,I)) \ (S,X,N,(S,(S,(S,(S)),phi),I)) is finite Element of bool ((S,X,N,phi) 'nor' (S,X,N,I))
((S,X,N,(S,(S,(S,(S)),phi),I)) \ ((S,X,N,phi) 'nor' (S,X,N,I))) \/ (((S,X,N,phi) 'nor' (S,X,N,I)) \ (S,X,N,(S,(S,(S,(S)),phi),I))) is finite set
S -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
[:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V167() set
(AllSymbolsOf S) -firstChar is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(AllSymbolsOf S) -pr1 is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total V201( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V167() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V167() set
K463((AllSymbolsOf S),(AllSymbolsOf S)) is non empty Relation-like [:(AllSymbolsOf S),(AllSymbolsOf S):] -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
MultPlace ((AllSymbolsOf S) -pr1) is non empty Relation-like ((AllSymbolsOf S) *) \ {{}} -defined AllSymbolsOf S -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):]
(S,(S,(S,(S,(S)),phi),I)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S,(S)),phi),I)) is set
(S,(S,(S,(S,(S)),phi),I)) `1 is set
(S,(S,(S,(S,(S)),phi),I)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (S) Element of ((AllSymbolsOf S) *) \ {{}}
(S,(S,(S,(S,(S)),phi),I)) `2 is set
(S,X,N,(S,(S,(S,(S,(S)),phi),I))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(S,X,N,(S,(S,(S,(S,(S)),phi),I))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
m1 is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite V167() set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite V167() set
((AllSymbolsOf X) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite V167() set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
phi is non empty set
phi * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of phi
phi \/ BOOLEAN is non empty set
PFuncs ((phi *),(phi \/ BOOLEAN)) is non empty functional M26(phi * ,phi \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X, PFuncs ((phi *),(phi \/ BOOLEAN))
(X,phi) is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))))
bool (Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN))))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf X -defined PFuncs ((phi *),(phi \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf X),(PFuncs ((phi *),(phi \/ BOOLEAN)))) : b₁ is (X,phi) } is set
I is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V164() (X,phi) Element of (X,phi)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X) is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite V167() set
(X,(X)) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like V199() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(X)] is non empty V34() set
{[1,(X)]} is non empty trivial Relation-like Function-like constant finite 1 -element V166() V167() V199() set
(X,(X,(X)),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,(X,(X,(X)),S),S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V199() non 0wff (X, max ((X,S),(X,S))) (X) (X) Element of ((AllSymbolsOf X) *) \ {{}}
(X,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((X,S),(X,S)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(X,phi,I,(X,S)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
(X,phi,I,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
'not' (X,phi,I,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean Element of BOOLEAN
1 - (X,phi,I,S) is complex ext-real V40() V41() set
(X,phi,I,(X,S)) \+\ ('not' (X,phi,I,S)) is finite set
(X,phi,I,(X,S)) \ ('not' (X,phi,I,S)) is finite set
(X,phi,I,(X,S)) typed\ ('not' (X,phi,I,S)) is finite Element of bool (X,phi,I,(X,S))
bool (X,phi,I,(X,S)) is non empty finite V25() set
(X,phi,I,(X,S)) \ ('not' (X,phi,I,S)) is finite Element of bool (X,phi,I,(X,S))
('not' (X,phi,I,S)) \ (X,phi,I,(X,S)) is finite set
('not' (X,phi,I,S)) typed\ (X,phi,I,(X,S)) is finite Element of bool ('not' (X,phi,I,S))
bool ('not' (X,phi,I,S)) is non empty finite V25() set
('not' (X,phi,I,S)) \ (X,phi,I,(X,S)) is finite Element of bool ('not' (X,phi,I,S))
((X,phi,I,(X,S)) \ ('not' (X,phi,I,S))) \/ (('not' (X,phi,I,S)) \ (X,phi,I,(X,S))) is finite set
(X,phi,I,S) 'nor' (X,phi,I,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
(X,phi,I,S) 'or' (X,phi,I,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
'not' (X,phi,I,S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
('not' (X,phi,I,S)) '&' ('not' (X,phi,I,S)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
('not' (X,phi,I,S)) * ('not' (X,phi,I,S)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
'not' (('not' (X,phi,I,S)) '&' ('not' (X,phi,I,S))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
1 - (('not' (X,phi,I,S)) '&' ('not' (X,phi,I,S))) is complex ext-real V40() V41() set
'not' ((X,phi,I,S) 'or' (X,phi,I,S)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() boolean set
1 - ((X,phi,I,S) 'or' (X,phi,I,S)) is complex ext-real V40() V41() set
(X,phi,I,(X,S)) \+\ ((X,phi,I,S) 'nor' (X,phi,I,S)) is finite set
(X,phi,I,(X,S)) \ ((X,phi,I,S) 'nor' (X,phi,I,S)) is finite set
(X,phi,I,(X,S)) typed\ ((X,phi,I,S) 'nor' (X,phi,I,S)) is finite Element of bool (X,phi,I,(X,S))
(X,phi,I,(X,S)) \ ((X,phi,I,S) 'nor' (X,phi,I,S)) is finite Element of bool (X,phi,I,(X,S))
((X,phi,I,S) 'nor' (X,phi,I,S)) \ (X,phi,I,(X,S)) is finite set
((X,phi,I,S) 'nor' (X,phi,I,S)) typed\ (X,phi,I,(X,S)) is finite Element of bool ((X,phi,I,S) 'nor' (X,phi,I,S))
bool ((X,phi,I,S) 'nor' (X,phi,I,S)) is non empty finite V25() set
((X,phi,I,S) 'nor' (X,phi,I,S)) \ (X,phi,I,(X,S)) is finite Element of bool ((X,phi,I,S) 'nor' (X,phi,I,S))
((X,phi,I,(X,S)) \ ((X,phi,I,S) 'nor' (X,phi,I,S))) \/ (((X,phi,I,S) 'nor' (X,phi,I,S)) \ (X,phi,I,(X,S))) is finite set
phi is set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V167() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite V25() FinSequence-membered V167() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V25() FinSequence-membered V166() V167() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V167() set
((AllSymbolsOf S) *) typed\ {{}} is functional V25() FinSequence-membered Element of bool ((AllSymbolsOf S) *)