:: FOMODEL3 semantic presentation

REAL is non empty non trivial non finite V166() set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V166() Element of bool REAL
bool REAL is non empty non trivial non finite V166() 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
{} 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
{{}} is non empty trivial functional finite finite-membered 1 -element V166() 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 finite-membered 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
{0,1} is non empty finite finite-membered set
omega is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V166() set
bool omega is non empty non trivial non finite V166() set
bool NAT is non empty non trivial non finite V166() set
COMPLEX is non empty non trivial non finite V166() set
RAT is non empty non trivial non finite V166() set
INT is non empty non trivial non finite V166() set
[:{{}},NAT:] is non empty non trivial Relation-like non finite V166() set
[{},{}] is non empty set
{[{},{}]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
[:{{}},NAT:] \ {[{},{}]} is non empty non trivial Relation-like {{}} -defined NAT -valued non finite V166() Element of bool [:{{}},NAT:]
bool [:{{}},NAT:] is non empty non trivial non finite V166() set
[:{{}},NAT:] typed\ {[{},{}]} is Relation-like {{}} -defined NAT -valued Element of bool [:{{}},NAT:]
NAT \/ ([:{{}},NAT:] \ {[{},{}]}) is non empty non trivial non finite V166() set
[:REAL,REAL:] is non empty non trivial Relation-like non finite V166() set
bool [:REAL,REAL:] is non empty non trivial non finite V166() set
K281() is V47() V75() L8()
the U1 of K281() is set
<REAL,+> is V47() L8()
K287() is V47() V75() SubStr of <REAL,+>
<NAT,+> is V47() V75() V97() uniquely-decomposable SubStr of K287()
<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 finite-membered set
K368(NAT) is V173() set
[:COMPLEX,COMPLEX:] is non empty non trivial Relation-like non finite V166() set
bool [:COMPLEX,COMPLEX:] is non empty non trivial non finite V166() set
[:1,1:] is non empty Relation-like finite set
bool [:1,1:] is non empty finite finite-membered set
[:[:1,1:],1:] is non empty Relation-like finite set
bool [:[:1,1:],1:] is non empty finite finite-membered set
3 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
dom {} 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
rng {} 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V165() V166() V192() FinSequence-yielding finite-support 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
- 2 is non empty finite complex ext-real non positive negative V40() V41() set
TRUE is boolean Element of BOOLEAN
FALSE is boolean Element of BOOLEAN
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
u is Element of AllSymbolsOf U
<*u*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
[1,u] is non empty set
{[1,u]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
{} .--> {} is trivial Relation-like {{}} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite set
bool [:{{}},{{}}:] is non empty finite finite-membered set
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
S is Relation-like NAT -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (((AllSymbolsOf U) *) \ {{}}) *
(U -multiCat) . S is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*u*> ^ ((U -multiCat) . S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
E is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
i is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of AllSymbolsOf U
E ^ i is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of AllSymbolsOf U
x is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of AllSymbolsOf U
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
S is non relational termal own ofAtomicFormula Element of AllSymbolsOf U
ar S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . 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
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf U) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial non finite V166() set
u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(U -termsOfMaxDepth) . u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
((U -termsOfMaxDepth) . u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
l is Relation-like NAT -defined (U -termsOfMaxDepth) . u -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of ((U -termsOfMaxDepth) . u) *
(U,S,l) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
<*S*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,S] is non empty set
{[1,S]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
(U -multiCat) . l is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*S*> ^ ((U -multiCat) . l) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
u + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
LettersOf U is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
{0} is non empty trivial functional finite finite-membered 1 -element V166() Element of bool NAT
0 * is non empty functional finite-membered FinSequence-membered FinSequenceSet of 0
{0} is non empty trivial functional finite finite-membered 1 -element V166() set
the adicity of U " {0} is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AtomicTermsOf U is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
LettersOf U is non empty non trivial non finite V166() set
1 -tuples_on (LettersOf U) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of LettersOf U
{ (Compound (b₁,((U -termsOfMaxDepth) . u))) where b₁ is ofAtomicFormula Element of AllSymbolsOf U : b₁ is operational } is set
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
I is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
I * is non empty functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
j is Relation-like NAT -defined (AllSymbolsOf U) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of ((AllSymbolsOf U) *) *
(U -multiCat) . j is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*S*> ^ ((U -multiCat) . j) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
rng j is finite set
Compound (S,((U -termsOfMaxDepth) . u)) is functional finite-membered FinSequence-membered V165() Element of K335((((AllSymbolsOf U) *) \ {{}}))
K395((AllSymbolsOf U),S) is non empty trivial Relation-like NAT -defined AllSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of 1 -tuples_on (AllSymbolsOf U)
1 -tuples_on (AllSymbolsOf U) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of AllSymbolsOf U
{ (K395((AllSymbolsOf U),S) ^ ((U -multiCat) . b₁)) where b₁ is Relation-like NAT -defined (AllSymbolsOf U) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of ((AllSymbolsOf U) *) * : ( rng b₁ c= (U -termsOfMaxDepth) . u & b₁ is abs (ar S) -element ) } is set
Jj is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
ar Jj 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of U . Jj is set
jJ 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 finite-membered cardinal 0 -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
<*S*> ^ jJ is non empty Relation-like NAT -defined Function-like finite 1 + 0 -element 1 + 0 -element FinSequence-like FinSubsequence-like finite-support set
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
<*S*> null jJ is Relation-like NAT -defined jJ \/ (dom <*S*>) -defined Seg (1 + jJ) -defined jJ \/ (rng <*S*>) -valued Function-like finite len <*S*> -element total FinSequence-like FinSubsequence-like finite-support set
dom <*S*> is non empty trivial finite 1 -element set
jJ \/ (dom <*S*>) is non empty finite set
1 + jJ is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
Seg (1 + jJ) is non empty finite 1 + jJ -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 + jJ ) } is set
rng <*S*> is non empty trivial finite 1 -element set
jJ \/ (rng <*S*>) is non empty finite set
len <*S*> is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
<*S*> \typed/ jJ is Relation-like NAT -defined finite Element of bool (<*S*> \/ jJ)
<*S*> \/ jJ is non empty Relation-like NAT -defined finite set
bool (<*S*> \/ jJ) is non empty finite finite-membered set
jJ ^ <*S*> is non empty Relation-like NAT -defined Function-like finite 0 + 1 -element 0 + 1 -element FinSequence-like FinSubsequence-like finite-support set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive 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
jJ is literal Element of LettersOf U
<*jJ*> is non empty trivial Relation-like NAT -defined TermSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf U) *) \ {{}}
TermSymbolsOf U is non empty set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
[1,jJ] is non empty set
{[1,jJ]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(U -termsOfMaxDepth) . 0 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
0 + (u + 1) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(U -termsOfMaxDepth) . (0 + (u + 1)) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
union { (Compound (b₁,((U -termsOfMaxDepth) . u))) where b₁ is ofAtomicFormula Element of AllSymbolsOf U : b₁ is operational } is set
(union { (Compound (b₁,((U -termsOfMaxDepth) . u))) where b₁ is ofAtomicFormula Element of AllSymbolsOf U : b₁ is operational } ) \/ ((U -termsOfMaxDepth) . u) is non empty set
(U -termsOfMaxDepth) . (u + 1) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
Jj is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is set
u 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
u + S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l is V51() V53() eligible Language-like
AllSymbolsOf l is non empty non trivial non finite V166() set
the U1 of l is set
(AllSymbolsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf l
((AllSymbolsOf l) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf l) *)
bool ((AllSymbolsOf l) *) is non empty non trivial non finite V166() set
((AllSymbolsOf l) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
K335((((AllSymbolsOf l) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf l) *) \ {{}}))
bool (((AllSymbolsOf l) *) \ {{}}) is non empty non trivial non finite V166() set
bool (bool (((AllSymbolsOf l) *) \ {{}})) is non empty non trivial non finite V166() set
l -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf l) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf l) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf l) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf l) *) \ {{}})):] is non empty non trivial non finite V166() set
(l -termsOfMaxDepth) . (u + S) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
(l -termsOfMaxDepth) . u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
U is set
u 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 V166() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
K335((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V166() set
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() set
S -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf S) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf S) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial non finite V166() set
(S -termsOfMaxDepth) . u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : not U in (S -termsOfMaxDepth) . b₁ } is set
E is set
i is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S -termsOfMaxDepth) . i is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
x is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u + x is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
U is V51() V53() eligible Language-like
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf U) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial non finite V166() set
l is Relation-like NAT -defined AllTermsOf U -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : not l . a₁ in (U -termsOfMaxDepth) . b₁ } is set
dom l is finite Element of bool NAT
{ H₁(b₁) where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : b₁ in dom l } is set
i is set
x is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
l . x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : not l . x in (U -termsOfMaxDepth) . b₁ } is set
rng l is finite set
O is non empty set
[:O,(AllTermsOf U):] is non empty Relation-like set
bool [:O,(AllTermsOf U):] is non empty set
UU is non empty Relation-like non empty-yielding O -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:O,(AllTermsOf U):]
III is Element of O
UU . III is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf U
E is Relation-like Function-like set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
E . X is set
i is finite finite-membered set
union i is finite set
x is finite set
NAT \ x is non empty non trivial non finite V166() Element of bool REAL
NAT typed\ x is Element of bool NAT
NAT \ x is non empty non trivial non finite V166() Element of bool NAT
O is set
UU is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(U -termsOfMaxDepth) . UU is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
((U -termsOfMaxDepth) . UU) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
III is set
l . III is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : not l . III in (U -termsOfMaxDepth) . b₁ } is set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
l . X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT : not l . X in (U -termsOfMaxDepth) . b₁ } is set
[:(dom l),((U -termsOfMaxDepth) . UU):] is Relation-like set
bool [:(dom l),((U -termsOfMaxDepth) . UU):] is non empty set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
u is non relational termal own ofAtomicFormula Element of AllSymbolsOf U
ar u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . u is set
abs (ar u) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
S is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar u) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
(U,u,S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
<*u*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,u] is non empty set
{[1,u]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
(U -multiCat) . S is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*u*> ^ ((U -multiCat) . S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf U) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial non finite V166() set
E is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(U -termsOfMaxDepth) . E is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
((U -termsOfMaxDepth) . E) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
i is Relation-like NAT -defined (U -termsOfMaxDepth) . E -valued Function-like finite abs (ar u) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of ((U -termsOfMaxDepth) . E) *
(U,u,i) is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal E + 1 -termal Element of ((AllSymbolsOf U) *) \ {{}}
TermSymbolsOf U is non empty set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
E + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(U -multiCat) . i is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*u*> ^ ((U -multiCat) . i) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
x is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
u is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
ar u is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . u is set
abs (ar u) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
S is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar u) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
(U,u,S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
<*u*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,u] is non empty set
{[1,u]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
(U -multiCat) . S is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*u*> ^ ((U -multiCat) . S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
[:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):] is non empty non trivial non finite V166() set
u is Element of AllSymbolsOf U
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
l is non empty Relation-like non empty-yielding (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
II is Relation-like NAT -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (((AllSymbolsOf U) *) \ {{}}) *
l . II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,II) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
<*u*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,u] is non empty set
{[1,u]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
(U -multiCat) . II is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*u*> ^ ((U -multiCat) . II) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
l is non empty Relation-like non empty-yielding (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
II is non empty Relation-like non empty-yielding (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
E is Relation-like NAT -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (((AllSymbolsOf U) *) \ {{}}) *
l . E is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,E) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
<*u*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,u] is non empty set
{[1,u]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
(U -multiCat) . E is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*u*> ^ ((U -multiCat) . E) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
II . E is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
u is non relational termal own ofAtomicFormula Element of AllSymbolsOf U
(U,u) is non empty Relation-like non empty-yielding (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
[:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):] is non empty non trivial non finite V166() set
ar u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . u is set
abs (ar u) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar u)) -tuples_on (AllTermsOf U) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf U
(U,u) | ((abs (ar u)) -tuples_on (AllTermsOf U)) is Relation-like (((AllSymbolsOf U) *) \ {{}}) * -defined (abs (ar u)) -tuples_on (AllTermsOf U) -defined (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
O is set
rng ((U,u) | ((abs (ar u)) -tuples_on (AllTermsOf U))) is set
(U,u) .: ((abs (ar u)) -tuples_on (AllTermsOf U)) is set
dom (U,u) is non empty functional finite-membered FinSequence-membered Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
UU is set
(U,u) . UU is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
III is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar u) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf U
X is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar u) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
I is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
I * is non empty functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
(U,u,X) is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
TermSymbolsOf U is non empty set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
<*u*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,u] is non empty set
{[1,u]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
(U -multiCat) . X is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*u*> ^ ((U -multiCat) . X) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(U,u) . X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AtomicFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : b₁ is 0wff } is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
u is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
(U,u) is non empty Relation-like non empty-yielding (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
[:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):] is non empty non trivial non finite V166() set
ar u is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . u is set
abs (ar u) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(abs (ar u)) -tuples_on (AllTermsOf U) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of AllTermsOf U
(U,u) | ((abs (ar u)) -tuples_on (AllTermsOf U)) is Relation-like (((AllSymbolsOf U) *) \ {{}}) * -defined (abs (ar u)) -tuples_on (AllTermsOf U) -defined (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
UU is set
rng ((U,u) | ((abs (ar u)) -tuples_on (AllTermsOf U))) is set
(U,u) .: ((abs (ar u)) -tuples_on (AllTermsOf U)) is set
dom (U,u) is non empty functional finite-membered FinSequence-membered Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
III is set
(U,u) . III is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
X is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar u) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf U
I is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar u) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
j is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
j * is non empty functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
(U,u,I) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
AtomicFormulaSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
TheNorSymbOf U is set
{(TheNorSymbOf U)} is non empty trivial finite 1 -element set
(AllSymbolsOf U) \ {(TheNorSymbOf U)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
(AllSymbolsOf U) typed\ {(TheNorSymbOf U)} is Element of bool (AllSymbolsOf U)
<*u*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,u] is non empty set
{[1,u]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
(U -multiCat) . I is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*u*> ^ ((U -multiCat) . I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(U,u) . I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
u is ofAtomicFormula Element of AllSymbolsOf U
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(U,u) is non empty Relation-like non empty-yielding (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
[:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):] is non empty non trivial non finite V166() set
ar u is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . u is set
abs (ar u) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(abs (ar u)) -tuples_on (AllTermsOf U) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf U
(U,u) | ((abs (ar u)) -tuples_on (AllTermsOf U)) is Relation-like (((AllSymbolsOf U) *) \ {{}}) * -defined (abs (ar u)) -tuples_on (AllTermsOf U) -defined (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
S is set
AtomicFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : b₁ is 0wff } is set
chi (S,(AtomicFormulasOf U)) is non empty Relation-like AtomicFormulasOf U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(AtomicFormulasOf U),BOOLEAN:]
[:(AtomicFormulasOf U),BOOLEAN:] is non empty Relation-like set
bool [:(AtomicFormulasOf U),BOOLEAN:] is non empty set
(chi (S,(AtomicFormulasOf U))) (*) ((U,u) | ((abs (ar u)) -tuples_on (AllTermsOf U))) is Relation-like (((AllSymbolsOf U) *) \ {{}}) * -defined BOOLEAN -valued Function-like set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
u is ofAtomicFormula Element of AllSymbolsOf U
S is set
(U,u,S) is set
ar u is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . u is set
abs (ar u) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(abs (ar u)) -tuples_on (AllTermsOf U) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
AtomicFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : b₁ is 0wff } is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
O is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
O * is non empty functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
[:((abs (ar u)) -tuples_on (AllTermsOf U)),(((AllSymbolsOf U) *) \ {{}}):] is non empty non trivial Relation-like non finite V166() set
bool [:((abs (ar u)) -tuples_on (AllTermsOf U)),(((AllSymbolsOf U) *) \ {{}}):] is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
(U,u) is non empty Relation-like non empty-yielding (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
[:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):] is non empty non trivial non finite V166() set
(U,u) | ((abs (ar u)) -tuples_on (AllTermsOf U)) is Relation-like (abs (ar u)) -tuples_on (AllTermsOf U) -defined (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
III is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
(U,III) is non empty Relation-like non empty-yielding (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
ar III is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U . III is set
abs (ar III) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar III)) -tuples_on (AllTermsOf U) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of AllTermsOf U
(U,III) | ((abs (ar III)) -tuples_on (AllTermsOf U)) is Relation-like (((AllSymbolsOf U) *) \ {{}}) * -defined (abs (ar III)) -tuples_on (AllTermsOf U) -defined (((AllSymbolsOf U) *) \ {{}}) * -defined (abs (ar III)) -tuples_on (AllTermsOf U) -defined (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued ((AllSymbolsOf U) *) \ {{}} -valued AtomicFormulasOf U -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
UU is non empty Relation-like non empty-yielding (abs (ar u)) -tuples_on (AllTermsOf U) -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((abs (ar u)) -tuples_on (AllTermsOf U)),(((AllSymbolsOf U) *) \ {{}}):]
rng UU is non empty set
[:((abs (ar u)) -tuples_on (AllTermsOf U)),(AtomicFormulasOf U):] is non empty Relation-like set
bool [:((abs (ar u)) -tuples_on (AllTermsOf U)),(AtomicFormulasOf U):] is non empty set
[:(AtomicFormulasOf U),BOOLEAN:] is non empty Relation-like set
bool [:(AtomicFormulasOf U),BOOLEAN:] is non empty set
chi (S,(AtomicFormulasOf U)) is non empty Relation-like AtomicFormulasOf U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(AtomicFormulasOf U),BOOLEAN:]
X is non empty Relation-like non empty-yielding (abs (ar u)) -tuples_on (AllTermsOf U) -defined AtomicFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((abs (ar u)) -tuples_on (AllTermsOf U)),(AtomicFormulasOf U):]
I is non empty Relation-like AtomicFormulasOf U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(AtomicFormulasOf U),BOOLEAN:]
I * X is non empty Relation-like (abs (ar u)) -tuples_on (AllTermsOf U) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:((abs (ar u)) -tuples_on (AllTermsOf U)),BOOLEAN:]
[:((abs (ar u)) -tuples_on (AllTermsOf U)),BOOLEAN:] is non empty Relation-like set
bool [:((abs (ar u)) -tuples_on (AllTermsOf U)),BOOLEAN:] is non empty set
III is non relational termal own ofAtomicFormula Element of AllSymbolsOf U
(U,III) is non empty Relation-like non empty-yielding (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
ar III is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of U . III is set
abs (ar III) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar III)) -tuples_on (AllTermsOf U) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf U
(U,III) | ((abs (ar III)) -tuples_on (AllTermsOf U)) is Relation-like (((AllSymbolsOf U) *) \ {{}}) * -defined (abs (ar III)) -tuples_on (AllTermsOf U) -defined (((AllSymbolsOf U) *) \ {{}}) * -defined (abs (ar III)) -tuples_on (AllTermsOf U) -defined (((AllSymbolsOf U) *) \ {{}}) * -defined ((AllSymbolsOf U) *) \ {{}} -valued ((AllSymbolsOf U) *) \ {{}} -valued AllTermsOf U -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) \ {{}}) *),(((AllSymbolsOf U) *) \ {{}}):]
UU is non empty Relation-like non empty-yielding (abs (ar u)) -tuples_on (AllTermsOf U) -defined ((AllSymbolsOf U) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((abs (ar u)) -tuples_on (AllTermsOf U)),(((AllSymbolsOf U) *) \ {{}}):]
rng UU is non empty set
[:((abs (ar u)) -tuples_on (AllTermsOf U)),(AllTermsOf U):] is non empty Relation-like set
bool [:((abs (ar u)) -tuples_on (AllTermsOf U)),(AllTermsOf U):] is non empty set
U is V51() V53() eligible Language-like
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
the U2 of U is Element of the U1 of U
the U3 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
AllSymbolsOf U is non empty non trivial non finite V166() set
u is set
II is set
E is own ofAtomicFormula Element of AllSymbolsOf U
ar E is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . E is set
abs (ar E) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(abs (ar E)) -tuples_on (AllTermsOf U) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
(U,E,u) is non empty Relation-like (abs (ar E)) -tuples_on (AllTermsOf U) -defined (AllTermsOf U) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of E, AllTermsOf U
i is non empty Relation-like (abs (ar E)) -tuples_on (AllTermsOf U) -defined (AllTermsOf U) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of E, AllTermsOf U
x is own ofAtomicFormula Element of AllSymbolsOf U
ar x is finite complex ext-real V40() V41() Element of INT
the adicity of U . x is set
abs (ar x) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar x)) -tuples_on (AllTermsOf U) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf U
(U,x,u) is non empty Relation-like (abs (ar x)) -tuples_on (AllTermsOf U) -defined (AllTermsOf U) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of x, AllTermsOf U
II is Relation-like Function-like set
dom II is set
E is own ofAtomicFormula Element of AllSymbolsOf U
II . E is set
(U,E,u) is non empty Relation-like (abs (ar E)) -tuples_on (AllTermsOf U) -defined (AllTermsOf U) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of E, AllTermsOf U
ar E is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . E is set
abs (ar E) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(abs (ar E)) -tuples_on (AllTermsOf U) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
II is Relation-like Function-like set
dom II is set
E is Relation-like Function-like set
dom E is set
i is set
x is own ofAtomicFormula Element of AllSymbolsOf U
II . x is set
(U,x,u) is non empty Relation-like (abs (ar x)) -tuples_on (AllTermsOf U) -defined (AllTermsOf U) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of x, AllTermsOf U
ar x is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . x is set
abs (ar x) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(abs (ar x)) -tuples_on (AllTermsOf U) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
E . x is set
II . i is set
E . i is set
U is V51() V53() eligible Language-like
u is set
(U,u) is Relation-like Function-like set
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
the U2 of U is Element of the U1 of U
the U3 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
II is set
dom (U,u) is set
AllSymbolsOf U is non empty non trivial non finite V166() set
E is own ofAtomicFormula Element of AllSymbolsOf U
(U,E,u) is non empty Relation-like (abs (ar E)) -tuples_on (AllTermsOf U) -defined (AllTermsOf U) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of E, AllTermsOf U
ar E is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . E is set
abs (ar E) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(abs (ar E)) -tuples_on (AllTermsOf U) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
(U,u) . II is set
II is Relation-like Function-like set
U is V51() V53() eligible Language-like
u is set
(U,u) is Relation-like Function-like Function-yielding V164() set
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllTermsOf U) \/ BOOLEAN is non empty set
II is own ofAtomicFormula Element of AllSymbolsOf U
(U,u) . II is Relation-like Function-like set
ar II is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . II is set
abs (ar II) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar II)) -tuples_on (AllTermsOf U) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf U
(U,II,u) is non empty Relation-like (abs (ar II)) -tuples_on (AllTermsOf U) -defined (AllTermsOf U) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of II, AllTermsOf U
U is V51() V53() eligible Language-like
u is set
(U,u) is Relation-like Function-like Function-yielding V164() Interpreter of U, AllTermsOf U
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
S is Relation-like Function-like set
U is V51() V53() eligible Language-like
u is set
(U,u) is Relation-like Function-like Function-yielding V164() U, AllTermsOf U -interpreter-like set
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
the U2 of U is Element of the U1 of U
the U3 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) is non empty functional M31((AllTermsOf U) * ,(AllTermsOf U) \/ BOOLEAN)
Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U,K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))
(AllTermsOf U) -InterpretersOf U is non empty functional Element of bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf U -defined K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) : b₁ is U, AllTermsOf U -interpreter-like } is set
(U,u) is Relation-like Function-like Function-yielding V164() U, AllTermsOf U -interpreter-like Interpreter of U, AllTermsOf U
dom (U,u) is set
(U,u) | (OwnSymbolsOf U) is Relation-like OwnSymbolsOf U -defined OwnSymbolsOf U -defined K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) -valued Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like set
U is non empty set
u is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
l -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
Seg l is finite l -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 <= l ) } is set
S is Relation-like U -defined u -valued Element of bool [:U,u:]
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
[:(l -tuples_on U),(l -tuples_on u):] is non empty Relation-like set
bool [:(l -tuples_on U),(l -tuples_on u):] is non empty set
x is set
O is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U
UU is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u
[O,UU] is non empty Element of [:(l -tuples_on U),(l -tuples_on u):]
U 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
u is non empty set
S is non empty set
[:u,S:] is non empty Relation-like set
bool [:u,S:] is non empty set
l is Relation-like u -defined S -valued Element of bool [:u,S:]
(u,S,l,U) is Relation-like U -tuples_on u -defined U -tuples_on S -valued Element of bool [:(U -tuples_on u),(U -tuples_on S):]
U -tuples_on u is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of u
U -tuples_on S is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of S
[:(U -tuples_on u),(U -tuples_on S):] is non empty Relation-like set
bool [:(U -tuples_on u),(U -tuples_on S):] is non empty set
Seg U 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 finite-membered cardinal U -element {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support 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 <= U ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on u, b₂ is Relation-like NAT -defined S -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on S : for b₃ being set holds
( not b₃ in Seg U or [(b₁ . b₃),(b₂ . b₃)] in l ) } is set
0 -tuples_on S is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of S
[:{{}},(0 -tuples_on S):] is non empty Relation-like set
Seg 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 proper finite finite-yielding finite-membered cardinal 0 -element {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support 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 <= 0 ) } is set
E is Relation-like NAT -defined u -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on u
i is Relation-like NAT -defined S -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on S
x is set
E . x is set
i . x is set
[(E . x),(i . x)] is non empty set
[E,i] is non empty Element of [:(U -tuples_on u),(U -tuples_on S):]
U is non empty set
u is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
l is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
l -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
l -tuples_on u is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of u
[:(l -tuples_on U),(l -tuples_on u):] is non empty Relation-like set
bool [:(l -tuples_on U),(l -tuples_on u):] is non empty set
S is Relation-like U -defined u -valued total quasi_total Element of bool [:U,u:]
(U,u,S,l) is Relation-like l -tuples_on U -defined l -tuples_on u -valued Element of bool [:(l -tuples_on U),(l -tuples_on u):]
Seg l is non empty finite l -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 <= l ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
dom S is Element of bool U
bool U is non empty set
x is set
Funcs ((Seg l),U) is non empty functional FUNCTION_DOMAIN of Seg l,U
O is non empty Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U
III is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
O . III is set
UU is Relation-like Seg l -defined U -valued Function-like total quasi_total finite-support Element of Funcs ((Seg l),U)
X is Element of Seg l
UU . X is Element of U
I is set
[(O . III),I] is non empty set
j is Element of u
[(O . III),j] is non empty set
III is Relation-like NAT -defined u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of u
len III is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
i is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
i -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
Seg i is finite i -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 <= i ) } is set
Funcs ((Seg i),u) is non empty functional FUNCTION_DOMAIN of Seg i,u
X is Relation-like NAT -defined u -valued Function-like finite i -element FinSequence-like FinSubsequence-like finite-support Element of i -tuples_on u
I is Relation-like Seg i -defined u -valued Function-like total quasi_total finite-support Element of Funcs ((Seg i),u)
dom I is finite Element of bool (Seg i)
bool (Seg i) is non empty finite finite-membered set
j is set
Jj is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
dom X is finite i -element Element of bool NAT
III /. Jj is Element of u
O . Jj is set
[(O . Jj),(III /. Jj)] is non empty set
O . j is set
X . j is set
[(O . j),(X . j)] is non empty set
[O,X] is non empty Element of [:(l -tuples_on U),(i -tuples_on u):]
[:(l -tuples_on U),(i -tuples_on u):] is non empty Relation-like set
dom (U,u,S,l) is functional finite-membered FinSequence-membered V165() Element of bool (l -tuples_on U)
bool (l -tuples_on U) is non empty set
x is Relation-like l -tuples_on U -defined l -tuples_on u -valued Element of bool [:(l -tuples_on U),(l -tuples_on u):]
U is non empty set
u is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
l -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
[:(l -tuples_on U),(l -tuples_on u):] is non empty Relation-like set
bool [:(l -tuples_on U),(l -tuples_on u):] is non empty set
S is Relation-like U -defined u -valued total quasi_total Element of bool [:U,u:]
(U,u,S,l) is Relation-like l -tuples_on U -defined l -tuples_on u -valued Element of bool [:(l -tuples_on U),(l -tuples_on u):]
Seg l is finite l -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 <= l ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
E is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
E -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
(U,u,S,E) is Relation-like E -tuples_on U -defined E -tuples_on u -valued total quasi_total Element of bool [:(E -tuples_on U),(E -tuples_on u):]
E -tuples_on u is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of u
[:(E -tuples_on U),(E -tuples_on u):] is non empty Relation-like set
bool [:(E -tuples_on U),(E -tuples_on u):] is non empty set
Seg E is non empty finite E -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 <= E ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite E -element FinSequence-like FinSubsequence-like finite-support Element of E -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite E -element FinSequence-like FinSubsequence-like finite-support Element of E -tuples_on u : for b₃ being set holds
( not b₃ in Seg E or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
i is Relation-like l -tuples_on U -defined l -tuples_on u -valued Element of bool [:(l -tuples_on U),(l -tuples_on u):]
E 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(U,u,S,E) is Relation-like E -tuples_on U -defined E -tuples_on u -valued Element of bool [:(E -tuples_on U),(E -tuples_on u):]
E -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
E -tuples_on u is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of u
[:(E -tuples_on U),(E -tuples_on u):] is non empty Relation-like set
bool [:(E -tuples_on U),(E -tuples_on u):] is non empty set
Seg E 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 finite-membered cardinal E -element {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support 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 <= E ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite E -element FinSequence-like FinSubsequence-like finite-support Element of E -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite E -element FinSequence-like FinSubsequence-like finite-support Element of E -tuples_on u : for b₃ being set holds
( not b₃ in Seg E or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
dom (U,u,S,l) is functional finite-membered FinSequence-membered Element of bool (l -tuples_on U)
bool (l -tuples_on U) is non empty set
i is Relation-like l -tuples_on U -defined l -tuples_on u -valued Element of bool [:(l -tuples_on U),(l -tuples_on u):]
U is non empty set
u is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
l 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
l -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
l -tuples_on u is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of u
[:(l -tuples_on U),(l -tuples_on u):] is non empty Relation-like set
bool [:(l -tuples_on U),(l -tuples_on u):] is non empty set
S is Relation-like U -defined u -valued Element of bool [:U,u:]
(U,u,S,l) is Relation-like l -tuples_on U -defined l -tuples_on u -valued Element of bool [:(l -tuples_on U),(l -tuples_on u):]
Seg l 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 finite-membered cardinal l -element {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support 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 <= l ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
i is set
x is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U
O is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u
[x,O] is non empty Element of [:(l -tuples_on U),(l -tuples_on u):]
E is Relation-like Function-like set
bool E is non empty set
i is Relation-like Function-like Element of bool E
x is Relation-like l -tuples_on U -defined l -tuples_on u -valued Element of bool [:(l -tuples_on U),(l -tuples_on u):]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is Relation-like U -defined U -valued Element of bool [:U,U:]
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(U,U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
S -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
[:(S -tuples_on U),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on U):] is non empty set
Seg S is finite S -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 <= S ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in u ) } is set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is Relation-like U -defined U -valued Element of bool [:U,U:]
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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
S -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
[:(S -tuples_on U),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on U):] is non empty set
(U,U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:(S -tuples_on U),(S -tuples_on U):]
Seg 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 finite-membered cardinal S -element {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support 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 <= S ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in u ) } is set
l is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
II is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
U is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
Seg U is non empty finite U -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 <= U ) } is set
u is non empty set
Funcs ((Seg U),u) is non empty functional FUNCTION_DOMAIN of Seg U,u
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is Relation-like Seg U -defined u -valued Function-like total quasi_total finite-support Element of Funcs ((Seg U),u)
l is Relation-like Seg U -defined u -valued Function-like total quasi_total finite-support Element of Funcs ((Seg U),u)
[S,l] is non empty Element of [:(Funcs ((Seg U),u)),(Funcs ((Seg U),u)):]
[:(Funcs ((Seg U),u)),(Funcs ((Seg U),u)):] is non empty Relation-like set
II is Relation-like u -defined u -valued Element of bool [:u,u:]
(u,II,U) is Relation-like U -tuples_on u -defined U -tuples_on u -valued Element of bool [:(U -tuples_on u),(U -tuples_on u):]
U -tuples_on u is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of u
[:(U -tuples_on u),(U -tuples_on u):] is non empty Relation-like set
bool [:(U -tuples_on u),(U -tuples_on u):] is non empty set
(u,u,II,U) is Relation-like U -tuples_on u -defined U -tuples_on u -valued Element of bool [:(U -tuples_on u),(U -tuples_on u):]
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined u -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on u : for b₃ being set holds
( not b₃ in Seg U or [(b₁ . b₃),(b₂ . b₃)] in II ) } is set
x is non empty Relation-like NAT -defined u -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on u
O is non empty Relation-like NAT -defined u -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on u
[x,O] is non empty Element of [:(U -tuples_on u),(U -tuples_on u):]
UU is Element of Seg U
S . UU is Element of u
l . UU is Element of u
[(S . UU),(l . UU)] is non empty Element of [:u,u:]
E is non empty Relation-like NAT -defined u -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on u
i is non empty Relation-like NAT -defined u -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on u
x is set
E . x is set
i . x is set
[(E . x),(i . x)] is non empty set
U is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
U -tuples_on u is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of u
[:(U -tuples_on u),(U -tuples_on u):] is non empty Relation-like set
bool [:(U -tuples_on u),(U -tuples_on u):] is non empty set
S is Relation-like u -defined u -valued total quasi_total symmetric Element of bool [:u,u:]
(u,S,U) is Relation-like U -tuples_on u -defined U -tuples_on u -valued Element of bool [:(U -tuples_on u),(U -tuples_on u):]
(u,u,S,U) is Relation-like U -tuples_on u -defined U -tuples_on u -valued total quasi_total Element of bool [:(U -tuples_on u),(U -tuples_on u):]
Seg U is non empty finite U -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 <= U ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined u -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on u : for b₃ being set holds
( not b₃ in Seg U or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
field S is set
dom S is set
rng S is set
(dom S) \/ (rng S) is set
field (u,S,U) is set
dom (u,S,U) is set
rng (u,S,U) is set
(dom (u,S,U)) \/ (rng (u,S,U)) is set
II is set
Funcs ((Seg U),u) is non empty functional FUNCTION_DOMAIN of Seg U,u
E is set
[II,E] is non empty set
i is Relation-like Seg U -defined u -valued Function-like total quasi_total finite-support Element of Funcs ((Seg U),u)
O is Element of Seg U
i . O is Element of u
x is Relation-like Seg U -defined u -valued Function-like total quasi_total finite-support Element of Funcs ((Seg U),u)
x . O is Element of u
[(i . O),(x . O)] is non empty Element of [:u,u:]
[(x . O),(i . O)] is non empty Element of [:u,u:]
[E,II] is non empty set
U is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
U -tuples_on u is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of u
[:(U -tuples_on u),(U -tuples_on u):] is non empty Relation-like set
bool [:(U -tuples_on u),(U -tuples_on u):] is non empty set
S is Relation-like u -defined u -valued total quasi_total transitive Element of bool [:u,u:]
(u,S,U) is Relation-like U -tuples_on u -defined U -tuples_on u -valued Element of bool [:(U -tuples_on u),(U -tuples_on u):]
(u,u,S,U) is Relation-like U -tuples_on u -defined U -tuples_on u -valued total quasi_total Element of bool [:(U -tuples_on u),(U -tuples_on u):]
Seg U is non empty finite U -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 <= U ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined u -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on u : for b₃ being set holds
( not b₃ in Seg U or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
field S is set
dom S is set
rng S is set
(dom S) \/ (rng S) is set
field (u,S,U) is set
dom (u,S,U) is set
rng (u,S,U) is set
(dom (u,S,U)) \/ (rng (u,S,U)) is set
II is set
Funcs ((Seg U),u) is non empty functional FUNCTION_DOMAIN of Seg U,u
E is set
i is set
[II,E] is non empty set
[E,i] is non empty set
x is Relation-like Seg U -defined u -valued Function-like total quasi_total finite-support Element of Funcs ((Seg U),u)
III is Element of Seg U
x . III is Element of u
O is Relation-like Seg U -defined u -valued Function-like total quasi_total finite-support Element of Funcs ((Seg U),u)
O . III is Element of u
UU is Relation-like Seg U -defined u -valued Function-like total quasi_total finite-support Element of Funcs ((Seg U),u)
UU . III is Element of u
[(x . III),(O . III)] is non empty Element of [:u,u:]
[(O . III),(UU . III)] is non empty Element of [:u,u:]
[(x . III),(UU . III)] is non empty Element of [:u,u:]
[II,i] is non empty set
U 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
U -tuples_on u is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of u
[:(U -tuples_on u),(U -tuples_on u):] is non empty Relation-like set
bool [:(U -tuples_on u),(U -tuples_on u):] is non empty set
S is Relation-like u -defined u -valued Element of bool [:u,u:]
(u,S,U) is Relation-like U -tuples_on u -defined U -tuples_on u -valued Element of bool [:(U -tuples_on u),(U -tuples_on u):]
(u,u,S,U) is Relation-like U -tuples_on u -defined U -tuples_on u -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:(U -tuples_on u),(U -tuples_on u):]
Seg U 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 finite-membered cardinal U -element {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support 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 <= U ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined u -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on u : for b₃ being set holds
( not b₃ in Seg U or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
II is set
[II,II] is non empty set
dom (u,S,U) is functional finite-membered FinSequence-membered V166() Element of bool (U -tuples_on u)
bool (U -tuples_on u) is non empty set
field (u,S,U) is set
dom (u,S,U) is set
rng (u,S,U) is set
(dom (u,S,U)) \/ (rng (u,S,U)) is set
II is set
E is set
[II,E] is non empty set
[E,II] is non empty set
II is set
E is set
i is set
[II,E] is non empty set
[E,i] is non empty set
[II,i] is non empty set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
[:(S -tuples_on U),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on U):] is non empty set
u is Relation-like U -defined U -valued total quasi_total symmetric Element of bool [:U,U:]
(U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
(U,U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total Element of bool [:(S -tuples_on U),(S -tuples_on U):]
Seg S is finite S -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 <= S ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in u ) } is set
l is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
[:(S -tuples_on U),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on U):] is non empty set
u is Relation-like U -defined U -valued total quasi_total symmetric Element of bool [:U,U:]
(U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total Element of bool [:(S -tuples_on U),(S -tuples_on U):]
(U,U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total Element of bool [:(S -tuples_on U),(S -tuples_on U):]
Seg S is finite S -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 <= S ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in u ) } is set
l is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
l is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
[:(S -tuples_on U),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on U):] is non empty set
u is Relation-like U -defined U -valued total quasi_total symmetric Element of bool [:U,U:]
(U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total symmetric Element of bool [:(S -tuples_on U),(S -tuples_on U):]
(U,U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total Element of bool [:(S -tuples_on U),(S -tuples_on U):]
Seg S is finite S -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 <= S ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in u ) } is set
l is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
[:(S -tuples_on U),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on U):] is non empty set
u is Relation-like U -defined U -valued total quasi_total transitive Element of bool [:U,U:]
(U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
(U,U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total Element of bool [:(S -tuples_on U),(S -tuples_on U):]
Seg S is finite S -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 <= S ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in u ) } is set
l is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
l is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
[:(S -tuples_on U),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on U):] is non empty set
u is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
(U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:(S -tuples_on U),(S -tuples_on U):]
(U,U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total Element of bool [:(S -tuples_on U),(S -tuples_on U):]
Seg S is finite S -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 <= S ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in u ) } is set
l is Relation-like S -tuples_on U -defined S -tuples_on U -valued Element of bool [:(S -tuples_on U),(S -tuples_on U):]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
bool U is non empty set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class S is non empty V165() V166() a_partition of U
bool u is non empty set
l is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
Class l is non empty V165() V166() a_partition of u
II is Relation-like set
{ [b₁,b₂] where b₁ is non empty Element of Class S, b₂ is non empty Element of Class l : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in II ) } is set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
l is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
II is Relation-like set
(U,u,S,l,II) is set
bool U is non empty set
Class S is non empty V165() V166() a_partition of U
bool u is non empty set
Class l is non empty V165() V166() a_partition of u
{ [b₁,b₂] where b₁ is non empty Element of Class S, b₂ is non empty Element of Class l : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in II ) } is set
[:(Class S),(Class l):] is non empty Relation-like set
bool [:(Class S),(Class l):] is non empty set
i is set
x is non empty Element of Class S
O is non empty Element of Class l
[x,O] is non empty Element of [:(Class S),(Class l):]
UU is set
III is set
[UU,III] is non empty set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is ofAtomicFormula Element of AllSymbolsOf U
ar S is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . 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
(abs (ar S)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
u \/ BOOLEAN is non empty set
id BOOLEAN is non empty Relation-like BOOLEAN -defined BOOLEAN -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive boolean-valued Element of bool [:BOOLEAN,BOOLEAN:]
[:BOOLEAN,BOOLEAN:] is non empty Relation-like set
bool [:BOOLEAN,BOOLEAN:] is non empty set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
l is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
II is set
U --> II is non empty Relation-like U -defined {II} -valued Function-like constant total quasi_total Element of bool [:U,{II}:]
{II} is non empty trivial finite 1 -element set
[:U,{II}:] is non empty Relation-like set
bool [:U,{II}:] is non empty set
dom (U --> II) is non empty Element of bool U
bool U is non empty set
rng (U --> II) is non empty trivial finite 1 -element set
x is set
O is set
[x,O] is non empty set
i is non empty Relation-like U -defined u -valued Function-like total quasi_total Element of bool [:U,u:]
i . x is set
i . O is set
[(i . x),(i . O)] is non empty set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is ofAtomicFormula Element of AllSymbolsOf U
ar S is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . 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
(abs (ar S)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
u \/ BOOLEAN is non empty set
l is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
[:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):] is non empty set
(u,l,(abs (ar S))) is Relation-like (abs (ar S)) -tuples_on u -defined (abs (ar S)) -tuples_on u -valued total quasi_total reflexive symmetric transitive Element of bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):]
(u,u,l,(abs (ar S))) is Relation-like (abs (ar S)) -tuples_on u -defined (abs (ar S)) -tuples_on u -valued total quasi_total Element of bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):]
Seg (abs (ar S)) is finite abs (ar S) -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 S) ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined u -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar S)) -tuples_on u : for b₃ being set holds
( not b₃ in Seg (abs (ar S)) or [(b₁ . b₃),(b₂ . b₃)] in l ) } is set
[:((abs (ar S)) -tuples_on u),u:] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on u),u:] is non empty set
the non empty Relation-like (abs (ar S)) -tuples_on u -defined u -valued Function-like total quasi_total ((u,l,(abs (ar S))),l) Element of bool [:((abs (ar S)) -tuples_on u),u:] is non empty Relation-like (abs (ar S)) -tuples_on u -defined u -valued Function-like total quasi_total ((u,l,(abs (ar S))),l) Element of bool [:((abs (ar S)) -tuples_on u),u:]
[:((abs (ar S)) -tuples_on u),BOOLEAN:] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on u),BOOLEAN:] is non empty set
the non empty Relation-like (abs (ar S)) -tuples_on u -defined BOOLEAN -valued Function-like total quasi_total boolean-valued ((u,l,(abs (ar S))), id BOOLEAN) Element of bool [:((abs (ar S)) -tuples_on u),BOOLEAN:] is non empty Relation-like (abs (ar S)) -tuples_on u -defined BOOLEAN -valued Function-like total quasi_total boolean-valued ((u,l,(abs (ar S))), id BOOLEAN) Element of bool [:((abs (ar S)) -tuples_on u),BOOLEAN:]
O is non empty Relation-like (abs (ar S)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of S,u
O is non empty Relation-like (abs (ar S)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of S,u
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
l is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
the non empty Relation-like U -defined u -valued Function-like total quasi_total (S,l) Element of bool [:U,u:] is non empty Relation-like U -defined u -valued Function-like total quasi_total (S,l) Element of bool [:U,u:]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:(S -tuples_on U),(S -tuples_on U):]
S -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
[:(S -tuples_on U),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on U):] is non empty set
(U,U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total Element of bool [:(S -tuples_on U),(S -tuples_on U):]
Seg S is finite S -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 <= S ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in u ) } is set
U is non empty set
bool U is non empty set
{_{U}_} is non empty V165() V166() a_partition of U
id U is non empty Relation-like U -defined U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
Class (id U) is non empty V165() V166() a_partition of U
u is non empty Element of {_{U}_}
l is set
{l} is non empty trivial finite 1 -element set
II is Element of U
{II} is non empty trivial finite 1 -element Element of bool U
S is Element of U
{S} is non empty trivial finite 1 -element Element of bool U
l is Element of U
{l} is non empty trivial finite 1 -element Element of bool U
U is non empty set
{_{U}_} is non empty V165() V166() a_partition of U
id U is non empty Relation-like U -defined U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
Class (id U) is non empty V165() V166() a_partition of U
[:{_{U}_},U:] is non empty Relation-like set
bool [:{_{U}_},U:] is non empty set
bool U is non empty set
u is non empty Relation-like {_{U}_} -defined U -valued Function-like total quasi_total Element of bool [:{_{U}_},U:]
S is non empty Element of {_{U}_}
u . S is Element of U
(U,S) is Element of U
u is non empty Relation-like {_{U}_} -defined U -valued Function-like total quasi_total Element of bool [:{_{U}_},U:]
S is non empty Relation-like {_{U}_} -defined U -valued Function-like total quasi_total Element of bool [:{_{U}_},U:]
l is non empty Element of {_{U}_}
u . l is Element of U
(U,l) is Element of U
S . l is Element of U
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
bool U is non empty set
u is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class u is non empty V165() V166() a_partition of U
S is non empty Element of Class u
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
bool U is non empty set
u is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class u is non empty V165() V166() a_partition of U
S is set
l is set
[S,l] is non empty set
II is non empty Element of Class u
i is set
Class (u,i) is Element of bool U
{i} is non empty trivial finite 1 -element set
u .: {i} is set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
bool U is non empty set
u is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class u is non empty V165() V166() a_partition of U
S is non empty Element of Class u
l is non empty Element of Class u
II is set
E is set
[II,E] is non empty set
x is Element of U
i is Relation-like U -defined U -valued total quasi_total reflexive symmetric Element of bool [:U,U:]
Class (i,II) is Element of bool U
{II} is non empty trivial finite 1 -element set
i .: {II} is set
EqClass (u,x) is non empty Element of Class u
{x} is non empty trivial finite 1 -element set
u .: {x} is set
O is Element of U
Class (i,E) is Element of bool U
{E} is non empty trivial finite 1 -element set
i .: {E} is set
EqClass (u,O) is non empty Element of Class u
{O} is non empty trivial finite 1 -element set
u .: {O} is set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
l is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
II is Relation-like Function-like (S,l) set
(U,u,S,l,II) is Relation-like Class S -defined Class l -valued Element of bool [:(Class S),(Class l):]
Class S is non empty V165() V166() a_partition of U
Class l is non empty V165() V166() a_partition of u
[:(Class S),(Class l):] is non empty Relation-like set
bool [:(Class S),(Class l):] is non empty set
bool U is non empty set
bool u is non empty set
{ [b₁,b₂] where b₁ is non empty Element of Class S, b₂ is non empty Element of Class l : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in II ) } is set
O is set
UU is set
[O,UU] is non empty set
X is non empty Element of Class S
I is non empty Element of Class l
[X,I] is non empty Element of [:(Class S),(Class l):]
j is set
Jj is set
[j,Jj] is non empty set
j is set
Jj is set
[j,Jj] is non empty set
III is set
[O,III] is non empty set
jJ is non empty Element of Class S
jJ is non empty Element of Class l
[jJ,jJ] is non empty Element of [:(Class S),(Class l):]
g is set
h is set
[g,h] is non empty set
G is set
n is set
[G,n] is non empty set
g is set
h is set
[g,h] is non empty set
g is set
h is set
[g,h] is non empty set
[j,g] is non empty set
II . g is set
II . j is set
[Jj,h] is non empty set
O is Relation-like set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class S is non empty V165() V166() a_partition of U
l is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
Class l is non empty V165() V166() a_partition of u
[:(Class S),(Class l):] is non empty Relation-like set
bool [:(Class S),(Class l):] is non empty set
II is Relation-like U -defined u -valued total quasi_total Element of bool [:U,u:]
(U,u,S,l,II) is Relation-like Class S -defined Class l -valued Element of bool [:(Class S),(Class l):]
bool U is non empty set
bool u is non empty set
{ [b₁,b₂] where b₁ is non empty Element of Class S, b₂ is non empty Element of Class l : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in II ) } is set
x is set
O is non empty Element of Class S
the Element of O is Element of O
dom II is Element of bool U
III is Element of U
X is set
[III,X] is non empty set
I is Element of u
i is non empty V165() V166() a_partition of u
EqClass (I,i) is Element of bool u
j is non empty Element of Class l
[x,j] is non empty set
dom (U,u,S,l,II) is V165() Element of bool (Class S)
bool (Class S) is non empty set
x is Relation-like Class S -defined Class l -valued Element of bool [:(Class S),(Class l):]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
l is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
II is non empty Relation-like U -defined u -valued Function-like total quasi_total (S,l) Element of bool [:U,u:]
(U,u,S,l,II) is set
bool U is non empty set
Class S is non empty V165() V166() a_partition of U
bool u is non empty set
Class l is non empty V165() V166() a_partition of u
{ [b₁,b₂] where b₁ is non empty Element of Class S, b₂ is non empty Element of Class l : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in II ) } is set
[:(Class S),(Class l):] is non empty Relation-like set
bool [:(Class S),(Class l):] is non empty set
(U,u,S,l,II) is non empty Relation-like non empty-yielding Class S -defined Class l -valued Function-like total quasi_total Element of bool [:(Class S),(Class l):]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class u is non empty V165() V166() a_partition of U
[:U,(Class u):] is non empty Relation-like set
bool [:U,(Class u):] is non empty set
bool U is non empty set
S is non empty Relation-like non empty-yielding U -defined Class u -valued Function-like total quasi_total Element of bool [:U,(Class u):]
l is Element of U
S . l is non empty Element of Class u
EqClass (u,l) is non empty Element of Class u
{l} is non empty trivial finite 1 -element set
u .: {l} is set
S is non empty Relation-like non empty-yielding U -defined Class u -valued Function-like total quasi_total Element of bool [:U,(Class u):]
l is non empty Relation-like non empty-yielding U -defined Class u -valued Function-like total quasi_total Element of bool [:U,(Class u):]
II is Element of U
S . II is non empty Element of Class u
EqClass (u,II) is non empty Element of Class u
bool U is non empty set
{II} is non empty trivial finite 1 -element set
u .: {II} is set
l . II is non empty Element of Class u
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class u is non empty V165() V166() a_partition of U
[:U,(Class u):] is non empty Relation-like set
bool [:U,(Class u):] is non empty set
(U,u) is non empty Relation-like non empty-yielding U -defined Class u -valued Function-like total quasi_total Element of bool [:U,(Class u):]
l is set
bool U is non empty set
II is Element of bool U
E is set
Class (u,E) is Element of bool U
{E} is non empty trivial finite 1 -element set
u .: {E} is set
i is Element of U
(U,u) . i is non empty Element of Class u
rng (U,u) is non empty set
l is non empty Relation-like non empty-yielding U -defined Class u -valued Function-like total quasi_total Element of bool [:U,(Class u):]
U is non empty set
u is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
S is Relation-like U -defined u -valued Element of bool [:U,u:]
rng S is Element of bool u
bool u is non empty set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
the Relation-like U -defined U -valued onto Element of bool [:U,U:] is Relation-like U -defined U -valued onto Element of bool [:U,U:]
U is non empty set
u is Relation-like U -valued set
u ~ is Relation-like set
rng u is Element of bool U
bool U is non empty set
dom (u ~) is set
S is Relation-like set
U is non empty set
u is Relation-like U -valued onto set
u ~ is Relation-like U -defined set
dom (u ~) is Element of bool U
bool U is non empty set
rng u is Element of bool U
S is Relation-like U -defined set
u is non empty set
U is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
[:u,U:] is non empty Relation-like set
bool [:u,U:] is non empty set
S is Relation-like U -defined u -valued onto Element of bool [:U,u:]
S ~ is Relation-like u -defined U -valued total quasi_total Element of bool [:u,U:]
l is Relation-like u -defined U -valued Element of bool [:u,U:]
U is non empty set
u is Relation-like U -valued onto set
u ~ is Relation-like U -defined total set
S is Relation-like U -defined set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class u is non empty V165() V166() a_partition of U
(U,u) is non empty Relation-like non empty-yielding U -defined Class u -valued Function-like total quasi_total onto Element of bool [:U,(Class u):]
[:U,(Class u):] is non empty Relation-like set
bool [:U,(Class u):] is non empty set
(U,u) ~ is Relation-like Class u -defined U -valued total quasi_total Element of bool [:(Class u),U:]
[:(Class u),U:] is non empty Relation-like set
bool [:(Class u),U:] is non empty set
S is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
S -tuples_on (Class u) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of Class u
S -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
(U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:(S -tuples_on U),(S -tuples_on U):]
[:(S -tuples_on U),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on U):] is non empty set
(U,U,u,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total Element of bool [:(S -tuples_on U),(S -tuples_on U):]
Seg S is non empty finite S -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 <= S ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in u ) } is set
Class (U,u,S) is non empty V165() V166() a_partition of S -tuples_on U
((Class u),U,((U,u) ~),S) is Relation-like S -tuples_on (Class u) -defined S -tuples_on U -valued total quasi_total Element of bool [:(S -tuples_on (Class u)),(S -tuples_on U):]
[:(S -tuples_on (Class u)),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on (Class u)),(S -tuples_on U):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on (Class u), b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in (U,u) ~ ) } is set
((S -tuples_on U),(U,u,S)) is non empty Relation-like non empty-yielding S -tuples_on U -defined Class (U,u,S) -valued Function-like total quasi_total onto Element of bool [:(S -tuples_on U),(Class (U,u,S)):]
[:(S -tuples_on U),(Class (U,u,S)):] is non empty Relation-like set
bool [:(S -tuples_on U),(Class (U,u,S)):] is non empty set
((Class u),U,((U,u) ~),S) * ((S -tuples_on U),(U,u,S)) is Relation-like S -tuples_on (Class u) -defined Class (U,u,S) -valued total quasi_total Element of bool [:(S -tuples_on (Class u)),(Class (U,u,S)):]
[:(S -tuples_on (Class u)),(Class (U,u,S)):] is non empty Relation-like set
bool [:(S -tuples_on (Class u)),(Class (U,u,S)):] is non empty set
E is Relation-like U -defined Class u -valued Element of bool [:U,(Class u):]
E ~ is Relation-like Class u -defined U -valued Element of bool [:(Class u),U:]
i is Relation-like Class u -defined U -valued Element of bool [:(Class u),U:]
((Class u),U,i,S) is Relation-like S -tuples_on (Class u) -defined S -tuples_on U -valued Element of bool [:(S -tuples_on (Class u)),(S -tuples_on U):]
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on (Class u), b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in i ) } is set
O is non empty Relation-like non empty-yielding S -tuples_on U -defined Class (U,u,S) -valued Function-like total quasi_total Element of bool [:(S -tuples_on U),(Class (U,u,S)):]
III is set
X is set
[III,X] is non empty set
x is Relation-like S -tuples_on (Class u) -defined S -tuples_on U -valued Element of bool [:(S -tuples_on (Class u)),(S -tuples_on U):]
UU is Relation-like S -tuples_on U -defined Class (U,u,S) -valued Element of bool [:(S -tuples_on U),(Class (U,u,S)):]
x * UU is Relation-like S -tuples_on (Class u) -defined Class (U,u,S) -valued Element of bool [:(S -tuples_on (Class u)),(Class (U,u,S)):]
I is set
[III,I] is non empty set
j is set
[III,j] is non empty set
[j,X] is non empty set
Jj is set
[III,Jj] is non empty set
[Jj,I] is non empty set
O . j is set
O . Jj is set
g is non empty Relation-like non empty-yielding NAT -defined Class u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on (Class u)
h is non empty Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U
[g,h] is non empty Element of [:(S -tuples_on (Class u)),(S -tuples_on U):]
G is non empty Relation-like non empty-yielding NAT -defined Class u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on (Class u)
n is non empty Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U
[G,n] is non empty Element of [:(S -tuples_on (Class u)),(S -tuples_on U):]
Funcs ((Seg S),U) is non empty functional FUNCTION_DOMAIN of Seg S,U
nE is set
g . nE is set
h . nE is set
[(g . nE),(h . nE)] is non empty set
G . nE is set
n . nE is set
[(G . nE),(n . nE)] is non empty set
[(h . nE),(g . nE)] is non empty set
II is non empty Relation-like non empty-yielding U -defined Class u -valued Function-like total quasi_total Element of bool [:U,(Class u):]
[(n . nE),(G . nE)] is non empty set
hh is Element of Seg S
h . hh is set
II . (h . hh) is set
g . hh is set
n . hh is set
II . (n . hh) is set
G . hh is set
Enn is Relation-like Seg S -defined U -valued Function-like total quasi_total finite-support Element of Funcs ((Seg S),U)
Enn . hh is Element of U
Class (u,(Enn . hh)) is Element of bool U
bool U is non empty set
{(Enn . hh)} is non empty trivial finite 1 -element set
u .: {(Enn . hh)} is set
En is Relation-like Seg S -defined U -valued Function-like total quasi_total finite-support Element of Funcs ((Seg S),U)
En . hh is Element of U
Class (u,(En . hh)) is Element of bool U
{(En . hh)} is non empty trivial finite 1 -element set
u .: {(En . hh)} is set
[(h . nE),(n . nE)] is non empty set
[j,Jj] is non empty set
jJ is non empty Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U
((S -tuples_on U),(U,u,S)) . jJ is non empty Element of Class (U,u,S)
Class ((U,u,S),jJ) is functional finite-membered FinSequence-membered V165() Element of bool (S -tuples_on U)
bool (S -tuples_on U) is non empty set
{jJ} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
(U,u,S) .: {jJ} is set
jJ is non empty Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U
((S -tuples_on U),(U,u,S)) . jJ is non empty Element of Class (U,u,S)
Class ((U,u,S),jJ) is functional finite-membered FinSequence-membered V165() Element of bool (S -tuples_on U)
{jJ} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
(U,u,S) .: {jJ} is set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class S is non empty V165() V166() a_partition of U
u -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class S
u -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
(U,S,u) is Relation-like u -tuples_on U -defined u -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:(u -tuples_on U),(u -tuples_on U):]
[:(u -tuples_on U),(u -tuples_on U):] is non empty Relation-like set
bool [:(u -tuples_on U),(u -tuples_on U):] is non empty set
(U,U,S,u) is Relation-like u -tuples_on U -defined u -tuples_on U -valued total quasi_total Element of bool [:(u -tuples_on U),(u -tuples_on U):]
Seg u is finite u -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 <= u ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
Class (U,S,u) is non empty V165() V166() a_partition of u -tuples_on U
(U,S) is non empty Relation-like non empty-yielding U -defined Class S -valued Function-like total quasi_total onto Element of bool [:U,(Class S):]
[:U,(Class S):] is non empty Relation-like set
bool [:U,(Class S):] is non empty set
(U,S) ~ is Relation-like Class S -defined U -valued total quasi_total Element of bool [:(Class S),U:]
[:(Class S),U:] is non empty Relation-like set
bool [:(Class S),U:] is non empty set
((Class S),U,((U,S) ~),u) is Relation-like u -tuples_on (Class S) -defined u -tuples_on U -valued total quasi_total Element of bool [:(u -tuples_on (Class S)),(u -tuples_on U):]
[:(u -tuples_on (Class S)),(u -tuples_on U):] is non empty Relation-like set
bool [:(u -tuples_on (Class S)),(u -tuples_on U):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class S -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on (Class S), b₂ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in (U,S) ~ ) } is set
((u -tuples_on U),(U,S,u)) is non empty Relation-like non empty-yielding u -tuples_on U -defined Class (U,S,u) -valued Function-like total quasi_total onto Element of bool [:(u -tuples_on U),(Class (U,S,u)):]
[:(u -tuples_on U),(Class (U,S,u)):] is non empty Relation-like set
bool [:(u -tuples_on U),(Class (U,S,u)):] is non empty set
((Class S),U,((U,S) ~),u) * ((u -tuples_on U),(U,S,u)) is Relation-like u -tuples_on (Class S) -defined Class (U,S,u) -valued total quasi_total Element of bool [:(u -tuples_on (Class S)),(Class (U,S,u)):]
[:(u -tuples_on (Class S)),(Class (U,S,u)):] is non empty Relation-like set
bool [:(u -tuples_on (Class S)),(Class (U,S,u)):] is non empty set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class S is non empty V165() V166() a_partition of U
u -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class S
u -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
(U,S,u) is Relation-like u -tuples_on U -defined u -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:(u -tuples_on U),(u -tuples_on U):]
[:(u -tuples_on U),(u -tuples_on U):] is non empty Relation-like set
bool [:(u -tuples_on U),(u -tuples_on U):] is non empty set
(U,U,S,u) is Relation-like u -tuples_on U -defined u -tuples_on U -valued total quasi_total Element of bool [:(u -tuples_on U),(u -tuples_on U):]
Seg u is finite u -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 <= u ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
Class (U,S,u) is non empty V165() V166() a_partition of u -tuples_on U
[:(u -tuples_on (Class S)),(Class (U,S,u)):] is non empty Relation-like set
bool [:(u -tuples_on (Class S)),(Class (U,S,u)):] is non empty set
(U,u,S) is Relation-like u -tuples_on (Class S) -defined Class (U,S,u) -valued Element of bool [:(u -tuples_on (Class S)),(Class (U,S,u)):]
(U,S) is non empty Relation-like non empty-yielding U -defined Class S -valued Function-like total quasi_total onto Element of bool [:U,(Class S):]
[:U,(Class S):] is non empty Relation-like set
bool [:U,(Class S):] is non empty set
(U,S) ~ is Relation-like Class S -defined U -valued total quasi_total Element of bool [:(Class S),U:]
[:(Class S),U:] is non empty Relation-like set
bool [:(Class S),U:] is non empty set
((Class S),U,((U,S) ~),u) is Relation-like u -tuples_on (Class S) -defined u -tuples_on U -valued total quasi_total Element of bool [:(u -tuples_on (Class S)),(u -tuples_on U):]
[:(u -tuples_on (Class S)),(u -tuples_on U):] is non empty Relation-like set
bool [:(u -tuples_on (Class S)),(u -tuples_on U):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class S -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on (Class S), b₂ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in (U,S) ~ ) } is set
((u -tuples_on U),(U,S,u)) is non empty Relation-like non empty-yielding u -tuples_on U -defined Class (U,S,u) -valued Function-like total quasi_total onto Element of bool [:(u -tuples_on U),(Class (U,S,u)):]
[:(u -tuples_on U),(Class (U,S,u)):] is non empty Relation-like set
bool [:(u -tuples_on U),(Class (U,S,u)):] is non empty set
((Class S),U,((U,S) ~),u) * ((u -tuples_on U),(U,S,u)) is Relation-like u -tuples_on (Class S) -defined Class (U,S,u) -valued total quasi_total Element of bool [:(u -tuples_on (Class S)),(Class (U,S,u)):]
l is Relation-like u -tuples_on (Class S) -defined Class (U,S,u) -valued Element of bool [:(u -tuples_on (Class S)),(Class (U,S,u)):]
i is Relation-like U -defined Class S -valued Element of bool [:U,(Class S):]
i ~ is Relation-like Class S -defined U -valued Element of bool [:(Class S),U:]
l 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
l -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of Class S
l -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
[:(l -tuples_on (Class S)),(l -tuples_on U):] is non empty Relation-like set
bool [:(l -tuples_on (Class S)),(l -tuples_on U):] is non empty set
x is Relation-like Class S -defined U -valued Element of bool [:(Class S),U:]
((Class S),U,x,l) is Relation-like l -tuples_on (Class S) -defined l -tuples_on U -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:(l -tuples_on (Class S)),(l -tuples_on U):]
Seg l 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 finite-membered cardinal l -element {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support 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 <= l ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on (Class S), b₂ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in x ) } is set
UU is non empty Relation-like non empty-yielding u -tuples_on U -defined Class (U,S,u) -valued Function-like total quasi_total Element of bool [:(u -tuples_on U),(Class (U,S,u)):]
O is Relation-like l -tuples_on (Class S) -defined l -tuples_on U -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:(l -tuples_on (Class S)),(l -tuples_on U):]
O * UU is Relation-like u -tuples_on U -defined l -tuples_on U -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:(u -tuples_on U),(l -tuples_on U):]
[:(u -tuples_on U),(l -tuples_on U):] is non empty Relation-like set
bool [:(u -tuples_on U),(l -tuples_on U):] is non empty set
III is Relation-like u -tuples_on (Class S) -defined Class (U,S,u) -valued Element of bool [:(u -tuples_on (Class S)),(Class (U,S,u)):]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class S is non empty V165() V166() a_partition of U
u -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class S
u -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
(U,S,u) is Relation-like u -tuples_on U -defined u -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:(u -tuples_on U),(u -tuples_on U):]
[:(u -tuples_on U),(u -tuples_on U):] is non empty Relation-like set
bool [:(u -tuples_on U),(u -tuples_on U):] is non empty set
(U,U,S,u) is Relation-like u -tuples_on U -defined u -tuples_on U -valued total quasi_total Element of bool [:(u -tuples_on U),(u -tuples_on U):]
Seg u is finite u -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 <= u ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
Class (U,S,u) is non empty V165() V166() a_partition of u -tuples_on U
[:(u -tuples_on (Class S)),(Class (U,S,u)):] is non empty Relation-like set
bool [:(u -tuples_on (Class S)),(Class (U,S,u)):] is non empty set
(U,u,S) is Relation-like u -tuples_on (Class S) -defined Class (U,S,u) -valued Function-like Element of bool [:(u -tuples_on (Class S)),(Class (U,S,u)):]
(U,S) is non empty Relation-like non empty-yielding U -defined Class S -valued Function-like total quasi_total onto Element of bool [:U,(Class S):]
[:U,(Class S):] is non empty Relation-like set
bool [:U,(Class S):] is non empty set
(U,S) ~ is Relation-like Class S -defined U -valued total quasi_total Element of bool [:(Class S),U:]
[:(Class S),U:] is non empty Relation-like set
bool [:(Class S),U:] is non empty set
((Class S),U,((U,S) ~),u) is Relation-like u -tuples_on (Class S) -defined u -tuples_on U -valued total quasi_total Element of bool [:(u -tuples_on (Class S)),(u -tuples_on U):]
[:(u -tuples_on (Class S)),(u -tuples_on U):] is non empty Relation-like set
bool [:(u -tuples_on (Class S)),(u -tuples_on U):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class S -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on (Class S), b₂ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in (U,S) ~ ) } is set
((u -tuples_on U),(U,S,u)) is non empty Relation-like non empty-yielding u -tuples_on U -defined Class (U,S,u) -valued Function-like total quasi_total onto Element of bool [:(u -tuples_on U),(Class (U,S,u)):]
[:(u -tuples_on U),(Class (U,S,u)):] is non empty Relation-like set
bool [:(u -tuples_on U),(Class (U,S,u)):] is non empty set
((Class S),U,((U,S) ~),u) * ((u -tuples_on U),(U,S,u)) is Relation-like u -tuples_on (Class S) -defined Class (U,S,u) -valued total quasi_total Element of bool [:(u -tuples_on (Class S)),(Class (U,S,u)):]
l is Relation-like u -tuples_on (Class S) -defined Class (U,S,u) -valued Element of bool [:(u -tuples_on (Class S)),(Class (U,S,u)):]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
(U,u,S) is non empty Relation-like non empty-yielding u -tuples_on (Class S) -defined Class (U,S,u) -valued Function-like total quasi_total Element of bool [:(u -tuples_on (Class S)),(Class (U,S,u)):]
Class S is non empty V165() V166() a_partition of U
u -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class S
u -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
(U,S,u) is Relation-like u -tuples_on U -defined u -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:(u -tuples_on U),(u -tuples_on U):]
[:(u -tuples_on U),(u -tuples_on U):] is non empty Relation-like set
bool [:(u -tuples_on U),(u -tuples_on U):] is non empty set
(U,U,S,u) is Relation-like u -tuples_on U -defined u -tuples_on U -valued total quasi_total Element of bool [:(u -tuples_on U),(u -tuples_on U):]
Seg u is finite u -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 <= u ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
Class (U,S,u) is non empty V165() V166() a_partition of u -tuples_on U
[:(u -tuples_on (Class S)),(Class (U,S,u)):] is non empty Relation-like set
bool [:(u -tuples_on (Class S)),(Class (U,S,u)):] is non empty set
(U,S) is non empty Relation-like non empty-yielding U -defined Class S -valued Function-like total quasi_total onto Element of bool [:U,(Class S):]
[:U,(Class S):] is non empty Relation-like set
bool [:U,(Class S):] is non empty set
(U,S) ~ is Relation-like Class S -defined U -valued total quasi_total Element of bool [:(Class S),U:]
[:(Class S),U:] is non empty Relation-like set
bool [:(Class S),U:] is non empty set
((Class S),U,((U,S) ~),u) is Relation-like u -tuples_on (Class S) -defined u -tuples_on U -valued total quasi_total Element of bool [:(u -tuples_on (Class S)),(u -tuples_on U):]
[:(u -tuples_on (Class S)),(u -tuples_on U):] is non empty Relation-like set
bool [:(u -tuples_on (Class S)),(u -tuples_on U):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class S -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on (Class S), b₂ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in (U,S) ~ ) } is set
((u -tuples_on U),(U,S,u)) is non empty Relation-like non empty-yielding u -tuples_on U -defined Class (U,S,u) -valued Function-like total quasi_total onto Element of bool [:(u -tuples_on U),(Class (U,S,u)):]
[:(u -tuples_on U),(Class (U,S,u)):] is non empty Relation-like set
bool [:(u -tuples_on U),(Class (U,S,u)):] is non empty set
((Class S),U,((U,S) ~),u) * ((u -tuples_on U),(U,S,u)) is Relation-like u -tuples_on (Class S) -defined Class (U,S,u) -valued total quasi_total Element of bool [:(u -tuples_on (Class S)),(Class (U,S,u)):]
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is ofAtomicFormula Element of AllSymbolsOf U
ar S is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . 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
(abs (ar S)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
u \/ BOOLEAN is non empty set
l is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
Class l is non empty V165() V166() a_partition of u
(abs (ar S)) -tuples_on (Class l) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class l
(u,l,(abs (ar S))) is Relation-like (abs (ar S)) -tuples_on u -defined (abs (ar S)) -tuples_on u -valued total quasi_total reflexive symmetric transitive Element of bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):]
[:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):] is non empty set
(u,u,l,(abs (ar S))) is Relation-like (abs (ar S)) -tuples_on u -defined (abs (ar S)) -tuples_on u -valued total quasi_total Element of bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):]
Seg (abs (ar S)) is finite abs (ar S) -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 S) ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined u -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar S)) -tuples_on u : for b₃ being set holds
( not b₃ in Seg (abs (ar S)) or [(b₁ . b₃),(b₂ . b₃)] in l ) } is set
Class (u,l,(abs (ar S))) is non empty V165() V166() a_partition of (abs (ar S)) -tuples_on u
(u,(abs (ar S)),l) is non empty Relation-like non empty-yielding (abs (ar S)) -tuples_on (Class l) -defined Class (u,l,(abs (ar S))) -valued Function-like total quasi_total Element of bool [:((abs (ar S)) -tuples_on (Class l)),(Class (u,l,(abs (ar S)))):]
[:((abs (ar S)) -tuples_on (Class l)),(Class (u,l,(abs (ar S)))):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on (Class l)),(Class (u,l,(abs (ar S)))):] is non empty set
(u,l) is non empty Relation-like non empty-yielding u -defined Class l -valued Function-like total quasi_total onto Element of bool [:u,(Class l):]
[:u,(Class l):] is non empty Relation-like set
bool [:u,(Class l):] is non empty set
(u,l) ~ is Relation-like Class l -defined u -valued total quasi_total Element of bool [:(Class l),u:]
[:(Class l),u:] is non empty Relation-like set
bool [:(Class l),u:] is non empty set
((Class l),u,((u,l) ~),(abs (ar S))) is Relation-like (abs (ar S)) -tuples_on (Class l) -defined (abs (ar S)) -tuples_on u -valued total quasi_total Element of bool [:((abs (ar S)) -tuples_on (Class l)),((abs (ar S)) -tuples_on u):]
[:((abs (ar S)) -tuples_on (Class l)),((abs (ar S)) -tuples_on u):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on (Class l)),((abs (ar S)) -tuples_on u):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class l -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar S)) -tuples_on (Class l), b₂ is Relation-like NAT -defined u -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar S)) -tuples_on u : for b₃ being set holds
( not b₃ in Seg (abs (ar S)) or [(b₁ . b₃),(b₂ . b₃)] in (u,l) ~ ) } is set
(((abs (ar S)) -tuples_on u),(u,l,(abs (ar S)))) is non empty Relation-like non empty-yielding (abs (ar S)) -tuples_on u -defined Class (u,l,(abs (ar S))) -valued Function-like total quasi_total onto Element of bool [:((abs (ar S)) -tuples_on u),(Class (u,l,(abs (ar S)))):]
[:((abs (ar S)) -tuples_on u),(Class (u,l,(abs (ar S)))):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on u),(Class (u,l,(abs (ar S)))):] is non empty set
((Class l),u,((u,l) ~),(abs (ar S))) * (((abs (ar S)) -tuples_on u),(u,l,(abs (ar S)))) is Relation-like (abs (ar S)) -tuples_on (Class l) -defined Class (u,l,(abs (ar S))) -valued total quasi_total Element of bool [:((abs (ar S)) -tuples_on (Class l)),(Class (u,l,(abs (ar S)))):]
II is non empty Relation-like (abs (ar S)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of S,u
(((abs (ar S)) -tuples_on u),u,(u,l,(abs (ar S))),l,II) is Relation-like Class (u,l,(abs (ar S))) -defined Class l -valued Element of bool [:(Class (u,l,(abs (ar S)))),(Class l):]
[:(Class (u,l,(abs (ar S)))),(Class l):] is non empty Relation-like set
bool [:(Class (u,l,(abs (ar S)))),(Class l):] is non empty set
bool ((abs (ar S)) -tuples_on u) is non empty set
bool u is non empty set
{ [b₁,b₂] where b₁ is non empty Element of Class (u,l,(abs (ar S))), b₂ is non empty Element of Class l : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in II ) } is set
(u,(abs (ar S)),l) * (((abs (ar S)) -tuples_on u),u,(u,l,(abs (ar S))),l,II) is Relation-like (abs (ar S)) -tuples_on (Class l) -defined Class l -valued Element of bool [:((abs (ar S)) -tuples_on (Class l)),(Class l):]
[:((abs (ar S)) -tuples_on (Class l)),(Class l):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on (Class l)),(Class l):] is non empty set
Class (id BOOLEAN) is non empty V165() V166() a_partition of BOOLEAN
{_{BOOLEAN}_} is non empty V165() V166() a_partition of BOOLEAN
id BOOLEAN is non empty Relation-like BOOLEAN -defined BOOLEAN -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive boolean-valued Element of bool [:BOOLEAN,BOOLEAN:]
Class (id BOOLEAN) is non empty V165() V166() a_partition of BOOLEAN
(((abs (ar S)) -tuples_on u),BOOLEAN,(u,l,(abs (ar S))),(id BOOLEAN),II) is Relation-like Class (u,l,(abs (ar S))) -defined Class (id BOOLEAN) -valued Element of bool [:(Class (u,l,(abs (ar S)))),(Class (id BOOLEAN)):]
[:(Class (u,l,(abs (ar S)))),(Class (id BOOLEAN)):] is non empty Relation-like set
bool [:(Class (u,l,(abs (ar S)))),(Class (id BOOLEAN)):] is non empty set
bool BOOLEAN is non empty set
{ [b₁,b₂] where b₁ is non empty Element of Class (u,l,(abs (ar S))), b₂ is non empty Element of Class (id BOOLEAN) : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in II ) } is set
(u,(abs (ar S)),l) * (((abs (ar S)) -tuples_on u),BOOLEAN,(u,l,(abs (ar S))),(id BOOLEAN),II) is Relation-like (abs (ar S)) -tuples_on (Class l) -defined Class (id BOOLEAN) -valued Element of bool [:((abs (ar S)) -tuples_on (Class l)),(Class (id BOOLEAN)):]
[:((abs (ar S)) -tuples_on (Class l)),(Class (id BOOLEAN)):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on (Class l)),(Class (id BOOLEAN)):] is non empty set
(BOOLEAN) is non empty Relation-like {_{BOOLEAN}_} -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:{_{BOOLEAN}_},BOOLEAN:]
[:{_{BOOLEAN}_},BOOLEAN:] is non empty Relation-like set
bool [:{_{BOOLEAN}_},BOOLEAN:] is non empty set
((u,(abs (ar S)),l) * (((abs (ar S)) -tuples_on u),BOOLEAN,(u,l,(abs (ar S))),(id BOOLEAN),II)) * (BOOLEAN) is Relation-like (abs (ar S)) -tuples_on (Class l) -defined BOOLEAN -valued Element of bool [:((abs (ar S)) -tuples_on (Class l)),BOOLEAN:]
[:((abs (ar S)) -tuples_on (Class l)),BOOLEAN:] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on (Class l)),BOOLEAN:] is non empty set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is ofAtomicFormula Element of AllSymbolsOf U
l is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
ar S is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . 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
(abs (ar S)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
u \/ BOOLEAN is non empty set
II is non empty Relation-like (abs (ar S)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total (U,u,S,l) Interpreter of S,u
(U,u,S,l,II) is set
Class l is non empty V165() V166() a_partition of u
(abs (ar S)) -tuples_on (Class l) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class l
(Class l) \/ BOOLEAN is non empty set
(u,(abs (ar S)),l) is non empty Relation-like non empty-yielding (abs (ar S)) -tuples_on (Class l) -defined Class (u,l,(abs (ar S))) -valued Function-like total quasi_total Element of bool [:((abs (ar S)) -tuples_on (Class l)),(Class (u,l,(abs (ar S)))):]
(u,l,(abs (ar S))) is Relation-like (abs (ar S)) -tuples_on u -defined (abs (ar S)) -tuples_on u -valued total quasi_total reflexive symmetric transitive Element of bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):]
[:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):] is non empty set
(u,u,l,(abs (ar S))) is Relation-like (abs (ar S)) -tuples_on u -defined (abs (ar S)) -tuples_on u -valued total quasi_total Element of bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):]
Seg (abs (ar S)) is finite abs (ar S) -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 S) ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined u -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar S)) -tuples_on u : for b₃ being set holds
( not b₃ in Seg (abs (ar S)) or [(b₁ . b₃),(b₂ . b₃)] in l ) } is set
Class (u,l,(abs (ar S))) is non empty V165() V166() a_partition of (abs (ar S)) -tuples_on u
[:((abs (ar S)) -tuples_on (Class l)),(Class (u,l,(abs (ar S)))):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on (Class l)),(Class (u,l,(abs (ar S)))):] is non empty set
(u,l) is non empty Relation-like non empty-yielding u -defined Class l -valued Function-like total quasi_total onto Element of bool [:u,(Class l):]
[:u,(Class l):] is non empty Relation-like set
bool [:u,(Class l):] is non empty set
(u,l) ~ is Relation-like Class l -defined u -valued total quasi_total Element of bool [:(Class l),u:]
[:(Class l),u:] is non empty Relation-like set
bool [:(Class l),u:] is non empty set
((Class l),u,((u,l) ~),(abs (ar S))) is Relation-like (abs (ar S)) -tuples_on (Class l) -defined (abs (ar S)) -tuples_on u -valued total quasi_total Element of bool [:((abs (ar S)) -tuples_on (Class l)),((abs (ar S)) -tuples_on u):]
[:((abs (ar S)) -tuples_on (Class l)),((abs (ar S)) -tuples_on u):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on (Class l)),((abs (ar S)) -tuples_on u):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class l -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar S)) -tuples_on (Class l), b₂ is Relation-like NAT -defined u -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar S)) -tuples_on u : for b₃ being set holds
( not b₃ in Seg (abs (ar S)) or [(b₁ . b₃),(b₂ . b₃)] in (u,l) ~ ) } is set
(((abs (ar S)) -tuples_on u),(u,l,(abs (ar S)))) is non empty Relation-like non empty-yielding (abs (ar S)) -tuples_on u -defined Class (u,l,(abs (ar S))) -valued Function-like total quasi_total onto Element of bool [:((abs (ar S)) -tuples_on u),(Class (u,l,(abs (ar S)))):]
[:((abs (ar S)) -tuples_on u),(Class (u,l,(abs (ar S)))):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on u),(Class (u,l,(abs (ar S)))):] is non empty set
((Class l),u,((u,l) ~),(abs (ar S))) * (((abs (ar S)) -tuples_on u),(u,l,(abs (ar S)))) is Relation-like (abs (ar S)) -tuples_on (Class l) -defined Class (u,l,(abs (ar S))) -valued total quasi_total Element of bool [:((abs (ar S)) -tuples_on (Class l)),(Class (u,l,(abs (ar S)))):]
UU is Relation-like (abs (ar S)) -tuples_on u -defined (abs (ar S)) -tuples_on u -valued total quasi_total reflexive symmetric transitive Element of bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):]
[:((abs (ar S)) -tuples_on u),u:] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on u),u:] is non empty set
Class UU is non empty V165() V166() a_partition of (abs (ar S)) -tuples_on u
[:(Class UU),(Class l):] is non empty Relation-like set
bool [:(Class UU),(Class l):] is non empty set
X is non empty Relation-like (abs (ar S)) -tuples_on u -defined u -valued Function-like total quasi_total (UU,l) Element of bool [:((abs (ar S)) -tuples_on u),u:]
(((abs (ar S)) -tuples_on u),u,UU,l,X) is non empty Relation-like non empty-yielding Class UU -defined Class l -valued Function-like total quasi_total Element of bool [:(Class UU),(Class l):]
bool ((abs (ar S)) -tuples_on u) is non empty set
bool u is non empty set
{ [b₁,b₂] where b₁ is non empty Element of Class UU, b₂ is non empty Element of Class l : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in X ) } is set
I is non empty Relation-like non empty-yielding Class UU -defined Class l -valued Function-like total quasi_total Element of bool [:(Class UU),(Class l):]
I * (u,(abs (ar S)),l) is Relation-like (abs (ar S)) -tuples_on (Class l) -defined Class l -valued Function-like Element of bool [:((abs (ar S)) -tuples_on (Class l)),(Class l):]
[:((abs (ar S)) -tuples_on (Class l)),(Class l):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on (Class l)),(Class l):] is non empty set
UU is Relation-like (abs (ar S)) -tuples_on u -defined (abs (ar S)) -tuples_on u -valued total quasi_total reflexive symmetric transitive Element of bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):]
[:((abs (ar S)) -tuples_on u),BOOLEAN:] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on u),BOOLEAN:] is non empty set
Class UU is non empty V165() V166() a_partition of (abs (ar S)) -tuples_on u
[:(Class UU),{_{BOOLEAN}_}:] is non empty Relation-like set
bool [:(Class UU),{_{BOOLEAN}_}:] is non empty set
X is non empty Relation-like (abs (ar S)) -tuples_on u -defined BOOLEAN -valued Function-like total quasi_total boolean-valued (UU, id BOOLEAN) Element of bool [:((abs (ar S)) -tuples_on u),BOOLEAN:]
(((abs (ar S)) -tuples_on u),BOOLEAN,UU,(id BOOLEAN),X) is non empty Relation-like non empty-yielding Class UU -defined Class (id BOOLEAN) -valued Function-like total quasi_total Element of bool [:(Class UU),(Class (id BOOLEAN)):]
[:(Class UU),(Class (id BOOLEAN)):] is non empty Relation-like set
bool [:(Class UU),(Class (id BOOLEAN)):] is non empty set
bool ((abs (ar S)) -tuples_on u) is non empty set
{ [b₁,b₂] where b₁ is non empty Element of Class UU, b₂ is non empty Element of Class (id BOOLEAN) : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in X ) } is set
j is non empty Relation-like non empty-yielding Class UU -defined {_{BOOLEAN}_} -valued Function-like total quasi_total Element of bool [:(Class UU),{_{BOOLEAN}_}:]
j * (u,(abs (ar S)),l) is Relation-like (abs (ar S)) -tuples_on (Class l) -defined {_{BOOLEAN}_} -valued Function-like Element of bool [:((abs (ar S)) -tuples_on (Class l)),{_{BOOLEAN}_}:]
[:((abs (ar S)) -tuples_on (Class l)),{_{BOOLEAN}_}:] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on (Class l)),{_{BOOLEAN}_}:] is non empty set
(BOOLEAN) * (j * (u,(abs (ar S)),l)) is Relation-like (abs (ar S)) -tuples_on (Class l) -defined BOOLEAN -valued Function-like Element of bool [:((abs (ar S)) -tuples_on (Class l)),BOOLEAN:]
[:((abs (ar S)) -tuples_on (Class l)),BOOLEAN:] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on (Class l)),BOOLEAN:] is non empty set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
bool U is non empty set
u is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class u is non empty V165() V166() a_partition of U
S is non empty Element of Class u
l is non empty Element of Class u
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
the U2 of U is Element of the U1 of U
the U3 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
u is Element of OwnSymbolsOf U
u is own Element of OwnSymbolsOf U
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is non relational termal own ofAtomicFormula Element of AllSymbolsOf U
ar S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . 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
(abs (ar S)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
u \/ BOOLEAN is non empty set
l is Relation-like u -defined u -valued Element of bool [:u,u:]
(u,l,(abs (ar S))) is Relation-like (abs (ar S)) -tuples_on u -defined (abs (ar S)) -tuples_on u -valued Element of bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):]
[:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):] is non empty set
(u,u,l,(abs (ar S))) is Relation-like (abs (ar S)) -tuples_on u -defined (abs (ar S)) -tuples_on u -valued Element of bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):]
Seg (abs (ar S)) is finite abs (ar S) -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 S) ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined u -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar S)) -tuples_on u : for b₃ being set holds
( not b₃ in Seg (abs (ar S)) or [(b₁ . b₃),(b₂ . b₃)] in l ) } is set
II is non empty Relation-like (abs (ar S)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of S,u
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
ar S is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . S is set
abs (ar S) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar S)) -tuples_on u is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of u
u \/ BOOLEAN is non empty set
l is Relation-like u -defined u -valued Element of bool [:u,u:]
(u,l,(abs (ar S))) is Relation-like (abs (ar S)) -tuples_on u -defined (abs (ar S)) -tuples_on u -valued Element of bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):]
[:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):] is non empty set
(u,u,l,(abs (ar S))) is Relation-like (abs (ar S)) -tuples_on u -defined (abs (ar S)) -tuples_on u -valued Element of bool [:((abs (ar S)) -tuples_on u),((abs (ar S)) -tuples_on u):]
Seg (abs (ar S)) is non empty finite abs (ar S) -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 S) ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined u -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar S)) -tuples_on u : for b₃ being set holds
( not b₃ in Seg (abs (ar S)) or [(b₁ . b₃),(b₂ . b₃)] in l ) } is set
II is non empty Relation-like (abs (ar S)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of S,u
u is non empty set
S is non empty set
[:u,S:] is non empty Relation-like set
bool [:u,S:] is non empty set
l is Relation-like u -defined S -valued Function-like Element of bool [:u,S:]
U is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u,S,l,U) is Relation-like U -tuples_on u -defined U -tuples_on S -valued Element of bool [:(U -tuples_on u),(U -tuples_on S):]
U -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
U -tuples_on S is non empty functional finite-membered FinSequence-membered FinSequenceSet of S
[:(U -tuples_on u),(U -tuples_on S):] is non empty Relation-like set
bool [:(U -tuples_on u),(U -tuples_on S):] is non empty set
Seg U is finite U -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 <= U ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on u, b₂ is Relation-like NAT -defined S -valued Function-like finite U -element FinSequence-like FinSubsequence-like finite-support Element of U -tuples_on S : for b₃ being set holds
( not b₃ in Seg U or [(b₁ . b₃),(b₂ . b₃)] in l ) } is set
E is Relation-like set
i is set
x is set
[i,x] is non empty set
E is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
E -tuples_on u is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of u
E -tuples_on S is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of S
Seg E is non empty finite E -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 <= E ) } is set
UU is non empty Relation-like NAT -defined u -valued Function-like finite E -element FinSequence-like FinSubsequence-like finite-support Element of E -tuples_on u
III is non empty Relation-like NAT -defined S -valued Function-like finite E -element FinSequence-like FinSubsequence-like finite-support Element of E -tuples_on S
[UU,III] is non empty Element of [:(E -tuples_on u),(E -tuples_on S):]
[:(E -tuples_on u),(E -tuples_on S):] is non empty Relation-like set
O is set
[i,O] is non empty set
X is non empty Relation-like NAT -defined u -valued Function-like finite E -element FinSequence-like FinSubsequence-like finite-support Element of E -tuples_on u
I is non empty Relation-like NAT -defined S -valued Function-like finite E -element FinSequence-like FinSubsequence-like finite-support Element of E -tuples_on S
[X,I] is non empty Element of [:(E -tuples_on u),(E -tuples_on S):]
Funcs ((Seg E),S) is non empty functional FUNCTION_DOMAIN of Seg E,S
j is Relation-like Function-like set
jJ is Element of Seg E
j . jJ is set
III . jJ is set
[(j . jJ),(III . jJ)] is non empty set
I . jJ is set
[(j . jJ),(I . jJ)] is non empty set
Jj is Relation-like Seg E -defined S -valued Function-like total quasi_total finite-support Element of Funcs ((Seg E),S)
Jj . jJ is Element of S
jJ is Relation-like Seg E -defined S -valued Function-like total quasi_total finite-support Element of Funcs ((Seg E),S)
jJ . jJ is Element of S
i is Relation-like set
U is non empty set
u is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
l is Relation-like U -defined u -valued Element of bool [:U,u:]
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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(U,u,l,S) is Relation-like S -tuples_on U -defined S -tuples_on u -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:(S -tuples_on U),(S -tuples_on u):]
S -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
S -tuples_on u is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of u
[:(S -tuples_on U),(S -tuples_on u):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on u):] is non empty set
Seg 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 finite-membered cardinal S -element {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support 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 <= S ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in l ) } is set
id {{}} is non empty Relation-like empty-yielding {{}} -defined {{}} -valued Function-like one-to-one finite total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() finite-support Element of bool [:{{}},{{}}:]
(U,u,l,S) \+\ (id {{}}) is Relation-like set
(U,u,l,S) \ (id {{}}) is Relation-like S -tuples_on U -defined S -tuples_on u -valued set
(U,u,l,S) typed\ (id {{}}) is Relation-like S -tuples_on U -defined S -tuples_on u -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool (U,u,l,S)
bool (U,u,l,S) is non empty set
(U,u,l,S) \ (id {{}}) is Relation-like S -tuples_on U -defined S -tuples_on u -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool (U,u,l,S)
(id {{}}) \ (U,u,l,S) is Relation-like empty-yielding {{}} -defined {{}} -valued finite set
(id {{}}) typed\ (U,u,l,S) is Relation-like empty-yielding {{}} -defined {{}} -valued Function-like finite Function-yielding V164() finite-support Element of bool (id {{}})
bool (id {{}}) is non empty finite finite-membered set
(id {{}}) \ (U,u,l,S) is Relation-like empty-yielding {{}} -defined {{}} -valued Function-like finite Function-yielding V164() finite-support Element of bool (id {{}})
((U,u,l,S) \ (id {{}})) \/ ((id {{}}) \ (U,u,l,S)) is Relation-like set
{[{},{}]} \+\ (id {{}}) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
{[{},{}]} \ (id {{}}) is Relation-like finite set
{[{},{}]} typed\ (id {{}}) is trivial Relation-like Function-like constant finite V165() finite-support Element of bool {[{},{}]}
bool {[{},{}]} is non empty finite finite-membered set
{[{},{}]} \ (id {{}}) is trivial Relation-like Function-like constant finite V165() finite-support Element of bool {[{},{}]}
(id {{}}) \ {[{},{}]} is Relation-like empty-yielding {{}} -defined {{}} -valued finite set
(id {{}}) typed\ {[{},{}]} is Relation-like empty-yielding {{}} -defined {{}} -valued Function-like finite Function-yielding V164() finite-support Element of bool (id {{}})
(id {{}}) \ {[{},{}]} is Relation-like empty-yielding {{}} -defined {{}} -valued Function-like finite Function-yielding V164() finite-support Element of bool (id {{}})
({[{},{}]} \ (id {{}})) \/ ((id {{}}) \ {[{},{}]}) is Relation-like finite set
U is set
u is functional set
U /\ u is set
U typed/\ u is Element of bool U
bool U is non empty set
U /\typed u is functional Element of bool u
bool u is non empty set
U is V51() V53() eligible Language-like
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
u is Relation-like NAT -defined AllTermsOf U -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
U -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf U) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial non finite V166() set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
U is V51() V53() eligible Language-like
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
U is V51() V53() eligible Language-like
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
the U2 of U is Element of the U1 of U
the U3 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
S is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
l is Relation-like Function-like Function-yielding V164() U,u -interpreter-like set
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
i is Relation-like Function-like set
dom i is set
x is own ofAtomicFormula Element of OwnSymbolsOf U
i . x is set
l . x is non empty Relation-like (abs (ar x)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of x,u
ar x is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . x is set
abs (ar x) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar x)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
u \/ BOOLEAN is non empty set
(U,u,x,S,(l . x)) is set
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
i is Relation-like Function-like set
dom i is set
x is Relation-like Function-like set
dom x is set
O is set
i . O is set
x . O is set
UU is own ofAtomicFormula Element of OwnSymbolsOf U
i . UU is set
l . UU is non empty Relation-like (abs (ar UU)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of UU,u
ar UU is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . UU is set
abs (ar UU) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar UU)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
u \/ BOOLEAN is non empty set
(U,u,UU,S,(l . UU)) is set
x . UU is set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
U is V51() V53() eligible Language-like
S is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
l is Relation-like Function-like Function-yielding V164() U,u -interpreter-like set
(U,u,S,l) is Relation-like Function-like set
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
the U2 of U is Element of the U1 of U
the U3 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
AllSymbolsOf U is non empty non trivial non finite V166() set
i is Relation-like Function-like set
dom i is set
x is own ofAtomicFormula Element of AllSymbolsOf U
O is own ofAtomicFormula Element of OwnSymbolsOf U
(U,u,S,l) . O is set
l . O is non empty Relation-like (abs (ar O)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of O,u
ar O is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . O is set
abs (ar O) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar O)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
u \/ BOOLEAN is non empty set
(U,u,O,S,(l . O)) is set
i . x is set
l . x is non empty Relation-like (abs (ar x)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of x,u
ar x is finite complex ext-real V40() V41() Element of INT
the adicity of U . x is set
abs (ar x) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar x)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
(U,u,x,S,(l . x)) is set
x is own ofAtomicFormula Element of AllSymbolsOf U
i . x is set
l . x is non empty Relation-like (abs (ar x)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of x,u
ar x is finite complex ext-real V40() V41() Element of INT
the adicity of U . x is set
abs (ar x) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar x)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
(U,u,x,S,(l . x)) is set
x is own ofAtomicFormula Element of OwnSymbolsOf U
i . x is set
l . x is non empty Relation-like (abs (ar x)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of x,u
ar x is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . x is set
abs (ar x) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar x)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
u \/ BOOLEAN is non empty set
(U,u,x,S,(l . x)) is set
U is V51() V53() eligible Language-like
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
the U2 of U is Element of the U1 of U
the U3 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
l is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
S is Relation-like Function-like Function-yielding V164() U,u -interpreter-like set
(U,u,l,S) is Relation-like Function-like set
dom (U,u,l,S) is set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
U is V51() V53() eligible Language-like
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
the U2 of U is Element of the U1 of U
the U3 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
u * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of u
u \/ BOOLEAN is non empty set
K546((u *),(u \/ BOOLEAN)) is non empty functional M31(u * ,u \/ BOOLEAN)
Funcs ((OwnSymbolsOf U),K546((u *),(u \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U,K546((u *),(u \/ BOOLEAN))
u -InterpretersOf U is non empty functional Element of bool (Funcs ((OwnSymbolsOf U),K546((u *),(u \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf U),K546((u *),(u \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf U -defined K546((u *),(u \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),K546((u *),(u \/ BOOLEAN))) : b₁ is U,u -interpreter-like } is set
S is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
PFuncs ((u *),(u \/ BOOLEAN)) is non empty functional set
i is Relation-like Function-like set
dom i is set
x is set
O is own ofAtomicFormula Element of OwnSymbolsOf U
i . O is set
ar O is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . O is set
abs (ar O) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar O)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
the non empty Relation-like (abs (ar O)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total (U,u,O,S) Interpreter of O,u is non empty Relation-like (abs (ar O)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total (U,u,O,S) Interpreter of O,u
i . x is set
AllSymbolsOf U is non empty non trivial non finite V166() set
x is own ofAtomicFormula Element of AllSymbolsOf U
i . x is set
ar x is finite complex ext-real V40() V41() Element of INT
the adicity of U . x is set
abs (ar x) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar x)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
O is own ofAtomicFormula Element of OwnSymbolsOf U
i . O is set
ar O is finite complex ext-real V40() V41() Element of INT
the adicity of U . O is set
abs (ar O) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar O)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
the non empty Relation-like (abs (ar O)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total (U,u,O,S) Interpreter of O,u is non empty Relation-like (abs (ar O)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total (U,u,O,S) Interpreter of O,u
x is Relation-like Function-like Interpreter of U,u
O is Relation-like Function-like Function-yielding V164() U,u -interpreter-like set
O | (OwnSymbolsOf U) is Relation-like OwnSymbolsOf U -defined OwnSymbolsOf U -defined K546((u *),(u \/ BOOLEAN)) -valued Function-like total Function-yielding V164() U,u -interpreter-like set
UU is Relation-like OwnSymbolsOf U -defined Function-like set
UU | (OwnSymbolsOf U) is Relation-like OwnSymbolsOf U -defined OwnSymbolsOf U -defined Function-like set
UU null (OwnSymbolsOf U) is Relation-like (OwnSymbolsOf U) \/ (dom UU) -defined (OwnSymbolsOf U) \/ (rng UU) -valued Function-like set
dom UU is set
(OwnSymbolsOf U) \/ (dom UU) is non empty set
rng UU is set
(OwnSymbolsOf U) \/ (rng UU) is non empty set
UU \typed/ (OwnSymbolsOf U) is Element of bool (UU \/ (OwnSymbolsOf U))
UU \/ (OwnSymbolsOf U) is non empty set
bool (UU \/ (OwnSymbolsOf U)) is non empty set
dom O is set
rng O is set
Funcs ((OwnSymbolsOf U),(PFuncs ((u *),(u \/ BOOLEAN)))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U, PFuncs ((u *),(u \/ BOOLEAN))
III is Relation-like OwnSymbolsOf U -defined PFuncs ((u *),(u \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),(PFuncs ((u *),(u \/ BOOLEAN))))
X is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U,u -interpreter-like Element of u -InterpretersOf U
I is own ofAtomicFormula Element of AllSymbolsOf U
j is own ofAtomicFormula Element of OwnSymbolsOf U
ar j is finite complex ext-real V40() V41() Element of INT
the adicity of U . j is set
abs (ar j) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar j)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
O . j is non empty Relation-like (abs (ar j)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of j,u
the non empty Relation-like (abs (ar j)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total (U,u,j,S) Interpreter of j,u is non empty Relation-like (abs (ar j)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total (U,u,j,S) Interpreter of j,u
X . I is non empty Relation-like (abs (ar I)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of I,u
ar I is finite complex ext-real V40() V41() Element of INT
the adicity of U . 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 u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
U is V51() V53() eligible Language-like
S is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
the U2 of U is Element of the U1 of U
the U3 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
u * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of u
u \/ BOOLEAN is non empty set
K546((u *),(u \/ BOOLEAN)) is non empty functional M31(u * ,u \/ BOOLEAN)
Funcs ((OwnSymbolsOf U),K546((u *),(u \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U,K546((u *),(u \/ BOOLEAN))
u -InterpretersOf U is non empty functional Element of bool (Funcs ((OwnSymbolsOf U),K546((u *),(u \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf U),K546((u *),(u \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf U -defined K546((u *),(u \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),K546((u *),(u \/ BOOLEAN))) : b₁ is U,u -interpreter-like } is set
the Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U,u -interpreter-like (U,u,S) Element of u -InterpretersOf U is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U,u -interpreter-like (U,u,S) Element of u -InterpretersOf U
l is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U,u -interpreter-like (U,u,S) Element of u -InterpretersOf U
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
S is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
l is own ofAtomicFormula Element of AllSymbolsOf U
ar l is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . l is set
abs (ar l) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar l)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
u \/ BOOLEAN is non empty set
II is Relation-like Function-like Function-yielding V164() U,u -interpreter-like (U,u,S) set
II . l is non empty Relation-like (abs (ar l)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of l,u
E is non empty Relation-like (abs (ar l)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of l,u
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
U is V51() V53() eligible Language-like
S is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
l is Relation-like Function-like Function-yielding V164() U,u -interpreter-like (U,u,S) set
(U,u,S,l) is Relation-like OwnSymbolsOf U -defined Function-like set
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
the U2 of U is Element of the U1 of U
the U3 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
Class S is non empty V165() V166() a_partition of u
(Class S) \/ BOOLEAN is non empty set
i is own ofAtomicFormula Element of OwnSymbolsOf U
(U,u,S,l) . i is set
ar i is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . 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 (Class S) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class S
(abs (ar i)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
u \/ BOOLEAN is non empty set
l . i is non empty Relation-like (abs (ar i)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total (U,u,i,S) Interpreter of i,u
x is non empty Relation-like (abs (ar i)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total (U,u,i,S) Interpreter of i,u
(U,u,i,S,x) is non empty Relation-like (abs (ar i)) -tuples_on (Class S) -defined (Class S) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of i, Class S
dom (U,u,S,l) is Element of bool (OwnSymbolsOf U)
bool (OwnSymbolsOf U) is non empty set
i is set
(U,u,S,l) . i is set
AllSymbolsOf U is non empty non trivial non finite V166() set
i is own ofAtomicFormula Element of AllSymbolsOf U
x is own ofAtomicFormula Element of OwnSymbolsOf U
(U,u,S,l) . x is set
ar x is finite complex ext-real V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . x is set
abs (ar x) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar x)) -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class S
(U,u,S,l) . i is set
ar i is finite complex ext-real V40() V41() Element of INT
the adicity of U . 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 (Class S) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class S
i is Relation-like Function-like set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
U is V51() V53() eligible Language-like
S is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
l is Relation-like Function-like Function-yielding V164() U,u -interpreter-like (U,u,S) set
(U,u,S,l) is Relation-like OwnSymbolsOf U -defined Function-like Function-yielding V164() U, Class S -interpreter-like set
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
the U2 of U is Element of the U1 of U
the U3 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
Class S is non empty V165() V166() a_partition of u
(Class S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of Class S
(Class S) \/ BOOLEAN is non empty set
K546(((Class S) *),((Class S) \/ BOOLEAN)) is non empty functional M31((Class S) * ,(Class S) \/ BOOLEAN)
Funcs ((OwnSymbolsOf U),K546(((Class S) *),((Class S) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U,K546(((Class S) *),((Class S) \/ BOOLEAN))
(Class S) -InterpretersOf U is non empty functional Element of bool (Funcs ((OwnSymbolsOf U),K546(((Class S) *),((Class S) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf U),K546(((Class S) *),((Class S) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf U -defined K546(((Class S) *),((Class S) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),K546(((Class S) *),((Class S) \/ BOOLEAN))) : b₁ is U, Class S -interpreter-like } is set
(U,u,S,l) null (OwnSymbolsOf U) is Relation-like (OwnSymbolsOf U) \/ (dom (U,u,S,l)) -defined (OwnSymbolsOf U) \/ (rng (U,u,S,l)) -valued Function-like set
dom (U,u,S,l) is set
(OwnSymbolsOf U) \/ (dom (U,u,S,l)) is non empty set
rng (U,u,S,l) is set
(OwnSymbolsOf U) \/ (rng (U,u,S,l)) is non empty set
(U,u,S,l) \typed/ (OwnSymbolsOf U) is Element of bool ((U,u,S,l) \/ (OwnSymbolsOf U))
(U,u,S,l) \/ (OwnSymbolsOf U) is non empty set
bool ((U,u,S,l) \/ (OwnSymbolsOf U)) is non empty set
(U,u,S,l) | (OwnSymbolsOf U) is Relation-like OwnSymbolsOf U -defined OwnSymbolsOf U -defined OwnSymbolsOf U -defined K546(((Class S) *),((Class S) \/ BOOLEAN)) -valued Function-like total Function-yielding V164() U, Class S -interpreter-like set
U is non empty set
u is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
S -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
l is Relation-like U -defined u -valued Element of bool [:U,u:]
(U,u,l,S) is Relation-like S -tuples_on U -defined S -tuples_on u -valued Element of bool [:(S -tuples_on U),(S -tuples_on u):]
[:(S -tuples_on U),(S -tuples_on u):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on u):] is non empty set
Seg S is finite S -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 <= S ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in l ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u : b₂ c= b₁ * l } is set
{ H₁(b₁,b₂) where b₁ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u : S₁[b₁,b₂] } is set
{ H₁(b₁,b₂) where b₁ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u : S₂[b₁,b₂] } is set
UU is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U
l (*) UU is Relation-like NAT -defined u -valued set
III is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u
len UU is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
len III is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
dom UU is finite S -element Element of bool NAT
dom III is finite S -element Element of bool NAT
{ [b₁,(UU . b₁)] where b₁ is Element of Seg S : b₁ in Seg S } is set
{ [b₁,(III . b₁)] where b₁ is Element of Seg S : b₁ in Seg S } is set
X is set
I is Element of Seg S
III . I is set
[I,(III . I)] is non empty set
UU . I is set
[(UU . I),(III . I)] is non empty set
[I,(UU . I)] is non empty set
UU * l is Relation-like NAT -defined u -valued Element of bool [:NAT,u:]
[:NAT,u:] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,u:] is non empty non trivial non finite V166() set
X is set
I is Element of Seg S
III . I is set
[I,(III . I)] is non empty set
j is set
[I,j] is non empty set
[j,(III . I)] is non empty set
UU . X is set
III . X is set
[(UU . X),(III . X)] is non empty set
X is set
UU . X is set
III . X is set
[(UU . X),(III . X)] is non empty set
U is non empty set
bool U is non empty set
u is non empty set
S is non empty set
[:U,S:] is non empty Relation-like set
bool [:U,S:] is non empty set
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
l -tuples_on S is non empty functional finite-membered FinSequence-membered FinSequenceSet of S
l -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
II is non empty Element of bool U
[:u,II:] is non empty Relation-like set
bool [:u,II:] is non empty set
l -tuples_on II is non empty functional finite-membered FinSequence-membered FinSequenceSet of II
E is Relation-like u -defined II -valued Element of bool [:u,II:]
(u,II,E,l) is Relation-like l -tuples_on u -defined l -tuples_on II -valued Element of bool [:(l -tuples_on u),(l -tuples_on II):]
[:(l -tuples_on u),(l -tuples_on II):] is non empty Relation-like set
bool [:(l -tuples_on u),(l -tuples_on II):] is non empty set
Seg l is finite l -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 <= l ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u, b₂ is Relation-like NAT -defined II -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on II : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in E ) } is set
i is Relation-like U -defined S -valued Element of bool [:U,S:]
(U,S,i,l) is Relation-like l -tuples_on U -defined l -tuples_on S -valued Element of bool [:(l -tuples_on U),(l -tuples_on S):]
[:(l -tuples_on U),(l -tuples_on S):] is non empty Relation-like set
bool [:(l -tuples_on U),(l -tuples_on S):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U, b₂ is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in i ) } is set
(u,II,E,l) * (U,S,i,l) is Relation-like l -tuples_on u -defined l -tuples_on S -valued Element of bool [:(l -tuples_on u),(l -tuples_on S):]
[:(l -tuples_on u),(l -tuples_on S):] is non empty Relation-like set
bool [:(l -tuples_on u),(l -tuples_on S):] is non empty set
E * i is Relation-like u -defined S -valued Element of bool [:u,S:]
[:u,S:] is non empty Relation-like set
bool [:u,S:] is non empty set
(u,S,(E * i),l) is Relation-like l -tuples_on u -defined l -tuples_on S -valued Element of bool [:(l -tuples_on u),(l -tuples_on S):]
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u, b₂ is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in E * i ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u, b₂ is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S : b₂ c= b₁ * (E * i) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u, b₂ is Relation-like NAT -defined II -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on II : b₂ c= b₁ * E } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U, b₂ is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S : b₂ c= b₁ * i } is set
jJ is set
g is set
h is set
[g,h] is non empty set
G is set
[g,G] is non empty set
[G,h] is non empty set
n is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u
Enn is Relation-like NAT -defined II -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on II
[n,Enn] is non empty Element of [:(l -tuples_on u),(l -tuples_on II):]
n * E is Relation-like NAT -defined II -valued Element of bool [:NAT,II:]
[:NAT,II:] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,II:] is non empty non trivial non finite V166() set
En is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U
nE is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S
[En,nE] is non empty Element of [:(l -tuples_on U),(l -tuples_on S):]
En * i is Relation-like NAT -defined S -valued Element of bool [:NAT,S:]
[:NAT,S:] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,S:] is non empty non trivial non finite V166() set
Enn * i is Relation-like NAT -defined S -valued Element of bool [:NAT,S:]
(n * E) * i is Relation-like NAT -defined S -valued Element of bool [:NAT,S:]
[n,nE] is non empty Element of [:(l -tuples_on u),(l -tuples_on S):]
n * (E * i) is Relation-like NAT -defined S -valued Element of bool [:NAT,S:]
U is non empty set
bool U is non empty set
u is non empty set
S is non empty set
[:U,S:] is non empty Relation-like set
bool [:U,S:] is non empty set
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
l -tuples_on S is non empty functional finite-membered FinSequence-membered FinSequenceSet of S
l -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
II is non empty Element of bool U
[:u,II:] is non empty Relation-like set
bool [:u,II:] is non empty set
l -tuples_on II is non empty functional finite-membered FinSequence-membered FinSequenceSet of II
E is Relation-like u -defined II -valued Element of bool [:u,II:]
(u,II,E,l) is Relation-like l -tuples_on u -defined l -tuples_on II -valued Element of bool [:(l -tuples_on u),(l -tuples_on II):]
[:(l -tuples_on u),(l -tuples_on II):] is non empty Relation-like set
bool [:(l -tuples_on u),(l -tuples_on II):] is non empty set
Seg l is finite l -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 <= l ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u, b₂ is Relation-like NAT -defined II -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on II : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in E ) } is set
i is Relation-like U -defined S -valued Element of bool [:U,S:]
E * i is Relation-like u -defined S -valued Element of bool [:u,S:]
[:u,S:] is non empty Relation-like set
bool [:u,S:] is non empty set
(u,S,(E * i),l) is Relation-like l -tuples_on u -defined l -tuples_on S -valued Element of bool [:(l -tuples_on u),(l -tuples_on S):]
[:(l -tuples_on u),(l -tuples_on S):] is non empty Relation-like set
bool [:(l -tuples_on u),(l -tuples_on S):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u, b₂ is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in E * i ) } is set
(U,S,i,l) is Relation-like l -tuples_on U -defined l -tuples_on S -valued Element of bool [:(l -tuples_on U),(l -tuples_on S):]
[:(l -tuples_on U),(l -tuples_on S):] is non empty Relation-like set
bool [:(l -tuples_on U),(l -tuples_on S):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U, b₂ is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in i ) } is set
(u,II,E,l) * (U,S,i,l) is Relation-like l -tuples_on u -defined l -tuples_on S -valued Element of bool [:(l -tuples_on u),(l -tuples_on S):]
g is set
h is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u
G is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S
[h,G] is non empty Element of [:(l -tuples_on u),(l -tuples_on S):]
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
h . n is set
G . n is set
[(h . n),(G . n)] is non empty set
Enn is set
[(h . n),Enn] is non empty set
[Enn,(G . n)] is non empty set
rng E is Element of bool II
bool II is non empty set
En is Element of II
[(h . n),En] is non empty set
[En,(G . n)] is non empty set
n is Relation-like NAT -defined II -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of II
dom n is finite Element of bool NAT
len n is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
jJ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
Enn is Relation-like NAT -defined II -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support FinSequence of II
En is Relation-like NAT -defined II -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on II
[h,En] is non empty Element of [:(l -tuples_on u),(l -tuples_on II):]
hh is set
h . hh is set
En . hh is set
[(h . hh),(En . hh)] is non empty set
nE is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U
[nE,G] is non empty Element of [:(l -tuples_on U),(l -tuples_on S):]
hh is set
nE . hh is set
G . hh is set
[(nE . hh),(G . hh)] is non empty set
U is non empty set
bool U is non empty set
u is non empty set
S is non empty set
[:U,S:] is non empty Relation-like set
bool [:U,S:] is non empty set
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
l -tuples_on S is non empty functional finite-membered FinSequence-membered FinSequenceSet of S
l -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
II is non empty Element of bool U
[:u,II:] is non empty Relation-like set
bool [:u,II:] is non empty set
l -tuples_on II is non empty functional finite-membered FinSequence-membered FinSequenceSet of II
E is Relation-like u -defined II -valued Element of bool [:u,II:]
(u,II,E,l) is Relation-like l -tuples_on u -defined l -tuples_on II -valued Element of bool [:(l -tuples_on u),(l -tuples_on II):]
[:(l -tuples_on u),(l -tuples_on II):] is non empty Relation-like set
bool [:(l -tuples_on u),(l -tuples_on II):] is non empty set
Seg l is finite l -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 <= l ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u, b₂ is Relation-like NAT -defined II -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on II : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in E ) } is set
i is Relation-like U -defined S -valued Element of bool [:U,S:]
E * i is Relation-like u -defined S -valued Element of bool [:u,S:]
[:u,S:] is non empty Relation-like set
bool [:u,S:] is non empty set
(u,S,(E * i),l) is Relation-like l -tuples_on u -defined l -tuples_on S -valued Element of bool [:(l -tuples_on u),(l -tuples_on S):]
[:(l -tuples_on u),(l -tuples_on S):] is non empty Relation-like set
bool [:(l -tuples_on u),(l -tuples_on S):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u, b₂ is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in E * i ) } is set
(U,S,i,l) is Relation-like l -tuples_on U -defined l -tuples_on S -valued Element of bool [:(l -tuples_on U),(l -tuples_on S):]
[:(l -tuples_on U),(l -tuples_on S):] is non empty Relation-like set
bool [:(l -tuples_on U),(l -tuples_on S):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U, b₂ is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in i ) } is set
(u,II,E,l) * (U,S,i,l) is Relation-like l -tuples_on u -defined l -tuples_on S -valued Element of bool [:(l -tuples_on u),(l -tuples_on S):]
U is non empty set
u is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
S is non empty set
[:u,S:] is non empty Relation-like set
bool [:u,S:] is non empty set
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
l -tuples_on S is non empty functional finite-membered FinSequence-membered FinSequenceSet of S
l -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
bool u is non empty set
u /\ u is set
u typed/\ u is Element of bool u
u /\typed u is Element of bool u
E is Relation-like U -defined u -valued Element of bool [:U,u:]
(U,u,E,l) is Relation-like l -tuples_on U -defined l -tuples_on u -valued Element of bool [:(l -tuples_on U),(l -tuples_on u):]
[:(l -tuples_on U),(l -tuples_on u):] is non empty Relation-like set
bool [:(l -tuples_on U),(l -tuples_on u):] is non empty set
Seg l is finite l -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 <= l ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in E ) } is set
i is Relation-like u -defined S -valued Element of bool [:u,S:]
E * i is Relation-like U -defined S -valued Element of bool [:U,S:]
[:U,S:] is non empty Relation-like set
bool [:U,S:] is non empty set
(U,S,(E * i),l) is Relation-like l -tuples_on U -defined l -tuples_on S -valued Element of bool [:(l -tuples_on U),(l -tuples_on S):]
[:(l -tuples_on U),(l -tuples_on S):] is non empty Relation-like set
bool [:(l -tuples_on U),(l -tuples_on S):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U, b₂ is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in E * i ) } is set
(u,S,i,l) is Relation-like l -tuples_on u -defined l -tuples_on S -valued Element of bool [:(l -tuples_on u),(l -tuples_on S):]
[:(l -tuples_on u),(l -tuples_on S):] is non empty Relation-like set
bool [:(l -tuples_on u),(l -tuples_on S):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on u, b₂ is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in i ) } is set
(U,u,E,l) * (u,S,i,l) is Relation-like l -tuples_on U -defined l -tuples_on S -valued Element of bool [:(l -tuples_on U),(l -tuples_on S):]
II is non empty Element of bool u
[:U,II:] is non empty Relation-like set
bool [:U,II:] is non empty set
x is Relation-like U -defined II -valued Element of bool [:U,II:]
x * i is Relation-like U -defined S -valued Element of bool [:U,S:]
(U,S,(x * i),l) is Relation-like l -tuples_on U -defined l -tuples_on S -valued Element of bool [:(l -tuples_on U),(l -tuples_on S):]
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U, b₂ is Relation-like NAT -defined S -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on S : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in x * i ) } is set
l -tuples_on II is non empty functional finite-membered FinSequence-membered FinSequenceSet of II
(U,II,x,l) is Relation-like l -tuples_on U -defined l -tuples_on II -valued Element of bool [:(l -tuples_on U),(l -tuples_on II):]
[:(l -tuples_on U),(l -tuples_on II):] is non empty Relation-like set
bool [:(l -tuples_on U),(l -tuples_on II):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on U, b₂ is Relation-like NAT -defined II -valued Function-like finite l -element FinSequence-like FinSubsequence-like finite-support Element of l -tuples_on II : for b₃ being set holds
( not b₃ in Seg l or [(b₁ . b₃),(b₂ . b₃)] in x ) } is set
(U,II,x,l) * (u,S,i,l) is Relation-like l -tuples_on U -defined l -tuples_on S -valued Element of bool [:(l -tuples_on U),(l -tuples_on S):]
U is non empty set
u is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
S -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
l is Relation-like U -defined u -valued Element of bool [:U,u:]
l ~ is Relation-like u -defined U -valued Element of bool [:u,U:]
[:u,U:] is non empty Relation-like set
bool [:u,U:] is non empty set
(u,U,(l ~),S) is Relation-like S -tuples_on u -defined S -tuples_on U -valued Element of bool [:(S -tuples_on u),(S -tuples_on U):]
[:(S -tuples_on u),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on u),(S -tuples_on U):] is non empty set
Seg S is finite S -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 <= S ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u, b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in l ~ ) } is set
(U,u,l,S) is Relation-like S -tuples_on U -defined S -tuples_on u -valued Element of bool [:(S -tuples_on U),(S -tuples_on u):]
[:(S -tuples_on U),(S -tuples_on u):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on u):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in l ) } is set
(U,u,l,S) ~ is Relation-like S -tuples_on u -defined S -tuples_on U -valued Element of bool [:(S -tuples_on u),(S -tuples_on U):]
{ [b₂,b₁] where b₁ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in l ) } is set
x is Relation-like u -defined U -valued Element of bool [:u,U:]
(u,U,x,S) is Relation-like S -tuples_on u -defined S -tuples_on U -valued Element of bool [:(S -tuples_on u),(S -tuples_on U):]
{ [b₁,b₂] where b₁ is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u, b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in x ) } is set
O is Relation-like S -tuples_on U -defined S -tuples_on u -valued Element of bool [:(S -tuples_on U),(S -tuples_on u):]
O ~ is Relation-like S -tuples_on u -defined S -tuples_on U -valued Element of bool [:(S -tuples_on u),(S -tuples_on U):]
X is set
UU is Relation-like S -tuples_on u -defined S -tuples_on U -valued Element of bool [:(S -tuples_on u),(S -tuples_on U):]
I is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u
j is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U
[I,j] is non empty Element of [:(S -tuples_on u),(S -tuples_on U):]
Jj is set
j . Jj is set
I . Jj is set
[(j . Jj),(I . Jj)] is non empty set
[(I . Jj),(j . Jj)] is non empty set
[j,I] is non empty Element of [:(S -tuples_on U),(S -tuples_on u):]
III is Relation-like S -tuples_on u -defined S -tuples_on U -valued Element of bool [:(S -tuples_on u),(S -tuples_on U):]
X is set
III ~ is Relation-like S -tuples_on U -defined S -tuples_on u -valued Element of bool [:(S -tuples_on U),(S -tuples_on u):]
I is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U
j is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u
[I,j] is non empty Element of [:(S -tuples_on U),(S -tuples_on u):]
Jj is set
j . Jj is set
I . Jj is set
[(j . Jj),(I . Jj)] is non empty set
[(I . Jj),(j . Jj)] is non empty set
[j,I] is non empty Element of [:(S -tuples_on u),(S -tuples_on U):]
UU ~ is Relation-like S -tuples_on U -defined S -tuples_on u -valued Element of bool [:(S -tuples_on U),(S -tuples_on u):]
(III ~) \ (UU ~) is Relation-like S -tuples_on U -defined S -tuples_on u -valued Element of bool [:(S -tuples_on U),(S -tuples_on u):]
(III ~) typed\ (UU ~) is Relation-like S -tuples_on U -defined S -tuples_on u -valued Element of bool (III ~)
bool (III ~) is non empty set
(III ~) \ (UU ~) is Relation-like S -tuples_on U -defined S -tuples_on u -valued Element of bool (III ~)
III \ UU is Relation-like S -tuples_on u -defined S -tuples_on U -valued Element of bool [:(S -tuples_on u),(S -tuples_on U):]
III typed\ UU is Relation-like S -tuples_on u -defined S -tuples_on U -valued Element of bool III
bool III is non empty set
III \ UU is Relation-like S -tuples_on u -defined S -tuples_on U -valued Element of bool III
(III \ UU) ~ is Relation-like S -tuples_on U -defined S -tuples_on u -valued Element of bool [:(S -tuples_on U),(S -tuples_on u):]
((III \ UU) ~) ~ is Relation-like S -tuples_on u -defined S -tuples_on U -valued Element of bool [:(S -tuples_on u),(S -tuples_on U):]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class S is non empty V165() V166() a_partition of U
(U,S) is non empty Relation-like non empty-yielding U -defined Class S -valued Function-like total quasi_total onto Element of bool [:U,(Class S):]
[:U,(Class S):] is non empty Relation-like set
bool [:U,(Class S):] is non empty set
l is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
Class l is non empty V165() V166() a_partition of u
(u,l) is non empty Relation-like non empty-yielding u -defined Class l -valued Function-like total quasi_total onto Element of bool [:u,(Class l):]
[:u,(Class l):] is non empty Relation-like set
bool [:u,(Class l):] is non empty set
II is non empty Relation-like U -defined u -valued Function-like total quasi_total (S,l) Element of bool [:U,u:]
(u,l) * II is non empty Relation-like non empty-yielding U -defined Class l -valued Function-like total quasi_total Element of bool [:U,(Class l):]
[:U,(Class l):] is non empty Relation-like set
bool [:U,(Class l):] is non empty set
(U,u,S,l,II) is non empty Relation-like non empty-yielding Class S -defined Class l -valued Function-like total quasi_total Element of bool [:(Class S),(Class l):]
[:(Class S),(Class l):] is non empty Relation-like set
bool [:(Class S),(Class l):] is non empty set
bool U is non empty set
bool u is non empty set
{ [b₁,b₂] where b₁ is non empty Element of Class S, b₂ is non empty Element of Class l : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in II ) } is set
(U,u,S,l,II) * (U,S) is non empty Relation-like non empty-yielding U -defined Class l -valued Function-like total quasi_total Element of bool [:U,(Class l):]
dom (U,u,S,l,II) is non empty V165() V166() Element of bool (Class S)
bool (Class S) is non empty set
i is non empty Relation-like non empty-yielding U -defined Class l -valued Function-like total quasi_total Element of bool [:U,(Class l):]
dom i is non empty Element of bool U
x is non empty Relation-like non empty-yielding U -defined Class l -valued Function-like total quasi_total Element of bool [:U,(Class l):]
dom x is non empty Element of bool U
O is Element of U
i . O is non empty Element of Class l
x . O is non empty Element of Class l
UU is non empty Element of Class l
II . O is Element of u
(u,l) . (II . O) is non empty Element of Class l
III is non empty Element of Class l
(U,S) . O is non empty Element of Class S
(U,u,S,l,II) . ((U,S) . O) is non empty Element of Class l
EqClass (S,O) is non empty Element of Class S
{O} is non empty trivial finite 1 -element set
S .: {O} is set
(U,u,S,l,II) . (EqClass (S,O)) is non empty Element of Class l
[(EqClass (S,O)),III] is non empty Element of [:(Class S),(Class l):]
X is non empty Element of Class S
I is non empty Element of Class l
[X,I] is non empty Element of [:(Class S),(Class l):]
j is set
Jj is set
[j,Jj] is non empty set
j is set
Jj is set
[j,Jj] is non empty set
jJ is set
jJ is set
[jJ,jJ] is non empty set
[j,O] is non empty set
dom II is non empty Element of bool U
II . j is set
[Jj,(II . O)] is non empty set
EqClass (l,(II . O)) is non empty Element of Class l
{(II . O)} is non empty trivial finite 1 -element set
l .: {(II . O)} is set
U is non empty set
u is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support set
II is non empty Relation-like U -defined u -valued Function-like total quasi_total Element of bool [:U,u:]
II (*) l is Relation-like NAT -defined u -valued Function-like finite S -element len l -element FinSequence-like FinSubsequence-like finite-support set
len l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(U,u,II,S) is non empty Relation-like S -tuples_on U -defined S -tuples_on u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(S -tuples_on U),(S -tuples_on u):]
S -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
S -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
[:(S -tuples_on U),(S -tuples_on u):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on u):] is non empty set
Seg S is finite S -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 <= S ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in II ) } is set
(U,u,II,S) . l is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom II is non empty Element of bool U
bool U is non empty set
dom (U,u,II,S) is non empty functional finite-membered FinSequence-membered Element of bool (S -tuples_on U)
bool (S -tuples_on U) is non empty set
i is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U
Funcs ((Seg S),U) is non empty functional FUNCTION_DOMAIN of Seg S,U
[:(Seg S),U:] is Relation-like set
bool [:(Seg S),U:] is non empty set
Funcs ((Seg S),u) is non empty functional FUNCTION_DOMAIN of Seg S,u
(U,u,II,S) . i is Relation-like NAT -defined Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u
[:(Seg S),u:] is Relation-like set
bool [:(Seg S),u:] is non empty set
O is Relation-like Seg S -defined u -valued Function-like total quasi_total finite-support Element of Funcs ((Seg S),u)
UU is Relation-like Seg S -defined u -valued Function-like total quasi_total finite-support Element of Funcs ((Seg S),u)
x is Relation-like Seg S -defined U -valued Function-like finite total quasi_total finite-support Element of bool [:(Seg S),U:]
dom x is finite Element of bool (Seg S)
bool (Seg S) is non empty finite finite-membered set
rng x is finite set
dom O is finite Element of bool (Seg S)
[l,O] is non empty set
I is Relation-like NAT -defined u -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on u
Jj is set
i . Jj is set
I . Jj is set
[(i . Jj),(I . Jj)] is non empty set
O . Jj is set
l . Jj is set
II . (l . Jj) is set
x . Jj is set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
(U,S,u) is Relation-like u -tuples_on U -defined u -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:(u -tuples_on U),(u -tuples_on U):]
[:(u -tuples_on U),(u -tuples_on U):] is non empty Relation-like set
bool [:(u -tuples_on U),(u -tuples_on U):] is non empty set
(U,U,S,u) is Relation-like u -tuples_on U -defined u -tuples_on U -valued total quasi_total Element of bool [:(u -tuples_on U),(u -tuples_on U):]
Seg u is finite u -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 <= u ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
Class (U,S,u) is non empty V165() V166() a_partition of u -tuples_on U
((u -tuples_on U),(U,S,u)) is non empty Relation-like non empty-yielding u -tuples_on U -defined Class (U,S,u) -valued Function-like total quasi_total onto Element of bool [:(u -tuples_on U),(Class (U,S,u)):]
[:(u -tuples_on U),(Class (U,S,u)):] is non empty Relation-like set
bool [:(u -tuples_on U),(Class (U,S,u)):] is non empty set
Class S is non empty V165() V166() a_partition of U
u -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class S
(U,S) is non empty Relation-like non empty-yielding U -defined Class S -valued Function-like total quasi_total onto Element of bool [:U,(Class S):]
[:U,(Class S):] is non empty Relation-like set
bool [:U,(Class S):] is non empty set
(U,(Class S),(U,S),u) is non empty Relation-like u -tuples_on U -defined u -tuples_on (Class S) -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(u -tuples_on U),(u -tuples_on (Class S)):]
[:(u -tuples_on U),(u -tuples_on (Class S)):] is non empty Relation-like set
bool [:(u -tuples_on U),(u -tuples_on (Class S)):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U, b₂ is Relation-like NAT -defined Class S -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on (Class S) : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in (U,S) ) } is set
(U,u,S) is non empty Relation-like non empty-yielding u -tuples_on (Class S) -defined Class (U,S,u) -valued Function-like total quasi_total Element of bool [:(u -tuples_on (Class S)),(Class (U,S,u)):]
[:(u -tuples_on (Class S)),(Class (U,S,u)):] is non empty Relation-like set
bool [:(u -tuples_on (Class S)),(Class (U,S,u)):] is non empty set
(U,S) ~ is Relation-like Class S -defined U -valued total quasi_total Element of bool [:(Class S),U:]
[:(Class S),U:] is non empty Relation-like set
bool [:(Class S),U:] is non empty set
((Class S),U,((U,S) ~),u) is Relation-like u -tuples_on (Class S) -defined u -tuples_on U -valued total quasi_total Element of bool [:(u -tuples_on (Class S)),(u -tuples_on U):]
[:(u -tuples_on (Class S)),(u -tuples_on U):] is non empty Relation-like set
bool [:(u -tuples_on (Class S)),(u -tuples_on U):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class S -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on (Class S), b₂ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in (U,S) ~ ) } is set
((Class S),U,((U,S) ~),u) * ((u -tuples_on U),(U,S,u)) is Relation-like u -tuples_on (Class S) -defined Class (U,S,u) -valued total quasi_total Element of bool [:(u -tuples_on (Class S)),(Class (U,S,u)):]
(U,u,S) * (U,(Class S),(U,S),u) is non empty Relation-like non empty-yielding u -tuples_on U -defined Class (U,S,u) -valued Function-like total quasi_total Element of bool [:(u -tuples_on U),(Class (U,S,u)):]
O is Relation-like U -defined Class S -valued Element of bool [:U,(Class S):]
O ~ is Relation-like Class S -defined U -valued Element of bool [:(Class S),U:]
((Class S),U,(O ~),u) is Relation-like u -tuples_on (Class S) -defined u -tuples_on U -valued Element of bool [:(u -tuples_on (Class S)),(u -tuples_on U):]
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class S -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on (Class S), b₂ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in O ~ ) } is set
(U,(Class S),O,u) is Relation-like u -tuples_on U -defined u -tuples_on (Class S) -valued Element of bool [:(u -tuples_on U),(u -tuples_on (Class S)):]
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on U, b₂ is Relation-like NAT -defined Class S -valued Function-like finite u -element FinSequence-like FinSubsequence-like finite-support Element of u -tuples_on (Class S) : for b₃ being set holds
( not b₃ in Seg u or [(b₁ . b₃),(b₂ . b₃)] in O ) } is set
(U,(Class S),O,u) ~ is Relation-like u -tuples_on (Class S) -defined u -tuples_on U -valued Element of bool [:(u -tuples_on (Class S)),(u -tuples_on U):]
dom ((u -tuples_on U),(U,S,u)) is non empty functional finite-membered FinSequence-membered Element of bool (u -tuples_on U)
bool (u -tuples_on U) is non empty set
dom ((U,u,S) * (U,(Class S),(U,S),u)) is non empty functional finite-membered FinSequence-membered Element of bool (u -tuples_on U)
x is Relation-like u -tuples_on U -defined u -tuples_on (Class S) -valued Element of bool [:(u -tuples_on U),(u -tuples_on (Class S)):]
UU is Relation-like u -tuples_on (Class S) -defined u -tuples_on U -valued Element of bool [:(u -tuples_on (Class S)),(u -tuples_on U):]
x * UU is Relation-like u -tuples_on U -defined u -tuples_on U -valued Element of bool [:(u -tuples_on U),(u -tuples_on U):]
(x * UU) * ((u -tuples_on U),(U,S,u)) is Relation-like u -tuples_on U -defined Class (U,S,u) -valued Element of bool [:(u -tuples_on U),(Class (U,S,u)):]
III is Relation-like u -tuples_on (Class S) -defined u -tuples_on U -valued Element of bool [:(u -tuples_on (Class S)),(u -tuples_on U):]
x * III is Relation-like u -tuples_on U -defined u -tuples_on U -valued Element of bool [:(u -tuples_on U),(u -tuples_on U):]
(x * III) * ((u -tuples_on U),(U,S,u)) is Relation-like u -tuples_on U -defined Class (U,S,u) -valued Element of bool [:(u -tuples_on U),(Class (U,S,u)):]
id (u -tuples_on U) is non empty Relation-like u -tuples_on U -defined u -tuples_on U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(u -tuples_on U),(u -tuples_on U):]
((u -tuples_on U),(U,S,u)) (*) (id (u -tuples_on U)) is Relation-like u -tuples_on U -defined Class (U,S,u) -valued Function-like total set
((u -tuples_on U),(U,S,u)) | (u -tuples_on U) is Relation-like u -tuples_on U -defined u -tuples_on U -defined Class (U,S,u) -valued Function-like Element of bool [:(u -tuples_on U),(Class (U,S,u)):]
((u -tuples_on U),(U,S,u)) null (u -tuples_on U) is Relation-like (u -tuples_on U) \/ (dom ((u -tuples_on U),(U,S,u))) -defined (u -tuples_on U) \/ (rng ((u -tuples_on U),(U,S,u))) -valued Function-like set
dom ((u -tuples_on U),(U,S,u)) is non empty set
(u -tuples_on U) \/ (dom ((u -tuples_on U),(U,S,u))) is non empty set
rng ((u -tuples_on U),(U,S,u)) is non empty set
(u -tuples_on U) \/ (rng ((u -tuples_on U),(U,S,u))) is non empty set
((u -tuples_on U),(U,S,u)) \typed/ (u -tuples_on U) is Element of bool (((u -tuples_on U),(U,S,u)) \/ (u -tuples_on U))
((u -tuples_on U),(U,S,u)) \/ (u -tuples_on U) is non empty set
bool (((u -tuples_on U),(U,S,u)) \/ (u -tuples_on U)) is non empty set
((u -tuples_on U),(U,S,u)) | (u -tuples_on U) is Relation-like u -tuples_on U -defined u -tuples_on U -defined Class (U,S,u) -valued Function-like set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
[:(S -tuples_on U),u:] is non empty Relation-like set
bool [:(S -tuples_on U),u:] is non empty set
E is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
(U,E,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:(S -tuples_on U),(S -tuples_on U):]
[:(S -tuples_on U),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on U),(S -tuples_on U):] is non empty set
(U,U,E,S) is Relation-like S -tuples_on U -defined S -tuples_on U -valued total quasi_total Element of bool [:(S -tuples_on U),(S -tuples_on U):]
Seg S is finite S -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 <= S ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in E ) } is set
Class E is non empty V165() V166() a_partition of U
S -tuples_on (Class E) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class E
Class (U,E,S) is non empty V165() V166() a_partition of S -tuples_on U
(U,S,E) is non empty Relation-like non empty-yielding S -tuples_on (Class E) -defined Class (U,E,S) -valued Function-like total quasi_total Element of bool [:(S -tuples_on (Class E)),(Class (U,E,S)):]
[:(S -tuples_on (Class E)),(Class (U,E,S)):] is non empty Relation-like set
bool [:(S -tuples_on (Class E)),(Class (U,E,S)):] is non empty set
(U,E) is non empty Relation-like non empty-yielding U -defined Class E -valued Function-like total quasi_total onto Element of bool [:U,(Class E):]
[:U,(Class E):] is non empty Relation-like set
bool [:U,(Class E):] is non empty set
(U,E) ~ is Relation-like Class E -defined U -valued total quasi_total Element of bool [:(Class E),U:]
[:(Class E),U:] is non empty Relation-like set
bool [:(Class E),U:] is non empty set
((Class E),U,((U,E) ~),S) is Relation-like S -tuples_on (Class E) -defined S -tuples_on U -valued total quasi_total Element of bool [:(S -tuples_on (Class E)),(S -tuples_on U):]
[:(S -tuples_on (Class E)),(S -tuples_on U):] is non empty Relation-like set
bool [:(S -tuples_on (Class E)),(S -tuples_on U):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class E -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on (Class E), b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in (U,E) ~ ) } is set
((S -tuples_on U),(U,E,S)) is non empty Relation-like non empty-yielding S -tuples_on U -defined Class (U,E,S) -valued Function-like total quasi_total onto Element of bool [:(S -tuples_on U),(Class (U,E,S)):]
[:(S -tuples_on U),(Class (U,E,S)):] is non empty Relation-like set
bool [:(S -tuples_on U),(Class (U,E,S)):] is non empty set
((Class E),U,((U,E) ~),S) * ((S -tuples_on U),(U,E,S)) is Relation-like S -tuples_on (Class E) -defined Class (U,E,S) -valued total quasi_total Element of bool [:(S -tuples_on (Class E)),(Class (U,E,S)):]
i is Relation-like u -defined u -valued total quasi_total reflexive symmetric transitive Element of bool [:u,u:]
Class i is non empty V165() V166() a_partition of u
(u,i) is non empty Relation-like non empty-yielding u -defined Class i -valued Function-like total quasi_total onto Element of bool [:u,(Class i):]
[:u,(Class i):] is non empty Relation-like set
bool [:u,(Class i):] is non empty set
x is non empty Relation-like S -tuples_on U -defined u -valued Function-like total quasi_total ((U,E,S),i) Element of bool [:(S -tuples_on U),u:]
((S -tuples_on U),u,(U,E,S),i,x) is non empty Relation-like non empty-yielding Class (U,E,S) -defined Class i -valued Function-like total quasi_total Element of bool [:(Class (U,E,S)),(Class i):]
[:(Class (U,E,S)),(Class i):] is non empty Relation-like set
bool [:(Class (U,E,S)),(Class i):] is non empty set
bool (S -tuples_on U) is non empty set
bool u is non empty set
{ [b₁,b₂] where b₁ is non empty Element of Class (U,E,S), b₂ is non empty Element of Class i : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in x ) } is set
((S -tuples_on U),u,(U,E,S),i,x) * (U,S,E) is non empty Relation-like non empty-yielding S -tuples_on (Class E) -defined Class i -valued Function-like total quasi_total Element of bool [:(S -tuples_on (Class E)),(Class i):]
[:(S -tuples_on (Class E)),(Class i):] is non empty Relation-like set
bool [:(S -tuples_on (Class E)),(Class i):] is non empty set
(u,i) * x is non empty Relation-like non empty-yielding S -tuples_on U -defined Class i -valued Function-like total quasi_total Element of bool [:(S -tuples_on U),(Class i):]
[:(S -tuples_on U),(Class i):] is non empty Relation-like set
bool [:(S -tuples_on U),(Class i):] is non empty set
((Class E),U,((U,E) ~),S) * ((u,i) * x) is Relation-like S -tuples_on (Class E) -defined Class i -valued total quasi_total Element of bool [:(S -tuples_on (Class E)),(Class i):]
O is non empty Relation-like non empty-yielding Class (U,E,S) -defined Class i -valued Function-like total quasi_total Element of bool [:(Class (U,E,S)),(Class i):]
O * (U,S,E) is non empty Relation-like non empty-yielding S -tuples_on (Class E) -defined Class i -valued Function-like total quasi_total Element of bool [:(S -tuples_on (Class E)),(Class i):]
III is Relation-like U -defined Class E -valued Element of bool [:U,(Class E):]
III ~ is Relation-like Class E -defined U -valued Element of bool [:(Class E),U:]
((Class E),U,(III ~),S) is Relation-like S -tuples_on (Class E) -defined S -tuples_on U -valued Element of bool [:(S -tuples_on (Class E)),(S -tuples_on U):]
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class E -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on (Class E), b₂ is Relation-like NAT -defined U -valued Function-like finite S -element FinSequence-like FinSubsequence-like finite-support Element of S -tuples_on U : for b₃ being set holds
( not b₃ in Seg S or [(b₁ . b₃),(b₂ . b₃)] in III ~ ) } is set
UU is Relation-like Class (U,E,S) -defined Class i -valued Element of bool [:(Class (U,E,S)),(Class i):]
((S -tuples_on U),(U,E,S)) * UU is Relation-like S -tuples_on U -defined Class i -valued Element of bool [:(S -tuples_on U),(Class i):]
((Class E),U,(III ~),S) * (((S -tuples_on U),(U,E,S)) * UU) is Relation-like S -tuples_on (Class E) -defined Class i -valued Element of bool [:(S -tuples_on (Class E)),(Class i):]
((Class E),U,(III ~),S) * ((u,i) * x) is Relation-like S -tuples_on (Class E) -defined Class i -valued Element of bool [:(S -tuples_on (Class E)),(Class i):]
U is set
{U} is non empty trivial finite 1 -element set
id {U} is non empty Relation-like {U} -defined {U} -valued Function-like one-to-one finite total quasi_total onto bijective reflexive symmetric antisymmetric transitive finite-support Element of bool [:{U},{U}:]
[:{U},{U}:] is non empty Relation-like finite set
bool [:{U},{U}:] is non empty finite finite-membered set
u is non empty set
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
S is Relation-like Function-like set
dom S is set
l is Relation-like u -defined u -valued total quasi_total reflexive Element of bool [:u,u:]
[U,U] is non empty set
{[U,U]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(id {U}) \+\ {[U,U]} 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(id {U}) \ {[U,U]} is Relation-like {U} -defined {U} -valued finite set
(id {U}) typed\ {[U,U]} is Relation-like {U} -defined {U} -valued Function-like finite finite-support Element of bool (id {U})
bool (id {U}) is non empty finite finite-membered set
(id {U}) \ {[U,U]} is Relation-like {U} -defined {U} -valued Function-like finite finite-support Element of bool (id {U})
{[U,U]} \ (id {U}) is Relation-like finite set
{[U,U]} typed\ (id {U}) is trivial Relation-like Function-like constant finite V165() finite-support Element of bool {[U,U]}
bool {[U,U]} is non empty finite finite-membered set
{[U,U]} \ (id {U}) is trivial Relation-like Function-like constant finite V165() finite-support Element of bool {[U,U]}
((id {U}) \ {[U,U]}) \/ ({[U,U]} \ (id {U})) is Relation-like finite set
E is non empty set
rng S is set
[:E,u:] is non empty Relation-like set
bool [:E,u:] is non empty set
O is set
UU is set
[O,UU] is non empty set
i is Element of E
S . i is set
x is non empty Relation-like E -defined u -valued Function-like total quasi_total Element of bool [:E,u:]
x . i is Element of u
S . O is set
S . UU is set
[(S . O),(S . UU)] is non empty set
U is non empty set
id U is non empty Relation-like U -defined U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
Class (id U) is non empty V165() V166() a_partition of U
{_{U}_} is non empty V165() V166() a_partition of U
id U is non empty Relation-like U -defined U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
Class (id U) is non empty V165() V166() a_partition of U
(U,(id U)) is non empty Relation-like non empty-yielding U -defined Class (id U) -valued Function-like total quasi_total onto Element of bool [:U,(Class (id U)):]
[:U,(Class (id U)):] is non empty Relation-like set
bool [:U,(Class (id U)):] is non empty set
(U) is non empty Relation-like {_{U}_} -defined U -valued Function-like total quasi_total Element of bool [:{_{U}_},U:]
[:{_{U}_},U:] is non empty Relation-like set
bool [:{_{U}_},U:] is non empty set
(U) * (U,(id U)) is Relation-like U -defined U -valued Function-like Element of bool [:U,U:]
dom (U,(id U)) is non empty Element of bool U
bool U is non empty set
dom (id U) is non empty Element of bool U
{ {b₁} where b₁ is Element of U : verum } is set
[:(Class (id U)),U:] is non empty Relation-like set
bool [:(Class (id U)),U:] is non empty set
UU is non empty Relation-like non empty-yielding U -defined Class (id U) -valued Function-like total quasi_total Element of bool [:U,(Class (id U)):]
O is non empty Relation-like Class (id U) -defined U -valued Function-like total quasi_total Element of bool [:(Class (id U)),U:]
O * UU is non empty Relation-like U -defined U -valued Function-like total quasi_total Element of bool [:U,U:]
I is Element of U
{I} is non empty trivial finite 1 -element Element of bool U
x is Relation-like Function-like set
i is Relation-like Function-like set
i (*) x is Relation-like Function-like set
(i (*) x) . I is set
x . I is set
i . (x . I) is set
Class ((id U),I) is Element of bool U
{I} is non empty trivial finite 1 -element set
(id U) .: {I} is finite set
(U) . (Class ((id U),I)) is set
Jj is non empty Element of {_{U}_}
(U) . Jj is Element of U
(U,Jj) is Element of U
(id U) . I is Element of U
(O * UU) . I is Element of U
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is Element of U
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l is V51() V53() eligible Language-like
AllTermsOf l is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
AllSymbolsOf l is non empty non trivial non finite V166() set
the U1 of l is set
(AllSymbolsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf l
((AllSymbolsOf l) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf l) *)
bool ((AllSymbolsOf l) *) is non empty non trivial non finite V166() set
((AllSymbolsOf l) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
bool (((AllSymbolsOf l) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf l) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf l) *) \ {{}}))
bool (bool (((AllSymbolsOf l) *) \ {{}})) is non empty non trivial non finite V166() set
l -termsOfMaxDepth is Relation-like Function-like set
rng (l -termsOfMaxDepth) is set
union (rng (l -termsOfMaxDepth)) is set
Funcs ((AllTermsOf l),U) is non empty functional FUNCTION_DOMAIN of AllTermsOf l,U
II is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class II is non empty V165() V166() a_partition of U
Funcs ((AllTermsOf l),(Class II)) is non empty functional FUNCTION_DOMAIN of AllTermsOf l, Class II
(U,II) is non empty Relation-like non empty-yielding U -defined Class II -valued Function-like total quasi_total onto Element of bool [:U,(Class II):]
[:U,(Class II):] is non empty Relation-like set
bool [:U,(Class II):] is non empty set
(U,II) . u is non empty Element of Class II
bool U is non empty set
i is Relation-like Function-like Function-yielding V164() l,U -interpreter-like (l,U,II) set
(l,U,II,i) is Relation-like OwnSymbolsOf l -defined Function-like total Function-yielding V164() l, Class II -interpreter-like Element of (Class II) -InterpretersOf l
OwnSymbolsOf l is non empty Element of bool (AllSymbolsOf l)
bool (AllSymbolsOf l) is non empty non trivial non finite V166() set
the U2 of l is Element of the U1 of l
the U3 of l is Element of the U1 of l
{ the U2 of l, the U3 of l} is non empty finite set
the U1 of l \ { the U2 of l, the U3 of l} is Element of bool the U1 of l
bool the U1 of l is non empty set
the U1 of l typed\ { the U2 of l, the U3 of l} is Element of bool the U1 of l
(Class II) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of Class II
(Class II) \/ BOOLEAN is non empty set
K546(((Class II) *),((Class II) \/ BOOLEAN)) is non empty functional M31((Class II) * ,(Class II) \/ BOOLEAN)
Funcs ((OwnSymbolsOf l),K546(((Class II) *),((Class II) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf l,K546(((Class II) *),((Class II) \/ BOOLEAN))
(Class II) -InterpretersOf l is non empty functional Element of bool (Funcs ((OwnSymbolsOf l),K546(((Class II) *),((Class II) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf l),K546(((Class II) *),((Class II) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf l -defined K546(((Class II) *),((Class II) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf l),K546(((Class II) *),((Class II) \/ BOOLEAN))) : b₁ is l, Class II -interpreter-like } is set
((l,U,II,i),((U,II) . u)) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf l),(Class II)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf l),(Class II))):]
[:NAT,(Funcs ((AllTermsOf l),(Class II))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllTermsOf l),(Class II))):] is non empty non trivial non finite V166() set
(((l,U,II,i),((U,II) . u)) -TermEval) . S is Relation-like Function-like Element of Funcs ((AllTermsOf l),(Class II))
(i,u) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf l),U) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf l),U)):]
[:NAT,(Funcs ((AllTermsOf l),U)):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllTermsOf l),U)):] is non empty non trivial non finite V166() set
((i,u) -TermEval) . S is Relation-like Function-like Element of Funcs ((AllTermsOf l),U)
(U,II) (*) (((i,u) -TermEval) . S) is Relation-like Class II -valued Function-like set
E is non empty Element of Class II
((l,U,II,i),E) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf l),(Class II)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf l),(Class II))):]
l -firstChar is non empty Relation-like ((AllSymbolsOf l) *) \ {{}} -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):]
[:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):] is non empty non trivial non finite V166() set
(AllSymbolsOf l) -firstChar is non empty Relation-like ((AllSymbolsOf l) *) \ {{}} -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):]
(AllSymbolsOf l) -pr1 is non empty Relation-like [:(AllSymbolsOf l),(AllSymbolsOf l):] -defined AllSymbolsOf l -valued Function-like total quasi_total V233( AllSymbolsOf l) Element of bool [:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):]
[:(AllSymbolsOf l),(AllSymbolsOf l):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf l),(AllSymbolsOf l)) is non empty Relation-like [:(AllSymbolsOf l),(AllSymbolsOf l):] -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):]
MultPlace ((AllSymbolsOf l) -pr1) is non empty Relation-like ((AllSymbolsOf l) *) \ {{}} -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):]
(((l,U,II,i),E) -TermEval) . 0 is Relation-like Function-like Element of Funcs ((AllTermsOf l),(Class II))
((i,u) -TermEval) . 0 is Relation-like Function-like Element of Funcs ((AllTermsOf l),U)
(U,II) (*) (((i,u) -TermEval) . 0) is Relation-like Class II -valued Function-like set
(AllTermsOf l) --> E is non empty Relation-like non-empty non empty-yielding AllTermsOf l -defined Class II -valued Function-like constant total quasi_total Element of bool [:(AllTermsOf l),(Class II):]
[:(AllTermsOf l),(Class II):] is non empty Relation-like set
bool [:(AllTermsOf l),(Class II):] is non empty set
{E} is non empty trivial finite 1 -element V165() V166() set
[:(AllTermsOf l),{E}:] is non empty Relation-like set
(AllTermsOf l) --> u is non empty Relation-like AllTermsOf l -defined U -valued Function-like constant total quasi_total Element of bool [:(AllTermsOf l),U:]
[:(AllTermsOf l),U:] is non empty Relation-like set
bool [:(AllTermsOf l),U:] is non empty set
{u} is non empty trivial finite 1 -element set
[:(AllTermsOf l),{u}:] is non empty Relation-like set
dom (U,II) is non empty Element of bool U
j is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(((l,U,II,i),E) -TermEval) . j is Relation-like Function-like Element of Funcs ((AllTermsOf l),(Class II))
((i,u) -TermEval) . j is Relation-like Function-like Element of Funcs ((AllTermsOf l),U)
(U,II) (*) (((i,u) -TermEval) . j) is Relation-like Class II -valued Function-like set
j + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(((l,U,II,i),E) -TermEval) . (j + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf l),(Class II))
((i,u) -TermEval) . (j + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf l),U)
(U,II) (*) (((i,u) -TermEval) . (j + 1)) is Relation-like Class II -valued Function-like set
Jj is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
((i,u) -TermEval) . Jj is Relation-like Function-like Element of Funcs ((AllTermsOf l),U)
jJ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
((i,u) -TermEval) . jJ is Relation-like Function-like Element of Funcs ((AllTermsOf l),U)
[:(AllTermsOf l),U:] is non empty Relation-like set
bool [:(AllTermsOf l),U:] is non empty set
(((l,U,II,i),E) -TermEval) . Jj is Relation-like Function-like Element of Funcs ((AllTermsOf l),(Class II))
(((l,U,II,i),E) -TermEval) . jJ is Relation-like Function-like Element of Funcs ((AllTermsOf l),(Class II))
[:(AllTermsOf l),(Class II):] is non empty Relation-like set
bool [:(AllTermsOf l),(Class II):] is non empty set
TermSymbolsOf l is non empty set
{ the U3 of l} is non empty trivial finite 1 -element set
the U1 of l \ { the U3 of l} is non empty Element of bool the U1 of l
the U1 of l typed\ { the U3 of l} is Element of bool the U1 of l
the adicity of l is non empty Relation-like the U1 of l \ { the U3 of l} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of l \ { the U3 of l}),INT:]
[:( the U1 of l \ { the U3 of l}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of l \ { the U3 of l}),INT:] is non empty non trivial non finite V166() set
the adicity of l " NAT is Element of bool ( the U1 of l \ { the U3 of l})
bool ( the U1 of l \ { the U3 of l}) is non empty set
n is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf l
Enn is non empty Relation-like NAT -defined TermSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf l) *) \ {{}}
(l -firstChar) . Enn is non relational termal own ofAtomicFormula Element of AllSymbolsOf l
i . ((l -firstChar) . Enn) is non empty Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total ((U,II,(abs (ar ((l -firstChar) . Enn)))),II) (l,U,(l -firstChar) . Enn,II) Interpreter of (l -firstChar) . Enn,U
ar ((l -firstChar) . Enn) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of l . ((l -firstChar) . Enn) is set
abs (ar ((l -firstChar) . Enn)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar ((l -firstChar) . Enn))) -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
U \/ BOOLEAN is non empty set
(U,II,(abs (ar ((l -firstChar) . Enn)))) is Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on U -defined (abs (ar ((l -firstChar) . Enn))) -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),((abs (ar ((l -firstChar) . Enn))) -tuples_on U):]
[:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),((abs (ar ((l -firstChar) . Enn))) -tuples_on U):] is non empty Relation-like set
bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),((abs (ar ((l -firstChar) . Enn))) -tuples_on U):] is non empty set
(U,U,II,(abs (ar ((l -firstChar) . Enn)))) is Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on U -defined (abs (ar ((l -firstChar) . Enn))) -tuples_on U -valued total quasi_total Element of bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),((abs (ar ((l -firstChar) . Enn))) -tuples_on U):]
Seg (abs (ar ((l -firstChar) . Enn))) is finite abs (ar ((l -firstChar) . Enn)) -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 ((l -firstChar) . Enn)) ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite abs (ar ((l -firstChar) . Enn)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((l -firstChar) . Enn))) -tuples_on U : for b₃ being set holds
( not b₃ in Seg (abs (ar ((l -firstChar) . Enn))) or [(b₁ . b₃),(b₂ . b₃)] in II ) } is set
(l,U,II,i) . ((l -firstChar) . Enn) is non empty Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II) -defined (Class II) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (l -firstChar) . Enn, Class II
(abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class II
SubTerms Enn is Relation-like NAT -defined (rng Enn) * -valued AllTermsOf l -valued Function-like finite abs (ar Enn) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf l) *
rng Enn is non empty finite set
(rng Enn) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng Enn
AllTermsOf l is non empty functional finite-membered FinSequence-membered AllSymbolsOf l -prefix l -prefix Element of bool ((AllSymbolsOf l) *)
ar Enn is finite complex ext-real V40() V41() Element of INT
abs (ar Enn) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
((AllSymbolsOf l) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf l) *
(AllTermsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf l) *) *)
bool (((AllSymbolsOf l) *) *) is non empty non trivial non finite V166() set
(U,II,(abs (ar ((l -firstChar) . Enn)))) is Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on U -defined (abs (ar ((l -firstChar) . Enn))) -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),((abs (ar ((l -firstChar) . Enn))) -tuples_on U):]
[:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),U:] is non empty Relation-like set
bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),U:] is non empty set
(l,U,((l -firstChar) . Enn),II,(i . ((l -firstChar) . Enn))) is non empty Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II) -defined (Class II) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (l -firstChar) . Enn, Class II
Class (U,II,(abs (ar ((l -firstChar) . Enn)))) is non empty V165() V166() a_partition of (abs (ar ((l -firstChar) . Enn))) -tuples_on U
(U,(abs (ar ((l -firstChar) . Enn))),II) is non empty Relation-like non empty-yielding (abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II) -defined Class (U,II,(abs (ar ((l -firstChar) . Enn)))) -valued Function-like total quasi_total Element of bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)),(Class (U,II,(abs (ar ((l -firstChar) . Enn))))):]
[:((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)),(Class (U,II,(abs (ar ((l -firstChar) . Enn))))):] is non empty Relation-like set
bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)),(Class (U,II,(abs (ar ((l -firstChar) . Enn))))):] is non empty set
(U,II) ~ is Relation-like Class II -defined U -valued total quasi_total Element of bool [:(Class II),U:]
[:(Class II),U:] is non empty Relation-like set
bool [:(Class II),U:] is non empty set
((Class II),U,((U,II) ~),(abs (ar ((l -firstChar) . Enn)))) is Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II) -defined (abs (ar ((l -firstChar) . Enn))) -tuples_on U -valued total quasi_total Element of bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)),((abs (ar ((l -firstChar) . Enn))) -tuples_on U):]
[:((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)),((abs (ar ((l -firstChar) . Enn))) -tuples_on U):] is non empty Relation-like set
bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)),((abs (ar ((l -firstChar) . Enn))) -tuples_on U):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class II -valued Function-like finite abs (ar ((l -firstChar) . Enn)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II), b₂ is Relation-like NAT -defined U -valued Function-like finite abs (ar ((l -firstChar) . Enn)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((l -firstChar) . Enn))) -tuples_on U : for b₃ being set holds
( not b₃ in Seg (abs (ar ((l -firstChar) . Enn))) or [(b₁ . b₃),(b₂ . b₃)] in (U,II) ~ ) } is set
(((abs (ar ((l -firstChar) . Enn))) -tuples_on U),(U,II,(abs (ar ((l -firstChar) . Enn))))) is non empty Relation-like non empty-yielding (abs (ar ((l -firstChar) . Enn))) -tuples_on U -defined Class (U,II,(abs (ar ((l -firstChar) . Enn)))) -valued Function-like total quasi_total onto Element of bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),(Class (U,II,(abs (ar ((l -firstChar) . Enn))))):]
[:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),(Class (U,II,(abs (ar ((l -firstChar) . Enn))))):] is non empty Relation-like set
bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),(Class (U,II,(abs (ar ((l -firstChar) . Enn))))):] is non empty set
((Class II),U,((U,II) ~),(abs (ar ((l -firstChar) . Enn)))) * (((abs (ar ((l -firstChar) . Enn))) -tuples_on U),(U,II,(abs (ar ((l -firstChar) . Enn))))) is Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II) -defined Class (U,II,(abs (ar ((l -firstChar) . Enn)))) -valued total quasi_total Element of bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)),(Class (U,II,(abs (ar ((l -firstChar) . Enn))))):]
ss is non empty Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on U -defined U -valued Function-like total quasi_total ((U,II,(abs (ar ((l -firstChar) . Enn)))),II) Element of bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),U:]
(((abs (ar ((l -firstChar) . Enn))) -tuples_on U),U,(U,II,(abs (ar ((l -firstChar) . Enn)))),II,ss) is non empty Relation-like non empty-yielding Class (U,II,(abs (ar ((l -firstChar) . Enn)))) -defined Class II -valued Function-like total quasi_total Element of bool [:(Class (U,II,(abs (ar ((l -firstChar) . Enn))))),(Class II):]
[:(Class (U,II,(abs (ar ((l -firstChar) . Enn))))),(Class II):] is non empty Relation-like set
bool [:(Class (U,II,(abs (ar ((l -firstChar) . Enn))))),(Class II):] is non empty set
bool ((abs (ar ((l -firstChar) . Enn))) -tuples_on U) is non empty set
{ [b₁,b₂] where b₁ is non empty Element of Class (U,II,(abs (ar ((l -firstChar) . Enn)))), b₂ is non empty Element of Class II : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in ss ) } is set
(((abs (ar ((l -firstChar) . Enn))) -tuples_on U),U,(U,II,(abs (ar ((l -firstChar) . Enn)))),II,ss) * (U,(abs (ar ((l -firstChar) . Enn))),II) is non empty Relation-like non empty-yielding (abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II) -defined Class II -valued Function-like total quasi_total Element of bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)),(Class II):]
[:((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)),(Class II):] is non empty Relation-like set
bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)),(Class II):] is non empty set
jJ is non empty Relation-like AllTermsOf l -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),U:]
jJ (*) (SubTerms Enn) is Relation-like NAT -defined U -valued Function-like finite finite-support set
(U,(Class II),(U,II),(abs (ar ((l -firstChar) . Enn)))) is non empty Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on U -defined (abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II) -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)):]
[:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)):] is non empty Relation-like set
bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),((abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II)):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite abs (ar ((l -firstChar) . Enn)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((l -firstChar) . Enn))) -tuples_on U, b₂ is Relation-like NAT -defined Class II -valued Function-like finite abs (ar ((l -firstChar) . Enn)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II) : for b₃ being set holds
( not b₃ in Seg (abs (ar ((l -firstChar) . Enn))) or [(b₁ . b₃),(b₂ . b₃)] in (U,II) ) } is set
dom (U,(Class II),(U,II),(abs (ar ((l -firstChar) . Enn)))) is non empty functional finite-membered FinSequence-membered Element of bool ((abs (ar ((l -firstChar) . Enn))) -tuples_on U)
dom ss is non empty functional finite-membered FinSequence-membered Element of bool ((abs (ar ((l -firstChar) . Enn))) -tuples_on U)
g is non empty Relation-like AllTermsOf l -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),U:]
dom g is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf l)
bool (AllTermsOf l) is non empty set
G is non empty Relation-like non empty-yielding AllTermsOf l -defined Class II -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),(Class II):]
G . n is non empty Element of Class II
((((l,U,II,i),E) -TermEval) . j) (*) (SubTerms Enn) is Relation-like NAT -defined Function-like finite finite-support set
((l,U,II,i) . ((l -firstChar) . Enn)) . (((((l,U,II,i),E) -TermEval) . j) (*) (SubTerms Enn)) is set
(l,U,((l -firstChar) . Enn),II,(i . ((l -firstChar) . Enn))) . (((((l,U,II,i),E) -TermEval) . j) (*) (SubTerms Enn)) is set
(U,II) (*) (jJ (*) (SubTerms Enn)) is Relation-like NAT -defined Class II -valued Function-like finite finite-support set
(l,U,((l -firstChar) . Enn),II,(i . ((l -firstChar) . Enn))) . ((U,II) (*) (jJ (*) (SubTerms Enn))) is set
(U,(Class II),(U,II),(abs (ar ((l -firstChar) . Enn)))) . (jJ (*) (SubTerms Enn)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(l,U,((l -firstChar) . Enn),II,(i . ((l -firstChar) . Enn))) . ((U,(Class II),(U,II),(abs (ar ((l -firstChar) . Enn)))) . (jJ (*) (SubTerms Enn))) is set
phi22 is Relation-like Function-like set
phi22 (*) (U,(abs (ar ((l -firstChar) . Enn))),II) is Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on (Class II) -defined Function-like set
(phi22 (*) (U,(abs (ar ((l -firstChar) . Enn))),II)) (*) (U,(Class II),(U,II),(abs (ar ((l -firstChar) . Enn)))) is Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on U -defined Function-like set
((phi22 (*) (U,(abs (ar ((l -firstChar) . Enn))),II)) (*) (U,(Class II),(U,II),(abs (ar ((l -firstChar) . Enn))))) . (jJ (*) (SubTerms Enn)) is set
(U,(abs (ar ((l -firstChar) . Enn))),II) * (U,(Class II),(U,II),(abs (ar ((l -firstChar) . Enn)))) is non empty Relation-like non empty-yielding (abs (ar ((l -firstChar) . Enn))) -tuples_on U -defined Class (U,II,(abs (ar ((l -firstChar) . Enn)))) -valued Function-like total quasi_total Element of bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),(Class (U,II,(abs (ar ((l -firstChar) . Enn))))):]
phi22 (*) ((U,(abs (ar ((l -firstChar) . Enn))),II) * (U,(Class II),(U,II),(abs (ar ((l -firstChar) . Enn))))) is Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on U -defined Function-like set
(phi22 (*) ((U,(abs (ar ((l -firstChar) . Enn))),II) * (U,(Class II),(U,II),(abs (ar ((l -firstChar) . Enn)))))) . (jJ (*) (SubTerms Enn)) is set
phi22 (*) (((abs (ar ((l -firstChar) . Enn))) -tuples_on U),(U,II,(abs (ar ((l -firstChar) . Enn))))) is Relation-like (abs (ar ((l -firstChar) . Enn))) -tuples_on U -defined Function-like set
(phi22 (*) (((abs (ar ((l -firstChar) . Enn))) -tuples_on U),(U,II,(abs (ar ((l -firstChar) . Enn)))))) . (jJ (*) (SubTerms Enn)) is set
(U,II) * ss is non empty Relation-like non empty-yielding (abs (ar ((l -firstChar) . Enn))) -tuples_on U -defined Class II -valued Function-like total quasi_total Element of bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),(Class II):]
[:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),(Class II):] is non empty Relation-like set
bool [:((abs (ar ((l -firstChar) . Enn))) -tuples_on U),(Class II):] is non empty set
((U,II) * ss) . (jJ (*) (SubTerms Enn)) is set
ss . (jJ (*) (SubTerms Enn)) is set
(U,II) . (ss . (jJ (*) (SubTerms Enn))) is set
(((i,u) -TermEval) . (j + 1)) . Enn is set
(U,II) . ((((i,u) -TermEval) . (j + 1)) . Enn) is set
(U,II) * g is non empty Relation-like non empty-yielding AllTermsOf l -defined Class II -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),(Class II):]
((U,II) * g) . n is non empty Element of Class II
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is V51() V53() eligible Language-like
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class S is non empty V165() V166() a_partition of U
(U,S) is non empty Relation-like non empty-yielding U -defined Class S -valued Function-like total quasi_total onto Element of bool [:U,(Class S):]
[:U,(Class S):] is non empty Relation-like set
bool [:U,(Class S):] is non empty set
the Element of U is Element of U
II is Relation-like Function-like Function-yielding V164() u,U -interpreter-like (u,U,S) set
(u,U,S,II) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u, Class S -interpreter-like Element of (Class S) -InterpretersOf u
OwnSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
the U2 of u is Element of the U1 of u
the U3 of u is Element of the U1 of u
{ the U2 of u, the U3 of u} is non empty finite set
the U1 of u \ { the U2 of u, the U3 of u} is Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U2 of u, the U3 of u} is Element of bool the U1 of u
(Class S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of Class S
(Class S) \/ BOOLEAN is non empty set
K546(((Class S) *),((Class S) \/ BOOLEAN)) is non empty functional M31((Class S) * ,(Class S) \/ BOOLEAN)
Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf u,K546(((Class S) *),((Class S) \/ BOOLEAN))
(Class S) -InterpretersOf u is non empty functional Element of bool (Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf u -defined K546(((Class S) *),((Class S) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN))) : b₁ is u, Class S -interpreter-like } is set
(u,U,S,II) -TermEval is non empty Relation-like non empty-yielding AllTermsOf u -defined Class S -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),(Class S):]
[:(AllTermsOf u),(Class S):] is non empty Relation-like set
bool [:(AllTermsOf u),(Class S):] is non empty set
II -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(U,S) * (II -TermEval) is non empty Relation-like non empty-yielding AllTermsOf u -defined Class S -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),(Class S):]
bool U is non empty set
(U,S) . the Element of U is non empty Element of Class S
u -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
[:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(AllSymbolsOf u) -pr1 is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total V233( AllSymbolsOf u) Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
[:(AllSymbolsOf u),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf u),(AllSymbolsOf u)) is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
MultPlace ((AllSymbolsOf u) -pr1) is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(II, the Element of U) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf u),U) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf u),U)):]
Funcs ((AllTermsOf u),U) is non empty functional FUNCTION_DOMAIN of AllTermsOf u,U
[:NAT,(Funcs ((AllTermsOf u),U)):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllTermsOf u),U)):] is non empty non trivial non finite V166() set
E is non empty Element of Class S
((u,U,S,II),E) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf u),(Class S)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf u),(Class S))):]
Funcs ((AllTermsOf u),(Class S)) is non empty functional FUNCTION_DOMAIN of AllTermsOf u, Class S
[:NAT,(Funcs ((AllTermsOf u),(Class S))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllTermsOf u),(Class S))):] is non empty non trivial non finite V166() set
u -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf u) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf u) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf u) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf u) *) \ {{}})):] is non empty non trivial non finite V166() set
jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u
jJ is Relation-like Function-like set
g is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
jJ . g is set
II -TermEval jJ is Element of U
(u,U,S,II) -TermEval jJ is non empty Element of Class S
g + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
((II, the Element of U) -TermEval) . n is Relation-like Function-like Element of Funcs ((AllTermsOf u),U)
dom (((II, the Element of U) -TermEval) . n) is set
dom (II -TermEval) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf u)
bool (AllTermsOf u) is non empty set
((u,U,S,II) -TermEval) . jJ is non empty Element of Class S
(((u,U,S,II),E) -TermEval) . (g + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf u),(Class S))
((((u,U,S,II),E) -TermEval) . (g + 1)) . jJ is set
((II, the Element of U) -TermEval) . (g + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf u),U)
(U,S) (*) (((II, the Element of U) -TermEval) . (g + 1)) is Relation-like Class S -valued Function-like set
((U,S) (*) (((II, the Element of U) -TermEval) . (g + 1))) . jJ is set
(((II, the Element of U) -TermEval) . (g + 1)) . jJ is set
(U,S) . ((((II, the Element of U) -TermEval) . (g + 1)) . jJ) is set
(U,S) . (II -TermEval jJ) is non empty Element of Class S
(II -TermEval) . jJ is Element of U
(U,S) . ((II -TermEval) . jJ) is non empty Element of Class S
((U,S) * (II -TermEval)) . jJ is non empty Element of Class S
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is V51() V53() eligible Language-like
AtomicFormulaSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
AllSymbolsOf u is non empty non trivial non finite V166() set
TheNorSymbOf u is set
the U3 of u is Element of the U1 of u
{(TheNorSymbOf u)} is non empty trivial finite 1 -element set
(AllSymbolsOf u) \ {(TheNorSymbOf u)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
(AllSymbolsOf u) typed\ {(TheNorSymbOf u)} is Element of bool (AllSymbolsOf u)
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
u -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
[:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(AllSymbolsOf u) -pr1 is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total V233( AllSymbolsOf u) Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
[:(AllSymbolsOf u),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf u),(AllSymbolsOf u)) is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
MultPlace ((AllSymbolsOf u) -pr1) is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
TheEqSymbOf u is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf u
the U2 of u is Element of the U1 of u
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class S is non empty V165() V166() a_partition of U
l is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
(u -firstChar) . l is low-compounding relational ofAtomicFormula Element of AllSymbolsOf u
II is Relation-like Function-like Function-yielding V164() u,U -interpreter-like (u,U,S) set
(u,U,S,II) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u, Class S -interpreter-like Element of (Class S) -InterpretersOf u
OwnSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
{ the U2 of u, the U3 of u} is non empty finite set
the U1 of u \ { the U2 of u, the U3 of u} is Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U2 of u, the U3 of u} is Element of bool the U1 of u
(Class S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of Class S
(Class S) \/ BOOLEAN is non empty set
K546(((Class S) *),((Class S) \/ BOOLEAN)) is non empty functional M31((Class S) * ,(Class S) \/ BOOLEAN)
Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf u,K546(((Class S) *),((Class S) \/ BOOLEAN))
(Class S) -InterpretersOf u is non empty functional Element of bool (Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf u -defined K546(((Class S) *),((Class S) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN))) : b₁ is u, Class S -interpreter-like } is set
(u,U,S,II) -AtomicEval l is boolean Element of BOOLEAN
(u,U,S,II) === is Relation-like Function-like Function-yielding V164() u, Class S -interpreter-like (u,U,S,II) -extension set
TheEqSymbOf u is Element of AtomicFormulaSymbolsOf u
(Class S) -deltaInterpreter is non empty Relation-like 2 -tuples_on (Class S) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on (Class S)),BOOLEAN:]
2 -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of Class S
[:(2 -tuples_on (Class S)),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on (Class S)),BOOLEAN:] is non empty set
[:((Class S) *),((Class S) *):] is non empty non trivial Relation-like non finite V166() set
(Class S) -concatenation is non empty Relation-like [:((Class S) *),((Class S) *):] -defined (Class S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((Class S) * ) Element of bool [:[:((Class S) *),((Class S) *):],((Class S) *):]
[:[:((Class S) *),((Class S) *):],((Class S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((Class S) *),((Class S) *):],((Class S) *):] is non empty non trivial non finite V166() set
1 -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of Class S
id (1 -tuples_on (Class S)) is non empty Relation-like non empty-yielding 1 -tuples_on (Class S) -defined 1 -tuples_on (Class S) -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(1 -tuples_on (Class S)),(1 -tuples_on (Class S)):]
[:(1 -tuples_on (Class S)),(1 -tuples_on (Class S)):] is non empty Relation-like set
bool [:(1 -tuples_on (Class S)),(1 -tuples_on (Class S)):] is non empty set
((Class S) -concatenation) .: (id (1 -tuples_on (Class S))) is functional finite-membered FinSequence-membered Element of bool ((Class S) *)
bool ((Class S) *) is non empty non trivial non finite V166() set
chi ((((Class S) -concatenation) .: (id (1 -tuples_on (Class S)))),(2 -tuples_on (Class S))) is non empty Relation-like 2 -tuples_on (Class S) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on (Class S)),BOOLEAN:]
(TheEqSymbOf u) .--> ((Class S) -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf u -defined {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on (Class S)),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf u)} is non empty trivial finite 1 -element set
{(TheEqSymbOf u)} --> ((Class S) -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on (Class S)),BOOLEAN:] -valued {((Class S) -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf u)},{((Class S) -deltaInterpreter)}:]
{((Class S) -deltaInterpreter)} is non empty trivial functional finite 1 -element V165() V166() set
[:{(TheEqSymbOf u)},{((Class S) -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf u)},{((Class S) -deltaInterpreter)}:] is non empty finite finite-membered set
(u,U,S,II) +* ((TheEqSymbOf u) .--> ((Class S) -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
((u,U,S,II) ===) . ((u -firstChar) . l) is non empty Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -defined (Class S) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . l, Class S
ar ((u -firstChar) . l) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
the adicity of u . ((u -firstChar) . l) is set
abs (ar ((u -firstChar) . l)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((u -firstChar) . l))) -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of Class S
SubTerms l is Relation-like NAT -defined (rng l) * -valued (TermSymbolsOf u) * -valued AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
rng l is non empty finite set
(rng l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng l
TermSymbolsOf u is non empty set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
(TermSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf u
AllTermsOf u is non empty functional finite-membered FinSequence-membered AllSymbolsOf u -prefix u -prefix Element of bool ((AllSymbolsOf u) *)
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
((AllSymbolsOf u) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf u) *
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf u) *) *)
bool (((AllSymbolsOf u) *) *) is non empty non trivial non finite V166() set
(u,U,S,II) -TermEval is non empty Relation-like non empty-yielding AllTermsOf u -defined Class S -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),(Class S):]
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
[:(AllTermsOf u),(Class S):] is non empty Relation-like set
bool [:(AllTermsOf u),(Class S):] is non empty set
((u,U,S,II) -TermEval) (*) (SubTerms l) is Relation-like NAT -defined Class S -valued Function-like finite finite-support set
(((u,U,S,II) ===) . ((u -firstChar) . l)) . (((u,U,S,II) -TermEval) (*) (SubTerms l)) is set
(u,U,S,II) -TruthEval l is boolean Element of BOOLEAN
II -AtomicEval l is boolean Element of BOOLEAN
II === is Relation-like Function-like Function-yielding V164() u,U -interpreter-like II -extension set
U -deltaInterpreter is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
2 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
[:(2 -tuples_on U),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on U),BOOLEAN:] is non empty set
U * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of U
[:(U *),(U *):] is non empty non trivial Relation-like non finite V166() set
U -concatenation is non empty Relation-like [:(U *),(U *):] -defined U * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233(U * ) Element of bool [:[:(U *),(U *):],(U *):]
[:[:(U *),(U *):],(U *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(U *),(U *):],(U *):] is non empty non trivial non finite V166() set
1 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
id (1 -tuples_on U) is non empty Relation-like non empty-yielding 1 -tuples_on U -defined 1 -tuples_on U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(1 -tuples_on U),(1 -tuples_on U):]
[:(1 -tuples_on U),(1 -tuples_on U):] is non empty Relation-like set
bool [:(1 -tuples_on U),(1 -tuples_on U):] is non empty set
(U -concatenation) .: (id (1 -tuples_on U)) is functional finite-membered FinSequence-membered Element of bool (U *)
bool (U *) is non empty non trivial non finite V166() set
chi (((U -concatenation) .: (id (1 -tuples_on U))),(2 -tuples_on U)) is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
(TheEqSymbOf u) .--> (U -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf u -defined {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf u)} --> (U -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued {(U -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:]
{(U -deltaInterpreter)} is non empty trivial functional finite 1 -element V165() V166() set
[:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty finite finite-membered set
II +* ((TheEqSymbOf u) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(II ===) . ((u -firstChar) . l) is non empty Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . l,U
(abs (ar ((u -firstChar) . l))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
U \/ BOOLEAN is non empty set
II -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(II -TermEval) (*) (SubTerms l) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((II ===) . ((u -firstChar) . l)) . ((II -TermEval) (*) (SubTerms l)) is set
(u,U,S,II) . ((u -firstChar) . l) is Relation-like Function-like set
II . ((u -firstChar) . l) is Relation-like Function-like set
(abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of AllTermsOf u
(U,S) is non empty Relation-like non empty-yielding U -defined Class S -valued Function-like total quasi_total onto Element of bool [:U,(Class S):]
[:U,(Class S):] is non empty Relation-like set
bool [:U,(Class S):] is non empty set
(U,S) * (II -TermEval) is non empty Relation-like non empty-yielding AllTermsOf u -defined Class S -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),(Class S):]
((AllTermsOf u),(Class S),((U,S) * (II -TermEval)),(abs (ar ((u -firstChar) . l)))) is non empty Relation-like non empty-yielding (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)):]
[:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)):] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)):] is non empty set
Seg (abs (ar ((u -firstChar) . l))) is non empty finite abs (ar ((u -firstChar) . l)) -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 ((u -firstChar) . l)) ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u), b₂ is Relation-like NAT -defined Class S -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) : for b₃ being set holds
( not b₃ in Seg (abs (ar ((u -firstChar) . l))) or [(b₁ . b₃),(b₂ . b₃)] in (U,S) * (II -TermEval) ) } is set
dom ((AllTermsOf u),(Class S),((U,S) * (II -TermEval)),(abs (ar ((u -firstChar) . l)))) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool ((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u))
bool ((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)) is non empty set
((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) is non empty Relation-like non empty-yielding (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined (abs (ar ((u -firstChar) . l))) -tuples_on U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),((abs (ar ((u -firstChar) . l))) -tuples_on U):]
[:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),((abs (ar ((u -firstChar) . l))) -tuples_on U):] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),((abs (ar ((u -firstChar) . l))) -tuples_on U):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u), b₂ is Relation-like NAT -defined U -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((u -firstChar) . l))) -tuples_on U : for b₃ being set holds
( not b₃ in Seg (abs (ar ((u -firstChar) . l))) or [(b₁ . b₃),(b₂ . b₃)] in II -TermEval ) } is set
dom ((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool ((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u))
((u,U,S,II) . ((u -firstChar) . l)) . (((u,U,S,II) -TermEval) (*) (SubTerms l)) is set
((U,S) * (II -TermEval)) (*) (SubTerms l) is Relation-like NAT -defined Class S -valued Function-like finite finite-support set
((u,U,S,II) . ((u -firstChar) . l)) . (((U,S) * (II -TermEval)) (*) (SubTerms l)) is set
((AllTermsOf u),(Class S),((U,S) * (II -TermEval)),(abs (ar ((u -firstChar) . l)))) . (SubTerms l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((u,U,S,II) . ((u -firstChar) . l)) . (((AllTermsOf u),(Class S),((U,S) * (II -TermEval)),(abs (ar ((u -firstChar) . l)))) . (SubTerms l)) is set
((u,U,S,II) . ((u -firstChar) . l)) (*) ((AllTermsOf u),(Class S),((U,S) * (II -TermEval)),(abs (ar ((u -firstChar) . l)))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Function-like set
(((u,U,S,II) . ((u -firstChar) . l)) (*) ((AllTermsOf u),(Class S),((U,S) * (II -TermEval)),(abs (ar ((u -firstChar) . l))))) . (SubTerms l) is set
En is own ofAtomicFormula Element of OwnSymbolsOf u
II . En is non empty Relation-like (abs (ar En)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total (u,U,En,S) Interpreter of En,U
ar En is finite complex ext-real V40() V41() Element of INT
the adicity of u . En is set
abs (ar En) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar En)) -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
(u,U,S,II) . En is non empty Relation-like (abs (ar En)) -tuples_on (Class S) -defined (Class S) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of En, Class S
(abs (ar En)) -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class S
(U,S,(abs (ar ((u -firstChar) . l)))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined (abs (ar ((u -firstChar) . l))) -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),((abs (ar ((u -firstChar) . l))) -tuples_on U):]
[:((abs (ar ((u -firstChar) . l))) -tuples_on U),((abs (ar ((u -firstChar) . l))) -tuples_on U):] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),((abs (ar ((u -firstChar) . l))) -tuples_on U):] is non empty set
(U,U,S,(abs (ar ((u -firstChar) . l)))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined (abs (ar ((u -firstChar) . l))) -tuples_on U -valued total quasi_total Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),((abs (ar ((u -firstChar) . l))) -tuples_on U):]
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((u -firstChar) . l))) -tuples_on U : for b₃ being set holds
( not b₃ in Seg (abs (ar ((u -firstChar) . l))) or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
[:((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN:] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN:] is non empty set
hhh is non empty Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued ((U,S,(abs (ar ((u -firstChar) . l)))), id BOOLEAN) Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN:]
(((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) is non empty Relation-like non empty-yielding Class (U,S,(abs (ar ((u -firstChar) . l)))) -defined Class (id BOOLEAN) -valued Function-like total quasi_total Element of bool [:(Class (U,S,(abs (ar ((u -firstChar) . l))))),(Class (id BOOLEAN)):]
Class (U,S,(abs (ar ((u -firstChar) . l)))) is non empty V165() V166() a_partition of (abs (ar ((u -firstChar) . l))) -tuples_on U
[:(Class (U,S,(abs (ar ((u -firstChar) . l))))),(Class (id BOOLEAN)):] is non empty Relation-like set
bool [:(Class (U,S,(abs (ar ((u -firstChar) . l))))),(Class (id BOOLEAN)):] is non empty set
bool ((abs (ar ((u -firstChar) . l))) -tuples_on U) is non empty set
{ [b₁,b₂] where b₁ is non empty Element of Class (U,S,(abs (ar ((u -firstChar) . l)))), b₂ is non empty Element of Class (id BOOLEAN) : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in hhh ) } is set
(U,(abs (ar ((u -firstChar) . l))),S) is non empty Relation-like non empty-yielding (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Function-like total quasi_total Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
[:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):] is non empty set
(U,S) ~ is Relation-like Class S -defined U -valued total quasi_total Element of bool [:(Class S),U:]
[:(Class S),U:] is non empty Relation-like set
bool [:(Class S),U:] is non empty set
((Class S),U,((U,S) ~),(abs (ar ((u -firstChar) . l)))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -defined (abs (ar ((u -firstChar) . l))) -tuples_on U -valued total quasi_total Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),((abs (ar ((u -firstChar) . l))) -tuples_on U):]
[:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),((abs (ar ((u -firstChar) . l))) -tuples_on U):] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),((abs (ar ((u -firstChar) . l))) -tuples_on U):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class S -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((u -firstChar) . l))) -tuples_on (Class S), b₂ is Relation-like NAT -defined U -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((u -firstChar) . l))) -tuples_on U : for b₃ being set holds
( not b₃ in Seg (abs (ar ((u -firstChar) . l))) or [(b₁ . b₃),(b₂ . b₃)] in (U,S) ~ ) } is set
(((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))) is non empty Relation-like non empty-yielding (abs (ar ((u -firstChar) . l))) -tuples_on U -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Function-like total quasi_total onto Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
[:((abs (ar ((u -firstChar) . l))) -tuples_on U),(Class (U,S,(abs (ar ((u -firstChar) . l))))):] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),(Class (U,S,(abs (ar ((u -firstChar) . l))))):] is non empty set
((Class S),U,((U,S) ~),(abs (ar ((u -firstChar) . l)))) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued total quasi_total Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
ss is Relation-like Function-like set
(u,U,En,S,(II . En)) is non empty Relation-like (abs (ar En)) -tuples_on (Class S) -defined (Class S) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of En, Class S
(((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (U,(abs (ar ((u -firstChar) . l))),S) is non empty Relation-like non empty-yielding (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -defined Class (id BOOLEAN) -valued Function-like total quasi_total Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),(Class (id BOOLEAN)):]
[:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),(Class (id BOOLEAN)):] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),(Class (id BOOLEAN)):] is non empty set
(BOOLEAN) * ((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (U,(abs (ar ((u -firstChar) . l))),S)) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -defined BOOLEAN -valued Function-like Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),BOOLEAN:]
[:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),BOOLEAN:] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),BOOLEAN:] is non empty set
(U,(abs (ar ((u -firstChar) . l))),S) * ((AllTermsOf u),(Class S),((U,S) * (II -TermEval)),(abs (ar ((u -firstChar) . l)))) is non empty Relation-like non empty-yielding (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Function-like total quasi_total Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
[:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):] is non empty set
(((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))) * ((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) is non empty Relation-like non empty-yielding (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Function-like total quasi_total Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
b1 is Relation-like U -defined Class S -valued Element of bool [:U,(Class S):]
(U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)):]
[:((abs (ar ((u -firstChar) . l))) -tuples_on U),((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)):] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((u -firstChar) . l))) -tuples_on U, b₂ is Relation-like NAT -defined Class S -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) : for b₃ being set holds
( not b₃ in Seg (abs (ar ((u -firstChar) . l))) or [(b₁ . b₃),(b₂ . b₃)] in b1 ) } is set
((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) * (U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)):]
b1 ~ is Relation-like Class S -defined U -valued Element of bool [:(Class S),U:]
((Class S),U,(b1 ~),(abs (ar ((u -firstChar) . l)))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -defined (abs (ar ((u -firstChar) . l))) -tuples_on U -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),((abs (ar ((u -firstChar) . l))) -tuples_on U):]
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class S -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((u -firstChar) . l))) -tuples_on (Class S), b₂ is Relation-like NAT -defined U -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like finite-support Element of (abs (ar ((u -firstChar) . l))) -tuples_on U : for b₃ being set holds
( not b₃ in Seg (abs (ar ((u -firstChar) . l))) or [(b₁ . b₃),(b₂ . b₃)] in b1 ~ ) } is set
((Class S),U,(b1 ~),(abs (ar ((u -firstChar) . l)))) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
(((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) * (U,(Class S),b1,(abs (ar ((u -firstChar) . l))))) * (((Class S),U,(b1 ~),(abs (ar ((u -firstChar) . l)))) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l)))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
(U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) * (((Class S),U,(b1 ~),(abs (ar ((u -firstChar) . l)))) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l)))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) * ((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) * (((Class S),U,(b1 ~),(abs (ar ((u -firstChar) . l)))) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
(U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) * ((Class S),U,(b1 ~),(abs (ar ((u -firstChar) . l)))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined (abs (ar ((u -firstChar) . l))) -tuples_on U -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),((abs (ar ((u -firstChar) . l))) -tuples_on U):]
((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) * ((Class S),U,(b1 ~),(abs (ar ((u -firstChar) . l))))) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) * (((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) * ((Class S),U,(b1 ~),(abs (ar ((u -firstChar) . l))))) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l)))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
(U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) ~ is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -defined (abs (ar ((u -firstChar) . l))) -tuples_on U -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (Class S)),((abs (ar ((u -firstChar) . l))) -tuples_on U):]
(U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) * ((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) ~) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined (abs (ar ((u -firstChar) . l))) -tuples_on U -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),((abs (ar ((u -firstChar) . l))) -tuples_on U):]
((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) * ((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) ~)) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) * (((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) * ((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) ~)) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l)))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) * ((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) * ((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) ~)) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined (abs (ar ((u -firstChar) . l))) -tuples_on U -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),((abs (ar ((u -firstChar) . l))) -tuples_on U):]
(((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) * ((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) * ((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) ~))) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
(((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) * (U,(Class S),b1,(abs (ar ((u -firstChar) . l))))) * ((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) ~) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined (abs (ar ((u -firstChar) . l))) -tuples_on U -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),((abs (ar ((u -firstChar) . l))) -tuples_on U):]
((((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) * (U,(Class S),b1,(abs (ar ((u -firstChar) . l))))) * ((U,(Class S),b1,(abs (ar ((u -firstChar) . l)))) ~)) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Class (U,S,(abs (ar ((u -firstChar) . l)))) -valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (U,S,(abs (ar ((u -firstChar) . l))))):]
ss (*) ((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (U,(abs (ar ((u -firstChar) . l))),S)) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -defined Function-like set
(ss (*) ((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (U,(abs (ar ((u -firstChar) . l))),S))) (*) ((AllTermsOf u),(Class S),((U,S) * (II -TermEval)),(abs (ar ((u -firstChar) . l)))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Function-like set
((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (U,(abs (ar ((u -firstChar) . l))),S)) * ((AllTermsOf u),(Class S),((U,S) * (II -TermEval)),(abs (ar ((u -firstChar) . l)))) is non empty Relation-like non empty-yielding (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Class (id BOOLEAN) -valued Function-like total quasi_total Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (id BOOLEAN)):]
[:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (id BOOLEAN)):] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (id BOOLEAN)):] is non empty set
ss (*) (((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (U,(abs (ar ((u -firstChar) . l))),S)) * ((AllTermsOf u),(Class S),((U,S) * (II -TermEval)),(abs (ar ((u -firstChar) . l))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Function-like set
(((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * ((((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))) * ((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l))))) is non empty Relation-like non empty-yielding (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Class (id BOOLEAN) -valued Function-like total quasi_total Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (id BOOLEAN)):]
ss (*) ((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * ((((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))) * ((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Function-like set
(((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))) is non empty Relation-like non empty-yielding (abs (ar ((u -firstChar) . l))) -tuples_on U -defined Class (id BOOLEAN) -valued Function-like total quasi_total Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),(Class (id BOOLEAN)):]
[:((abs (ar ((u -firstChar) . l))) -tuples_on U),(Class (id BOOLEAN)):] is non empty Relation-like set
bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),(Class (id BOOLEAN)):] is non empty set
((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l)))))) * ((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) is non empty Relation-like non empty-yielding (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Class (id BOOLEAN) -valued Function-like total quasi_total Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u)),(Class (id BOOLEAN)):]
ss (*) (((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l)))))) * ((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Function-like set
(ss (*) (((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l)))))) * ((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))))) . (SubTerms l) is set
ss (*) ((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l)))))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined Function-like set
(ss (*) ((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))))) (*) ((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (AllTermsOf u) -defined Function-like set
((ss (*) ((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))))) (*) ((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l))))) . (SubTerms l) is set
((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) . (SubTerms l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(ss (*) ((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))))) . (((AllTermsOf u),U,(II -TermEval),(abs (ar ((u -firstChar) . l)))) . (SubTerms l)) is set
(ss (*) ((((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN,(U,S,(abs (ar ((u -firstChar) . l)))),(id BOOLEAN),hhh) * (((abs (ar ((u -firstChar) . l))) -tuples_on U),(U,S,(abs (ar ((u -firstChar) . l))))))) . ((II -TermEval) (*) (SubTerms l)) is set
(BOOLEAN,(id BOOLEAN)) is non empty Relation-like non empty-yielding BOOLEAN -defined Class (id BOOLEAN) -valued Function-like total quasi_total onto Element of bool [:BOOLEAN,(Class (id BOOLEAN)):]
[:BOOLEAN,(Class (id BOOLEAN)):] is non empty Relation-like set
bool [:BOOLEAN,(Class (id BOOLEAN)):] is non empty set
(BOOLEAN,(id BOOLEAN)) * hhh is non empty Relation-like non empty-yielding (abs (ar ((u -firstChar) . l))) -tuples_on U -defined Class (id BOOLEAN) -valued Function-like total quasi_total Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),(Class (id BOOLEAN)):]
ss (*) ((BOOLEAN,(id BOOLEAN)) * hhh) is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined Function-like set
(ss (*) ((BOOLEAN,(id BOOLEAN)) * hhh)) . ((II -TermEval) (*) (SubTerms l)) is set
ss (*) (BOOLEAN,(id BOOLEAN)) is Relation-like BOOLEAN -defined Function-like set
(ss (*) (BOOLEAN,(id BOOLEAN))) (*) hhh is Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined Function-like set
((ss (*) (BOOLEAN,(id BOOLEAN))) (*) hhh) . ((II -TermEval) (*) (SubTerms l)) is set
(id BOOLEAN) * hhh is non empty Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:((abs (ar ((u -firstChar) . l))) -tuples_on U),BOOLEAN:]
((id BOOLEAN) * hhh) . ((II -TermEval) (*) (SubTerms l)) is boolean set
hhh . ((II -TermEval) (*) (SubTerms l)) is boolean set
U is set
u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u + 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 V166() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
AllTermsOf S is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() set
S -termsOfMaxDepth is Relation-like Function-like set
rng (S -termsOfMaxDepth) is set
union (rng (S -termsOfMaxDepth)) is set
TermSymbolsOf S is non empty 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 V166() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V166() 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
Funcs ((AllTermsOf S),(AllTermsOf S)) is non empty functional FUNCTION_DOMAIN of AllTermsOf S, AllTermsOf S
(S,U) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S, AllTermsOf S -interpreter-like Element of (AllTermsOf S) -InterpretersOf S
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V166() set
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
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf S
(AllTermsOf S) \/ BOOLEAN is non empty set
K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN)) is non empty functional M31((AllTermsOf S) * ,(AllTermsOf S) \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S,K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN))
(AllTermsOf S) -InterpretersOf S is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf S),K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN))) : b₁ is S, AllTermsOf S -interpreter-like } is set
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf S
((S,U),l) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf S),(AllTermsOf S)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf S),(AllTermsOf S))):]
[:NAT,(Funcs ((AllTermsOf S),(AllTermsOf S))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllTermsOf S),(AllTermsOf S))):] is non empty non trivial non finite V166() set
(((S,U),l) -TermEval) . (u + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf S),(AllTermsOf S))
II is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
((((S,U),l) -TermEval) . (u + 1)) . II 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 V166() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V166() 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 V233( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V166() set
K415((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) . II is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
ar ((S -firstChar) . II) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of S . ((S -firstChar) . II) is set
abs (ar ((S -firstChar) . II)) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
S -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
((AllSymbolsOf S) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf S) *
[:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf S) -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
(AllSymbolsOf S) -concatenation is non empty Relation-like [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf S) * ) Element of bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):]
[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf S) -concatenation) is non empty Relation-like (((AllSymbolsOf S) *) *) \ {{}} -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):]
(((AllSymbolsOf S) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf S) *) *)
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf S) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf S) *) *)
[:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf S) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
AllSymbolsOf S is non empty non trivial non finite V166() set
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(((AllSymbolsOf S) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) *)
((AllSymbolsOf S) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf S) *
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V166() set
(S,((S -firstChar) . II)) is non empty Relation-like non empty-yielding (((AllSymbolsOf S) *) \ {{}}) * -defined ((AllSymbolsOf S) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):]
[:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V166() set
(abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S) is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf S
(S,((S -firstChar) . II)) | ((abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S)) is Relation-like (((AllSymbolsOf S) *) \ {{}}) * -defined (abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S) -defined (((AllSymbolsOf S) *) \ {{}}) * -defined (abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S) -defined (((AllSymbolsOf S) *) \ {{}}) * -defined ((AllSymbolsOf S) *) \ {{}} -valued ((AllSymbolsOf S) *) \ {{}} -valued AllTermsOf S -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):]
[:((abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S)),(AllTermsOf S):] is non empty Relation-like set
bool [:((abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S)),(AllTermsOf S):] is non empty set
(S,((S -firstChar) . II),U) is non empty Relation-like (abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S) -defined (AllTermsOf S) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . II, AllTermsOf S
Jj is non empty Relation-like non empty-yielding (abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S) -defined AllTermsOf S -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S)),(AllTermsOf S):]
dom Jj is non empty functional finite-membered FinSequence-membered V166() Element of bool ((abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S))
bool ((abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S)) is non empty set
0 -tuples_on (AllTermsOf S) is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf S
dom ((S,((S -firstChar) . II)) | ((abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S))) is functional finite-membered FinSequence-membered V166() Element of bool ((abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S))
(S,U) . ((S -firstChar) . II) is non empty Relation-like (abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S) -defined (AllTermsOf S) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . II, AllTermsOf S
((S,U) . ((S -firstChar) . II)) . {} is set
Jj . {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((S,((S -firstChar) . II)) | ((abs (ar ((S -firstChar) . II))) -tuples_on (AllTermsOf S))) . {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(S,((S -firstChar) . II)) . {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
jJ is Relation-like NAT -defined ((AllSymbolsOf S) *) \ {{}} -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (((AllSymbolsOf S) *) \ {{}}) *
(S,((S -firstChar) . II),jJ) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf S) *) \ {{}}
<*((S -firstChar) . II)*> is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
[1,((S -firstChar) . II)] is non empty set
{[1,((S -firstChar) . II)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(S -multiCat) . jJ is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf S) *
<*((S -firstChar) . II)*> ^ ((S -multiCat) . jJ) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((S -firstChar) . II)*> null {} is Relation-like NAT -defined {} \/ (dom <*((S -firstChar) . II)*>) -defined Seg (1 + {}) -defined {} \/ (rng <*((S -firstChar) . II)*>) -valued Function-like finite len <*((S -firstChar) . II)*> -element total FinSequence-like FinSubsequence-like finite-support set
dom <*((S -firstChar) . II)*> is non empty trivial finite 1 -element set
{} \/ (dom <*((S -firstChar) . II)*>) is non empty finite set
1 + {} is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
Seg (1 + {}) is non empty 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
rng <*((S -firstChar) . II)*> is non empty trivial finite 1 -element set
{} \/ (rng <*((S -firstChar) . II)*>) is non empty finite set
len <*((S -firstChar) . II)*> is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
<*((S -firstChar) . II)*> \typed/ {} is Relation-like NAT -defined finite Element of bool (<*((S -firstChar) . II)*> \/ {})
<*((S -firstChar) . II)*> \/ {} is non empty Relation-like NAT -defined finite set
bool (<*((S -firstChar) . II)*> \/ {}) is non empty finite finite-membered set
<*((S -firstChar) . II)*> ^ {} is non empty Relation-like NAT -defined Function-like finite 1 + {} -element FinSequence-like FinSubsequence-like finite-support set
{} ^ <*((S -firstChar) . II)*> is non empty Relation-like NAT -defined Function-like finite {} + 1 -element {} + 1 -element FinSequence-like FinSubsequence-like finite-support 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
U is set
u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u + 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 V166() set
the U1 of S is set
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
AllTermsOf S is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() set
S -termsOfMaxDepth is Relation-like Function-like set
rng (S -termsOfMaxDepth) is set
union (rng (S -termsOfMaxDepth)) is set
Funcs ((AllTermsOf S),(AllTermsOf S)) is non empty functional FUNCTION_DOMAIN of AllTermsOf S, AllTermsOf S
(S,U) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S, AllTermsOf S -interpreter-like Element of (AllTermsOf S) -InterpretersOf S
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V166() 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
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf S
(AllTermsOf S) \/ BOOLEAN is non empty set
K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN)) is non empty functional M31((AllTermsOf S) * ,(AllTermsOf S) \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S,K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN))
(AllTermsOf S) -InterpretersOf S is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf S),K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN))) : b₁ is S, AllTermsOf S -interpreter-like } is set
S -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf S) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf S) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial non finite V166() set
(S -termsOfMaxDepth) . u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
id ((S -termsOfMaxDepth) . u) is non empty Relation-like non empty-yielding (S -termsOfMaxDepth) . u -defined (S -termsOfMaxDepth) . u -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:((S -termsOfMaxDepth) . u),((S -termsOfMaxDepth) . u):]
[:((S -termsOfMaxDepth) . u),((S -termsOfMaxDepth) . u):] is non empty Relation-like set
bool [:((S -termsOfMaxDepth) . u),((S -termsOfMaxDepth) . u):] is non empty set
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf S
((S,U),l) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf S),(AllTermsOf S)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf S),(AllTermsOf S))):]
[:NAT,(Funcs ((AllTermsOf S),(AllTermsOf S))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllTermsOf S),(AllTermsOf S))):] is non empty non trivial non finite V166() set
(((S,U),l) -TermEval) . (u + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf S),(AllTermsOf S))
((((S,U),l) -TermEval) . (u + 1)) | ((S -termsOfMaxDepth) . u) is Relation-like (S -termsOfMaxDepth) . u -defined Function-like 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 V166() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V166() 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 V233( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V166() set
K415((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):]
AllSymbolsOf S is non empty non trivial non finite V166() 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
(((S,U),l) -TermEval) . (0 + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf S),(AllTermsOf S))
(S -termsOfMaxDepth) . 0 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
((((S,U),l) -TermEval) . (0 + 1)) | ((S -termsOfMaxDepth) . 0) is Relation-like (S -termsOfMaxDepth) . 0 -defined Function-like set
id ((S -termsOfMaxDepth) . 0) is non empty Relation-like non empty-yielding (S -termsOfMaxDepth) . 0 -defined (S -termsOfMaxDepth) . 0 -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:((S -termsOfMaxDepth) . 0),((S -termsOfMaxDepth) . 0):]
[:((S -termsOfMaxDepth) . 0),((S -termsOfMaxDepth) . 0):] is non empty Relation-like set
bool [:((S -termsOfMaxDepth) . 0),((S -termsOfMaxDepth) . 0):] is non empty set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(((S,U),l) -TermEval) . X is Relation-like Function-like Element of Funcs ((AllTermsOf S),(AllTermsOf S))
[:(AllTermsOf S),(AllTermsOf S):] is non empty Relation-like set
bool [:(AllTermsOf S),(AllTermsOf S):] is non empty set
III is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S -termsOfMaxDepth) . III is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
[:((S -termsOfMaxDepth) . 0),(AllTermsOf S):] is non empty Relation-like set
bool [:((S -termsOfMaxDepth) . 0),(AllTermsOf S):] is non empty set
(((S,U),l) -TermEval) . 1 is Relation-like Function-like Element of Funcs ((AllTermsOf S),(AllTermsOf S))
((((S,U),l) -TermEval) . 1) | ((S -termsOfMaxDepth) . 0) is Relation-like (S -termsOfMaxDepth) . 0 -defined Function-like set
I is non empty Relation-like non empty-yielding (S -termsOfMaxDepth) . 0 -defined AllTermsOf S -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((S -termsOfMaxDepth) . 0),(AllTermsOf S):]
dom I is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool ((S -termsOfMaxDepth) . 0)
bool ((S -termsOfMaxDepth) . 0) is non empty set
j is set
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 V166() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V166() 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
Jj is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (S -termsOfMaxDepth) . III
I . j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support 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
(((S,U),l) -TermEval) . (0 + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf S),(AllTermsOf S))
jJ is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
((((S,U),l) -TermEval) . (0 + 1)) . jJ is set
III is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
III + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(((S,U),l) -TermEval) . (III + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf S),(AllTermsOf S))
(S -termsOfMaxDepth) . III is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
((((S,U),l) -TermEval) . (III + 1)) | ((S -termsOfMaxDepth) . III) is Relation-like (S -termsOfMaxDepth) . III -defined Function-like set
id ((S -termsOfMaxDepth) . III) is non empty Relation-like non empty-yielding (S -termsOfMaxDepth) . III -defined (S -termsOfMaxDepth) . III -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:((S -termsOfMaxDepth) . III),((S -termsOfMaxDepth) . III):]
[:((S -termsOfMaxDepth) . III),((S -termsOfMaxDepth) . III):] is non empty Relation-like set
bool [:((S -termsOfMaxDepth) . III),((S -termsOfMaxDepth) . III):] is non empty set
(III + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(((S,U),l) -TermEval) . ((III + 1) + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf S),(AllTermsOf S))
(S -termsOfMaxDepth) . (III + 1) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
((((S,U),l) -TermEval) . ((III + 1) + 1)) | ((S -termsOfMaxDepth) . (III + 1)) is Relation-like (S -termsOfMaxDepth) . (III + 1) -defined Function-like set
id ((S -termsOfMaxDepth) . (III + 1)) is non empty Relation-like non empty-yielding (S -termsOfMaxDepth) . (III + 1) -defined (S -termsOfMaxDepth) . (III + 1) -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:((S -termsOfMaxDepth) . (III + 1)),((S -termsOfMaxDepth) . (III + 1)):]
[:((S -termsOfMaxDepth) . (III + 1)),((S -termsOfMaxDepth) . (III + 1)):] is non empty Relation-like set
bool [:((S -termsOfMaxDepth) . (III + 1)),((S -termsOfMaxDepth) . (III + 1)):] is non empty set
(III + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
j is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(((S,U),l) -TermEval) . j is Relation-like Function-like Element of Funcs ((AllTermsOf S),(AllTermsOf S))
[:(AllTermsOf S),(AllTermsOf S):] is non empty Relation-like set
bool [:(AllTermsOf S),(AllTermsOf S):] 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 -termsOfMaxDepth) . I is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
[:((S -termsOfMaxDepth) . I),(AllTermsOf S):] is non empty Relation-like set
bool [:((S -termsOfMaxDepth) . I),(AllTermsOf S):] is non empty set
((((S,U),l) -TermEval) . j) | ((S -termsOfMaxDepth) . I) is Relation-like (S -termsOfMaxDepth) . I -defined Function-like set
Jj is non empty Relation-like non empty-yielding (S -termsOfMaxDepth) . I -defined AllTermsOf S -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((S -termsOfMaxDepth) . I),(AllTermsOf S):]
dom Jj is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool ((S -termsOfMaxDepth) . I)
bool ((S -termsOfMaxDepth) . I) is non empty set
id ((S -termsOfMaxDepth) . I) is non empty Relation-like non empty-yielding (S -termsOfMaxDepth) . I -defined (S -termsOfMaxDepth) . I -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:((S -termsOfMaxDepth) . I),((S -termsOfMaxDepth) . I):]
[:((S -termsOfMaxDepth) . I),((S -termsOfMaxDepth) . I):] is non empty Relation-like set
bool [:((S -termsOfMaxDepth) . I),((S -termsOfMaxDepth) . I):] is non empty set
dom (id ((S -termsOfMaxDepth) . I)) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool ((S -termsOfMaxDepth) . I)
jJ is set
X is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
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 -termsOfMaxDepth) . (X + 1) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((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 V166() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V166() 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
jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (S -termsOfMaxDepth) . (X + 1)
g is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal X + 1 -termal Element of ((AllSymbolsOf S) *) \ {{}}
(S -firstChar) . g is non relational termal own ofAtomicFormula Element of AllSymbolsOf S
ar ((S -firstChar) . g) 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) . g) is set
abs (ar ((S -firstChar) . g)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar ((S -firstChar) . g))) -tuples_on (AllTermsOf S) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf S
(S,((S -firstChar) . g),U) is non empty Relation-like (abs (ar ((S -firstChar) . g))) -tuples_on (AllTermsOf S) -defined (AllTermsOf S) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . g, AllTermsOf S
dom (S,((S -firstChar) . g),U) is non empty functional finite-membered FinSequence-membered Element of bool ((abs (ar ((S -firstChar) . g))) -tuples_on (AllTermsOf S))
bool ((abs (ar ((S -firstChar) . g))) -tuples_on (AllTermsOf S)) is non empty set
SubTerms g is Relation-like NAT -defined (S -termsOfMaxDepth) . X -valued (rng g) * -valued AllTermsOf S -valued Function-like finite abs (ar g) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
K335(((AllSymbolsOf S) *)) is non empty non trivial non finite V166() Element of bool (bool ((AllSymbolsOf S) *))
bool (bool ((AllSymbolsOf S) *)) is non empty non trivial non finite V166() set
S -termsOfMaxDepth is non empty Relation-like NAT -defined K335(((AllSymbolsOf S) *)) -valued Function-like total quasi_total Element of bool [:NAT,K335(((AllSymbolsOf S) *)):]
[:NAT,K335(((AllSymbolsOf S) *)):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335(((AllSymbolsOf S) *)):] is non empty non trivial non finite V166() set
(S -termsOfMaxDepth) . X is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335(((AllSymbolsOf S) *))
rng g is non empty finite set
(rng g) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng g
AllTermsOf S is non empty functional finite-membered FinSequence-membered AllSymbolsOf S -prefix S -prefix Element of bool ((AllSymbolsOf S) *)
ar g is finite complex ext-real V40() V41() Element of INT
abs (ar g) 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 finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf S) *
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) *)
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V166() set
n is Relation-like (S -termsOfMaxDepth) . III -valued Function-like Function-yielding V164() FinSequence-yielding set
Enn is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of dom (S,((S -firstChar) . g),U)
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(((AllSymbolsOf S) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) *)
((AllSymbolsOf S) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf S) *
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V166() set
(S,((S -firstChar) . g)) is non empty Relation-like non empty-yielding (((AllSymbolsOf S) *) \ {{}}) * -defined ((AllSymbolsOf S) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):]
[:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite V166() set
(S,((S -firstChar) . g)) | ((abs (ar ((S -firstChar) . g))) -tuples_on (AllTermsOf S)) is Relation-like (abs (ar ((S -firstChar) . g))) -tuples_on (AllTermsOf S) -defined (((AllSymbolsOf S) *) \ {{}}) * -defined (abs (ar ((S -firstChar) . g))) -tuples_on (AllTermsOf S) -defined (((AllSymbolsOf S) *) \ {{}}) * -defined ((AllSymbolsOf S) *) \ {{}} -valued ((AllSymbolsOf S) *) \ {{}} -valued AllTermsOf S -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):]
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf S) *) \ {{}}) *)
(((AllSymbolsOf S) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf S) *) \ {{}}
bool ((((AllSymbolsOf S) *) \ {{}}) *) is non empty non trivial non finite V166() set
n null ((S -termsOfMaxDepth) . III) is Relation-like ((S -termsOfMaxDepth) . III) \/ (dom n) -defined ((S -termsOfMaxDepth) . III) \/ (rng n) -valued Function-like set
dom n is set
((S -termsOfMaxDepth) . III) \/ (dom n) is non empty set
rng n is set
((S -termsOfMaxDepth) . III) \/ (rng n) is non empty set
n \typed/ ((S -termsOfMaxDepth) . III) is Element of bool (n \/ ((S -termsOfMaxDepth) . III))
n \/ ((S -termsOfMaxDepth) . III) is non empty set
bool (n \/ ((S -termsOfMaxDepth) . III)) is non empty set
id ((S -termsOfMaxDepth) . (X + 1)) is non empty Relation-like non empty-yielding (S -termsOfMaxDepth) . (X + 1) -defined (S -termsOfMaxDepth) . (X + 1) -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:((S -termsOfMaxDepth) . (X + 1)),((S -termsOfMaxDepth) . (X + 1)):]
[:((S -termsOfMaxDepth) . (X + 1)),((S -termsOfMaxDepth) . (X + 1)):] is non empty Relation-like set
bool [:((S -termsOfMaxDepth) . (X + 1)),((S -termsOfMaxDepth) . (X + 1)):] is non empty set
(id ((S -termsOfMaxDepth) . (X + 1))) . jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (S -termsOfMaxDepth) . (X + 1)
{((id ((S -termsOfMaxDepth) . (X + 1))) . jJ)} is non empty trivial functional finite finite-membered 1 -element FinSequence-membered V165() V166() Element of bool ((S -termsOfMaxDepth) . (X + 1))
bool ((S -termsOfMaxDepth) . (X + 1)) is non empty set
{jJ} is non empty trivial functional finite finite-membered 1 -element FinSequence-membered V165() V166() Element of bool ((S -termsOfMaxDepth) . (X + 1))
{((id ((S -termsOfMaxDepth) . (X + 1))) . jJ)} \ {jJ} 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V165() V166() V192() FinSequence-yielding finite-support Element of bool ((S -termsOfMaxDepth) . (X + 1))
{((id ((S -termsOfMaxDepth) . (X + 1))) . jJ)} typed\ {jJ} is trivial functional finite finite-membered FinSequence-membered V165() Element of bool {((id ((S -termsOfMaxDepth) . (X + 1))) . jJ)}
bool {((id ((S -termsOfMaxDepth) . (X + 1))) . jJ)} is non empty finite finite-membered set
{((id ((S -termsOfMaxDepth) . (X + 1))) . jJ)} \ {jJ} 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V165() V166() V192() FinSequence-yielding finite-support Element of bool {((id ((S -termsOfMaxDepth) . (X + 1))) . jJ)}
Jj . jJ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((((S,U),l) -TermEval) . j) . jJ is set
(S,U) . ((S -firstChar) . g) is non empty Relation-like (abs (ar ((S -firstChar) . g))) -tuples_on (AllTermsOf S) -defined (AllTermsOf S) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . g, AllTermsOf S
((S -termsOfMaxDepth) . III) |` n is Relation-like (S -termsOfMaxDepth) . III -valued (S -termsOfMaxDepth) . III -valued Function-like Function-yielding V164() FinSequence-yielding set
((((S,U),l) -TermEval) . (III + 1)) (*) (((S -termsOfMaxDepth) . III) |` n) is Relation-like Function-like set
((S,U) . ((S -firstChar) . g)) . (((((S,U),l) -TermEval) . (III + 1)) (*) (((S -termsOfMaxDepth) . III) |` n)) is set
(id ((S -termsOfMaxDepth) . III)) (*) n is Relation-like (S -termsOfMaxDepth) . III -valued Function-like Function-yielding V164() FinSequence-yielding set
((((S,U),l) -TermEval) . (III + 1)) (*) ((id ((S -termsOfMaxDepth) . III)) (*) n) is Relation-like Function-like set
((S,U) . ((S -firstChar) . g)) . (((((S,U),l) -TermEval) . (III + 1)) (*) ((id ((S -termsOfMaxDepth) . III)) (*) n)) is set
((((S,U),l) -TermEval) . (III + 1)) (*) (id ((S -termsOfMaxDepth) . III)) is Relation-like (S -termsOfMaxDepth) . III -defined Function-like set
(((((S,U),l) -TermEval) . (III + 1)) (*) (id ((S -termsOfMaxDepth) . III))) (*) n is Relation-like Function-like set
((S,U) . ((S -firstChar) . g)) . ((((((S,U),l) -TermEval) . (III + 1)) (*) (id ((S -termsOfMaxDepth) . III))) (*) n) is set
(((((S,U),l) -TermEval) . (III + 1)) | ((S -termsOfMaxDepth) . III)) (*) n is Relation-like Function-like set
((S,U) . ((S -firstChar) . g)) . ((((((S,U),l) -TermEval) . (III + 1)) | ((S -termsOfMaxDepth) . III)) (*) n) is set
((S,U) . ((S -firstChar) . g)) . (((S -termsOfMaxDepth) . III) |` n) is set
(S,((S -firstChar) . g),U) . n is set
En is Relation-like NAT -defined ((AllSymbolsOf S) *) \ {{}} -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (((AllSymbolsOf S) *) \ {{}}) *
(S,((S -firstChar) . g)) . En is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf S) *) \ {{}}
(S,((S -firstChar) . g),En) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf S) *) \ {{}}
<*((S -firstChar) . g)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf S) *) \ {{}}
[1,((S -firstChar) . g)] is non empty set
{[1,((S -firstChar) . g)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
S -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
[:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf S) -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
(AllSymbolsOf S) -concatenation is non empty Relation-like [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf S) * ) Element of bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):]
[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf S) -concatenation) is non empty Relation-like (((AllSymbolsOf S) *) *) \ {{}} -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):]
(((AllSymbolsOf S) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf S) *) *)
(((AllSymbolsOf S) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf S) *) *)
[:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf S) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
(S -multiCat) . En is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf S) *
<*((S -firstChar) . g)*> ^ ((S -multiCat) . En) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(id ((S -termsOfMaxDepth) . (III + 1))) . jJ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U is set
u is V51() V53() eligible Language-like
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
(u,U) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u, AllTermsOf u -interpreter-like Element of (AllTermsOf u) -InterpretersOf u
OwnSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
the U2 of u is Element of the U1 of u
the U3 of u is Element of the U1 of u
{ the U2 of u, the U3 of u} is non empty finite set
the U1 of u \ { the U2 of u, the U3 of u} is Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U2 of u, the U3 of u} is Element of bool the U1 of u
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf u
(AllTermsOf u) \/ BOOLEAN is non empty set
K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN)) is non empty functional M31((AllTermsOf u) * ,(AllTermsOf u) \/ BOOLEAN)
Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf u,K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))
(AllTermsOf u) -InterpretersOf u is non empty functional Element of bool (Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf u -defined K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))) : b₁ is u, AllTermsOf u -interpreter-like } is set
(u,U) -TermEval is non empty Relation-like non empty-yielding AllTermsOf u -defined AllTermsOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf u),(AllTermsOf u):]
[:(AllTermsOf u),(AllTermsOf u):] is non empty Relation-like set
bool [:(AllTermsOf u),(AllTermsOf u):] is non empty set
id (AllTermsOf u) is non empty Relation-like non empty-yielding AllTermsOf u -defined AllTermsOf u -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf u),(AllTermsOf u):]
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u
((u,U), the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf u),(AllTermsOf u)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf u),(AllTermsOf u))):]
Funcs ((AllTermsOf u),(AllTermsOf u)) is non empty functional FUNCTION_DOMAIN of AllTermsOf u, AllTermsOf u
[:NAT,(Funcs ((AllTermsOf u),(AllTermsOf u))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllTermsOf u),(AllTermsOf u))):] is non empty non trivial non finite V166() set
u -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf u) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf u) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf u) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf u) *) \ {{}})):] is non empty non trivial non finite V166() set
u -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
[:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(AllSymbolsOf u) -pr1 is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total V233( AllSymbolsOf u) Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
[:(AllSymbolsOf u),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf u),(AllSymbolsOf u)) is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
MultPlace ((AllSymbolsOf u) -pr1) is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
AllSymbolsOf u is non empty non trivial non finite V166() set
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u
UU is Relation-like Function-like set
j is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
UU . j is set
(u -termsOfMaxDepth) . j is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
j + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(u,U) -TermEval I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u
jJ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(((u,U), the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u) -TermEval) . jJ is Relation-like Function-like Element of Funcs ((AllTermsOf u),(AllTermsOf u))
(((u,U), the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u) -TermEval) . (j + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf u),(AllTermsOf u))
h is non empty Relation-like non empty-yielding AllTermsOf u -defined AllTermsOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf u),(AllTermsOf u):]
h | ((u -termsOfMaxDepth) . j) is Relation-like AllTermsOf u -defined (u -termsOfMaxDepth) . j -defined AllTermsOf u -defined AllTermsOf u -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf u),(AllTermsOf u):]
Jj is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (u -termsOfMaxDepth) . j
(h | ((u -termsOfMaxDepth) . j)) . Jj is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
h . Jj is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((h | ((u -termsOfMaxDepth) . j)) . Jj) \+\ (h . Jj) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
((h | ((u -termsOfMaxDepth) . j)) . Jj) \ (h . Jj) is Relation-like NAT -defined finite set
((h | ((u -termsOfMaxDepth) . j)) . Jj) typed\ (h . Jj) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((h | ((u -termsOfMaxDepth) . j)) . Jj)
bool ((h | ((u -termsOfMaxDepth) . j)) . Jj) is non empty finite finite-membered set
((h | ((u -termsOfMaxDepth) . j)) . Jj) \ (h . Jj) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((h | ((u -termsOfMaxDepth) . j)) . Jj)
(h . Jj) \ ((h | ((u -termsOfMaxDepth) . j)) . Jj) is Relation-like NAT -defined finite set
(h . Jj) typed\ ((h | ((u -termsOfMaxDepth) . j)) . Jj) is Relation-like NAT -defined Function-like finite finite-support Element of bool (h . Jj)
bool (h . Jj) is non empty finite finite-membered set
(h . Jj) \ ((h | ((u -termsOfMaxDepth) . j)) . Jj) is Relation-like NAT -defined Function-like finite finite-support Element of bool (h . Jj)
(((h | ((u -termsOfMaxDepth) . j)) . Jj) \ (h . Jj)) \/ ((h . Jj) \ ((h | ((u -termsOfMaxDepth) . j)) . Jj)) is Relation-like NAT -defined finite set
id ((u -termsOfMaxDepth) . j) is non empty Relation-like non empty-yielding (u -termsOfMaxDepth) . j -defined (u -termsOfMaxDepth) . j -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:((u -termsOfMaxDepth) . j),((u -termsOfMaxDepth) . j):]
[:((u -termsOfMaxDepth) . j),((u -termsOfMaxDepth) . j):] is non empty Relation-like set
bool [:((u -termsOfMaxDepth) . j),((u -termsOfMaxDepth) . j):] is non empty set
jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (u -termsOfMaxDepth) . j
(id ((u -termsOfMaxDepth) . j)) . jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (u -termsOfMaxDepth) . j
{((id ((u -termsOfMaxDepth) . j)) . jJ)} is non empty trivial functional finite finite-membered 1 -element FinSequence-membered V165() V166() Element of bool ((u -termsOfMaxDepth) . j)
bool ((u -termsOfMaxDepth) . j) is non empty set
{jJ} is non empty trivial functional finite finite-membered 1 -element FinSequence-membered V165() V166() Element of bool ((u -termsOfMaxDepth) . j)
{((id ((u -termsOfMaxDepth) . j)) . jJ)} \ {jJ} 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V165() V166() V192() FinSequence-yielding finite-support Element of bool ((u -termsOfMaxDepth) . j)
{((id ((u -termsOfMaxDepth) . j)) . jJ)} typed\ {jJ} is trivial functional finite finite-membered FinSequence-membered V165() Element of bool {((id ((u -termsOfMaxDepth) . j)) . jJ)}
bool {((id ((u -termsOfMaxDepth) . j)) . jJ)} is non empty finite finite-membered set
{((id ((u -termsOfMaxDepth) . j)) . jJ)} \ {jJ} 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V165() V166() V192() FinSequence-yielding finite-support Element of bool {((id ((u -termsOfMaxDepth) . j)) . jJ)}
(id (AllTermsOf u)) . I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u
{((id (AllTermsOf u)) . I)} is non empty trivial functional finite finite-membered 1 -element FinSequence-membered V165() V166() Element of bool (AllTermsOf u)
bool (AllTermsOf u) is non empty set
{I} is non empty trivial functional finite finite-membered 1 -element FinSequence-membered V165() V166() Element of bool (AllTermsOf u)
{((id (AllTermsOf u)) . I)} \ {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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V165() V166() V192() FinSequence-yielding finite-support Element of bool (AllTermsOf u)
{((id (AllTermsOf u)) . I)} typed\ {I} is trivial functional finite finite-membered FinSequence-membered V165() Element of bool {((id (AllTermsOf u)) . I)}
bool {((id (AllTermsOf u)) . I)} is non empty finite finite-membered set
{((id (AllTermsOf u)) . I)} \ {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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V165() V166() V192() FinSequence-yielding finite-support Element of bool {((id (AllTermsOf u)) . I)}
III is non empty Relation-like non empty-yielding AllTermsOf u -defined AllTermsOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf u),(AllTermsOf u):]
III . I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u
h . I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u
X is non empty Relation-like non empty-yielding AllTermsOf u -defined AllTermsOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf u),(AllTermsOf u):]
X . I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u
U is non empty set
u is non empty set
[:U,u:] is non empty Relation-like set
bool [:U,u:] is non empty set
S is Relation-like U -defined u -valued Element of bool [:U,u:]
(U,u,S,0) is Relation-like 0 -tuples_on U -defined 0 -tuples_on u -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:(0 -tuples_on U),(0 -tuples_on u):]
0 -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
0 -tuples_on u is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of u
[:(0 -tuples_on U),(0 -tuples_on u):] is non empty Relation-like set
bool [:(0 -tuples_on U),(0 -tuples_on u):] is non empty set
Seg 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 proper finite finite-yielding finite-membered cardinal 0 -element {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support 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 <= 0 ) } is set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined U -valued Function-like finite 0 -element FinSequence-like FinSubsequence-like finite-support Element of 0 -tuples_on U, b₂ is Relation-like NAT -defined u -valued Function-like finite 0 -element FinSequence-like FinSubsequence-like finite-support Element of 0 -tuples_on u : for b₃ being set holds
( not b₃ in Seg 0 or [(b₁ . b₃),(b₂ . b₃)] in S ) } is set
(U,u,S,0) \+\ (id {{}}) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(U,u,S,0) \ (id {{}}) is Relation-like 0 -tuples_on U -defined 0 -tuples_on u -valued set
(U,u,S,0) typed\ (id {{}}) is Relation-like 0 -tuples_on U -defined 0 -tuples_on u -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool (U,u,S,0)
bool (U,u,S,0) is non empty set
(U,u,S,0) \ (id {{}}) is Relation-like 0 -tuples_on U -defined 0 -tuples_on u -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool (U,u,S,0)
(id {{}}) \ (U,u,S,0) is Relation-like empty-yielding {{}} -defined {{}} -valued finite set
(id {{}}) typed\ (U,u,S,0) is Relation-like empty-yielding {{}} -defined {{}} -valued Function-like finite Function-yielding V164() finite-support Element of bool (id {{}})
(id {{}}) \ (U,u,S,0) is Relation-like empty-yielding {{}} -defined {{}} -valued Function-like finite Function-yielding V164() finite-support Element of bool (id {{}})
((U,u,S,0) \ (id {{}})) \/ ((id {{}}) \ (U,u,S,0)) is Relation-like set
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is V51() V53() eligible Language-like
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
Class S is non empty V165() V166() a_partition of U
l is Relation-like Function-like Function-yielding V164() u,U -interpreter-like (u,U,S) set
(u,U,S,l) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u, Class S -interpreter-like Element of (Class S) -InterpretersOf u
OwnSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
the U2 of u is Element of the U1 of u
the U3 of u is Element of the U1 of u
{ the U2 of u, the U3 of u} is non empty finite set
the U1 of u \ { the U2 of u, the U3 of u} is Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U2 of u, the U3 of u} is Element of bool the U1 of u
(Class S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of Class S
(Class S) \/ BOOLEAN is non empty set
K546(((Class S) *),((Class S) \/ BOOLEAN)) is non empty functional M31((Class S) * ,(Class S) \/ BOOLEAN)
Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf u,K546(((Class S) *),((Class S) \/ BOOLEAN))
(Class S) -InterpretersOf u is non empty functional Element of bool (Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf u -defined K546(((Class S) *),((Class S) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN))) : b₁ is u, Class S -interpreter-like } is set
(u,U,S,l) -TermEval is non empty Relation-like non empty-yielding AllTermsOf u -defined Class S -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),(Class S):]
[:(AllTermsOf u),(Class S):] is non empty Relation-like set
bool [:(AllTermsOf u),(Class S):] is non empty set
l -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(U,S) is non empty Relation-like non empty-yielding U -defined Class S -valued Function-like total quasi_total onto Element of bool [:U,(Class S):]
[:U,(Class S):] is non empty Relation-like set
bool [:U,(Class S):] is non empty set
(U,S) * (l -TermEval) is non empty Relation-like non empty-yielding AllTermsOf u -defined Class S -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),(Class S):]
u is V51() V53() eligible Language-like
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
U is set
(u,U) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u, AllTermsOf u -interpreter-like Element of (AllTermsOf u) -InterpretersOf u
OwnSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
the U2 of u is Element of the U1 of u
the U3 of u is Element of the U1 of u
{ the U2 of u, the U3 of u} is non empty finite set
the U1 of u \ { the U2 of u, the U3 of u} is Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U2 of u, the U3 of u} is Element of bool the U1 of u
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf u
(AllTermsOf u) \/ BOOLEAN is non empty set
K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN)) is non empty functional M31((AllTermsOf u) * ,(AllTermsOf u) \/ BOOLEAN)
Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf u,K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))
(AllTermsOf u) -InterpretersOf u is non empty functional Element of bool (Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf u -defined K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))) : b₁ is u, AllTermsOf u -interpreter-like } is set
(u,U) -TermEval is non empty Relation-like non empty-yielding AllTermsOf u -defined AllTermsOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf u),(AllTermsOf u):]
[:(AllTermsOf u),(AllTermsOf u):] is non empty Relation-like set
bool [:(AllTermsOf u),(AllTermsOf u):] is non empty set
id (AllTermsOf u) is non empty Relation-like non empty-yielding AllTermsOf u -defined AllTermsOf u -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf u),(AllTermsOf u):]
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
u is V51() V53() eligible Language-like
AtomicFormulaSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
AllSymbolsOf u is non empty non trivial non finite V166() set
TheNorSymbOf u is set
the U3 of u is Element of the U1 of u
{(TheNorSymbOf u)} is non empty trivial finite 1 -element set
(AllSymbolsOf u) \ {(TheNorSymbOf u)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
(AllSymbolsOf u) typed\ {(TheNorSymbOf u)} is Element of bool (AllSymbolsOf u)
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
S is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
u -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
[:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(AllSymbolsOf u) -pr1 is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total V233( AllSymbolsOf u) Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
[:(AllSymbolsOf u),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf u),(AllSymbolsOf u)) is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
MultPlace ((AllSymbolsOf u) -pr1) is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
l is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
(u -firstChar) . l is low-compounding relational ofAtomicFormula Element of AllSymbolsOf u
TheEqSymbOf u is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf u
the U2 of u is Element of the U1 of u
Class S is non empty V165() V166() a_partition of U
II is Relation-like Function-like Function-yielding V164() u,U -interpreter-like (u,U,S) set
(u,U,S,II) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u, Class S -interpreter-like Element of (Class S) -InterpretersOf u
OwnSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
{ the U2 of u, the U3 of u} is non empty finite set
the U1 of u \ { the U2 of u, the U3 of u} is Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U2 of u, the U3 of u} is Element of bool the U1 of u
(Class S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of Class S
(Class S) \/ BOOLEAN is non empty set
K546(((Class S) *),((Class S) \/ BOOLEAN)) is non empty functional M31((Class S) * ,(Class S) \/ BOOLEAN)
Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf u,K546(((Class S) *),((Class S) \/ BOOLEAN))
(Class S) -InterpretersOf u is non empty functional Element of bool (Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf u -defined K546(((Class S) *),((Class S) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf u),K546(((Class S) *),((Class S) \/ BOOLEAN))) : b₁ is u, Class S -interpreter-like } is set
(u,U,S,II) -AtomicEval l is boolean Element of BOOLEAN
(u,U,S,II) === is Relation-like Function-like Function-yielding V164() u, Class S -interpreter-like (u,U,S,II) -extension set
TheEqSymbOf u is Element of AtomicFormulaSymbolsOf u
(Class S) -deltaInterpreter is non empty Relation-like 2 -tuples_on (Class S) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on (Class S)),BOOLEAN:]
2 -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of Class S
[:(2 -tuples_on (Class S)),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on (Class S)),BOOLEAN:] is non empty set
[:((Class S) *),((Class S) *):] is non empty non trivial Relation-like non finite V166() set
(Class S) -concatenation is non empty Relation-like [:((Class S) *),((Class S) *):] -defined (Class S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((Class S) * ) Element of bool [:[:((Class S) *),((Class S) *):],((Class S) *):]
[:[:((Class S) *),((Class S) *):],((Class S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((Class S) *),((Class S) *):],((Class S) *):] is non empty non trivial non finite V166() set
1 -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of Class S
id (1 -tuples_on (Class S)) is non empty Relation-like non empty-yielding 1 -tuples_on (Class S) -defined 1 -tuples_on (Class S) -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(1 -tuples_on (Class S)),(1 -tuples_on (Class S)):]
[:(1 -tuples_on (Class S)),(1 -tuples_on (Class S)):] is non empty Relation-like set
bool [:(1 -tuples_on (Class S)),(1 -tuples_on (Class S)):] is non empty set
((Class S) -concatenation) .: (id (1 -tuples_on (Class S))) is functional finite-membered FinSequence-membered Element of bool ((Class S) *)
bool ((Class S) *) is non empty non trivial non finite V166() set
chi ((((Class S) -concatenation) .: (id (1 -tuples_on (Class S)))),(2 -tuples_on (Class S))) is non empty Relation-like 2 -tuples_on (Class S) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on (Class S)),BOOLEAN:]
(TheEqSymbOf u) .--> ((Class S) -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf u -defined {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on (Class S)),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf u)} is non empty trivial finite 1 -element set
{(TheEqSymbOf u)} --> ((Class S) -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on (Class S)),BOOLEAN:] -valued {((Class S) -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf u)},{((Class S) -deltaInterpreter)}:]
{((Class S) -deltaInterpreter)} is non empty trivial functional finite 1 -element V165() V166() set
[:{(TheEqSymbOf u)},{((Class S) -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf u)},{((Class S) -deltaInterpreter)}:] is non empty finite finite-membered set
(u,U,S,II) +* ((TheEqSymbOf u) .--> ((Class S) -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
((u,U,S,II) ===) . ((u -firstChar) . l) is non empty Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on (Class S) -defined (Class S) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . l, Class S
ar ((u -firstChar) . l) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
the adicity of u . ((u -firstChar) . l) is set
abs (ar ((u -firstChar) . l)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((u -firstChar) . l))) -tuples_on (Class S) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of Class S
SubTerms l is Relation-like NAT -defined (rng l) * -valued (TermSymbolsOf u) * -valued AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
rng l is non empty finite set
(rng l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng l
TermSymbolsOf u is non empty set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
(TermSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf u
AllTermsOf u is non empty functional finite-membered FinSequence-membered AllSymbolsOf u -prefix u -prefix Element of bool ((AllSymbolsOf u) *)
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
((AllSymbolsOf u) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf u) *
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf u) *) *)
bool (((AllSymbolsOf u) *) *) is non empty non trivial non finite V166() set
(u,U,S,II) -TermEval is non empty Relation-like non empty-yielding AllTermsOf u -defined Class S -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),(Class S):]
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
[:(AllTermsOf u),(Class S):] is non empty Relation-like set
bool [:(AllTermsOf u),(Class S):] is non empty set
((u,U,S,II) -TermEval) (*) (SubTerms l) is Relation-like NAT -defined Class S -valued Function-like finite finite-support set
(((u,U,S,II) ===) . ((u -firstChar) . l)) . (((u,U,S,II) -TermEval) (*) (SubTerms l)) is set
(u,U,S,II) -TruthEval l is boolean Element of BOOLEAN
II -AtomicEval l is boolean Element of BOOLEAN
II === is Relation-like Function-like Function-yielding V164() u,U -interpreter-like II -extension set
U -deltaInterpreter is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
2 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
[:(2 -tuples_on U),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on U),BOOLEAN:] is non empty set
U * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of U
[:(U *),(U *):] is non empty non trivial Relation-like non finite V166() set
U -concatenation is non empty Relation-like [:(U *),(U *):] -defined U * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233(U * ) Element of bool [:[:(U *),(U *):],(U *):]
[:[:(U *),(U *):],(U *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(U *),(U *):],(U *):] is non empty non trivial non finite V166() set
1 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
id (1 -tuples_on U) is non empty Relation-like non empty-yielding 1 -tuples_on U -defined 1 -tuples_on U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(1 -tuples_on U),(1 -tuples_on U):]
[:(1 -tuples_on U),(1 -tuples_on U):] is non empty Relation-like set
bool [:(1 -tuples_on U),(1 -tuples_on U):] is non empty set
(U -concatenation) .: (id (1 -tuples_on U)) is functional finite-membered FinSequence-membered Element of bool (U *)
bool (U *) is non empty non trivial non finite V166() set
chi (((U -concatenation) .: (id (1 -tuples_on U))),(2 -tuples_on U)) is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
(TheEqSymbOf u) .--> (U -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf u -defined {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf u)} --> (U -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued {(U -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:]
{(U -deltaInterpreter)} is non empty trivial functional finite 1 -element V165() V166() set
[:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty finite finite-membered set
II +* ((TheEqSymbOf u) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(II ===) . ((u -firstChar) . l) is non empty Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . l,U
(abs (ar ((u -firstChar) . l))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
U \/ BOOLEAN is non empty set
II -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(II -TermEval) (*) (SubTerms l) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((II ===) . ((u -firstChar) . l)) . ((II -TermEval) (*) (SubTerms l)) is set
U is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u is V51() V53() eligible Language-like
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
AllSymbolsOf u is non empty non trivial non finite V166() set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
u -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf u) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf u) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf u) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf u) *) \ {{}})):] is non empty non trivial non finite V166() set
(u -termsOfMaxDepth) . U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
[:((u -termsOfMaxDepth) . U),((u -termsOfMaxDepth) . U):] is non empty Relation-like set
bool [:((u -termsOfMaxDepth) . U),((u -termsOfMaxDepth) . U):] is non empty set
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
l is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
S SubstWith l is non empty Relation-like (AllSymbolsOf u) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):]
[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
(S SubstWith l) | ((u -termsOfMaxDepth) . U) is Relation-like (AllSymbolsOf u) * -defined (u -termsOfMaxDepth) . U -defined (AllSymbolsOf u) * -defined (AllSymbolsOf u) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):]
u -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
[:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(AllSymbolsOf u) -pr1 is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total V233( AllSymbolsOf u) Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
[:(AllSymbolsOf u),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf u),(AllSymbolsOf u)) is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
MultPlace ((AllSymbolsOf u) -pr1) is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
u -multiCat is non empty Relation-like ((AllSymbolsOf u) *) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):]
((AllSymbolsOf u) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf u) *
[:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -multiCat is non empty Relation-like ((AllSymbolsOf u) *) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):]
(AllSymbolsOf u) -concatenation is non empty Relation-like [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf u) * ) Element of bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):]
[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf u) -concatenation) is non empty Relation-like (((AllSymbolsOf u) *) *) \ {{}} -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):]
(((AllSymbolsOf u) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf u) *) *)
bool (((AllSymbolsOf u) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf u) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf u) *) *)
[:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf u) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
(AllSymbolsOf u) -concatenation is non empty Relation-like [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf u) * ) Element of bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):]
[:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf u) -concatenation) is non empty Relation-like (((AllSymbolsOf u) *) *) \ {{}} -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):]
((AllSymbolsOf u) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf u) *
(((AllSymbolsOf u) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf u) *) *)
bool (((AllSymbolsOf u) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf u) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf u) *) *)
[:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
TermSymbolsOf u is non empty set
the U3 of u is Element of the U1 of u
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
(u -termsOfMaxDepth) . 0 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
I is non empty trivial Relation-like NAT -defined TermSymbolsOf u -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf u) *) \ {{}}
(S SubstWith l) . I is Relation-like NAT -defined AllSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf u) *
(u -firstChar) . I is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
<*((u -firstChar) . I)*> is non empty trivial Relation-like NAT -defined TermSymbolsOf u -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf u) *) \ {{}}
[1,((u -firstChar) . I)] is non empty set
{[1,((u -firstChar) . I)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(S SubstWith l) . <*((u -firstChar) . I)*> is Relation-like NAT -defined AllSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf u) *
<*l*> is non empty trivial Relation-like NAT -defined TermSymbolsOf u -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf u) *) \ {{}}
[1,l] is non empty set
{[1,l]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(S SubstWith l) | ((u -termsOfMaxDepth) . 0) is Relation-like (AllSymbolsOf u) * -defined (u -termsOfMaxDepth) . 0 -defined (AllSymbolsOf u) * -defined (AllSymbolsOf u) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):]
[:((u -termsOfMaxDepth) . 0),((u -termsOfMaxDepth) . 0):] is non empty Relation-like set
bool [:((u -termsOfMaxDepth) . 0),((u -termsOfMaxDepth) . 0):] is non empty set
I is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(u -termsOfMaxDepth) . I is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
j is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
(S SubstWith l) | j is Relation-like (AllSymbolsOf u) * -defined j -defined (AllSymbolsOf u) * -defined (AllSymbolsOf u) * -valued Function-like total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):]
dom ((S SubstWith l) | j) is functional finite-membered FinSequence-membered Element of bool j
bool j is non empty set
jJ is set
jJ is non empty trivial Relation-like NAT -defined TermSymbolsOf u -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf u) *) \ {{}}
(u -firstChar) . jJ is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
h is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of j
((S SubstWith l) | j) . h is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(S SubstWith l) . h is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((S SubstWith l) | j) . h) \+\ ((S SubstWith l) . h) is Relation-like finite set
(((S SubstWith l) | j) . h) \ ((S SubstWith l) . h) is Relation-like NAT -defined finite set
(((S SubstWith l) | j) . h) typed\ ((S SubstWith l) . h) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((S SubstWith l) | j) . h)
bool (((S SubstWith l) | j) . h) is non empty finite finite-membered set
(((S SubstWith l) | j) . h) \ ((S SubstWith l) . h) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((S SubstWith l) | j) . h)
((S SubstWith l) . h) \ (((S SubstWith l) | j) . h) is Relation-like NAT -defined finite set
((S SubstWith l) . h) typed\ (((S SubstWith l) | j) . h) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((S SubstWith l) . h)
bool ((S SubstWith l) . h) is non empty finite finite-membered set
((S SubstWith l) . h) \ (((S SubstWith l) | j) . h) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((S SubstWith l) . h)
((((S SubstWith l) | j) . h) \ ((S SubstWith l) . h)) \/ (((S SubstWith l) . h) \ (((S SubstWith l) | j) . h)) is Relation-like NAT -defined finite set
((S SubstWith l) | j) . jJ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(S SubstWith l) . jJ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((S SubstWith l) | j) . jJ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
I is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u -termsOfMaxDepth) . I is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
(S SubstWith l) | ((u -termsOfMaxDepth) . I) is Relation-like (AllSymbolsOf u) * -defined (u -termsOfMaxDepth) . I -defined (AllSymbolsOf u) * -defined (AllSymbolsOf u) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):]
[:((u -termsOfMaxDepth) . I),((u -termsOfMaxDepth) . I):] is non empty Relation-like set
bool [:((u -termsOfMaxDepth) . I),((u -termsOfMaxDepth) . I):] is non empty 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
(u -termsOfMaxDepth) . (I + 1) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
(S SubstWith l) | ((u -termsOfMaxDepth) . (I + 1)) is Relation-like (AllSymbolsOf u) * -defined (u -termsOfMaxDepth) . (I + 1) -defined (AllSymbolsOf u) * -defined (AllSymbolsOf u) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):]
[:((u -termsOfMaxDepth) . (I + 1)),((u -termsOfMaxDepth) . (I + 1)):] is non empty Relation-like set
bool [:((u -termsOfMaxDepth) . (I + 1)),((u -termsOfMaxDepth) . (I + 1)):] is non empty set
j is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(u -termsOfMaxDepth) . j is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
Jj is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(u -termsOfMaxDepth) . Jj is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
[:((u -termsOfMaxDepth) . j),((u -termsOfMaxDepth) . j):] is non empty Relation-like set
bool [:((u -termsOfMaxDepth) . j),((u -termsOfMaxDepth) . j):] is non empty set
jJ is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
(S SubstWith l) | jJ is Relation-like (AllSymbolsOf u) * -defined jJ -defined (AllSymbolsOf u) * -defined (AllSymbolsOf u) * -valued Function-like total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):]
dom ((S SubstWith l) | jJ) is functional finite-membered FinSequence-membered Element of bool jJ
bool jJ is non empty set
G is set
j + 1 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 NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of jJ
Enn is non empty Relation-like NAT -defined TermSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal j + 1 -termal Element of ((AllSymbolsOf u) *) \ {{}}
SubTerms Enn is Relation-like NAT -defined (u -termsOfMaxDepth) . j -valued (rng Enn) * -valued AllTermsOf u -valued Function-like finite abs (ar Enn) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
K335(((AllSymbolsOf u) *)) is non empty non trivial non finite V166() Element of bool (bool ((AllSymbolsOf u) *))
bool (bool ((AllSymbolsOf u) *)) is non empty non trivial non finite V166() set
u -termsOfMaxDepth is non empty Relation-like NAT -defined K335(((AllSymbolsOf u) *)) -valued Function-like total quasi_total Element of bool [:NAT,K335(((AllSymbolsOf u) *)):]
[:NAT,K335(((AllSymbolsOf u) *)):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335(((AllSymbolsOf u) *)):] is non empty non trivial non finite V166() set
(u -termsOfMaxDepth) . j is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335(((AllSymbolsOf u) *))
rng Enn is non empty finite set
(rng Enn) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng Enn
AllTermsOf u is non empty functional finite-membered FinSequence-membered AllSymbolsOf u -prefix u -prefix Element of bool ((AllSymbolsOf u) *)
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
ar Enn is finite complex ext-real V40() V41() Element of INT
(u -firstChar) . Enn is non relational termal own ofAtomicFormula Element of AllSymbolsOf u
ar ((u -firstChar) . Enn) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of u . ((u -firstChar) . Enn) is set
abs (ar Enn) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf u) *) *)
g is non empty Relation-like non empty-yielding (u -termsOfMaxDepth) . j -defined (u -termsOfMaxDepth) . j -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((u -termsOfMaxDepth) . j),((u -termsOfMaxDepth) . j):]
dom g is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool ((u -termsOfMaxDepth) . j)
bool ((u -termsOfMaxDepth) . j) is non empty set
rng (SubTerms Enn) is finite set
(S SubstWith l) (*) (SubTerms Enn) is Relation-like NAT -defined (AllSymbolsOf u) * -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
g (*) (SubTerms Enn) is Relation-like NAT -defined (u -termsOfMaxDepth) . j -valued Function-like finite abs (ar Enn) -element len (SubTerms Enn) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support set
len (SubTerms Enn) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
nE is non relational termal own ofAtomicFormula Element of AllSymbolsOf u
ar nE is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of u . nE is set
abs (ar nE) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(((AllSymbolsOf u) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf u) *) \ {{}}
((u -termsOfMaxDepth) . j) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf u) *) \ {{}}) *)
bool ((((AllSymbolsOf u) *) \ {{}}) *) is non empty non trivial non finite V166() set
((S SubstWith l) | jJ) . n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(S SubstWith l) . n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((S SubstWith l) | jJ) . n) \+\ ((S SubstWith l) . n) is Relation-like finite set
(((S SubstWith l) | jJ) . n) \ ((S SubstWith l) . n) is Relation-like NAT -defined finite set
(((S SubstWith l) | jJ) . n) typed\ ((S SubstWith l) . n) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((S SubstWith l) | jJ) . n)
bool (((S SubstWith l) | jJ) . n) is non empty finite finite-membered set
(((S SubstWith l) | jJ) . n) \ ((S SubstWith l) . n) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((S SubstWith l) | jJ) . n)
((S SubstWith l) . n) \ (((S SubstWith l) | jJ) . n) is Relation-like NAT -defined finite set
((S SubstWith l) . n) typed\ (((S SubstWith l) | jJ) . n) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((S SubstWith l) . n)
bool ((S SubstWith l) . n) is non empty finite finite-membered set
((S SubstWith l) . n) \ (((S SubstWith l) | jJ) . n) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((S SubstWith l) . n)
((((S SubstWith l) | jJ) . n) \ ((S SubstWith l) . n)) \/ (((S SubstWith l) . n) \ (((S SubstWith l) | jJ) . n)) is Relation-like NAT -defined finite set
((S SubstWith l) | jJ) . G is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(S SubstWith l) . G is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*nE*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
[1,nE] is non empty set
{[1,nE]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(S SubstWith l) . <*nE*> is Relation-like NAT -defined AllSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf u) *
<*l*> is non empty trivial Relation-like NAT -defined TermSymbolsOf u -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf u) *) \ {{}}
[1,l] is non empty set
{[1,l]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
ar l 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of u . l is set
s is non relational termal own ofAtomicFormula Element of AllSymbolsOf u
<*s*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
[1,s] is non empty set
{[1,s]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
ar s is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of u . 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
hhh is Relation-like NAT -defined (u -termsOfMaxDepth) . j -valued Function-like finite abs (ar nE) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of ((u -termsOfMaxDepth) . j) *
(S SubstWith l) . Enn is Relation-like NAT -defined AllSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf u) *
<*((u -firstChar) . Enn)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
[1,((u -firstChar) . Enn)] is non empty set
{[1,((u -firstChar) . Enn)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(u -multiCat) . (SubTerms Enn) is Relation-like NAT -defined AllSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf u) *
<*((u -firstChar) . Enn)*> ^ ((u -multiCat) . (SubTerms Enn)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(S SubstWith l) . (<*((u -firstChar) . Enn)*> ^ ((u -multiCat) . (SubTerms Enn))) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(S SubstWith l) . ((u -multiCat) . (SubTerms Enn)) is Relation-like NAT -defined AllSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf u) *
((S SubstWith l) . <*nE*>) ^ ((S SubstWith l) . ((u -multiCat) . (SubTerms Enn))) is Relation-like NAT -defined AllSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support set
ss is Relation-like NAT -defined (u -termsOfMaxDepth) . j -valued Function-like finite abs (ar s) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of ((u -termsOfMaxDepth) . j) *
(u,s,ss) is non empty Relation-like NAT -defined TermSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal j + 1 -termal Element of ((AllSymbolsOf u) *) \ {{}}
(u -multiCat) . ss is Relation-like NAT -defined AllSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf u) *
<*s*> ^ ((u -multiCat) . ss) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u -termsOfMaxDepth) . (j + 1) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is set
S is Element of AllSymbolsOf U
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
(u,S) -SymbolSubstIn l is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
l +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len l is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(len l) + 0 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng l is non empty finite set
l \/ (rng l) is non empty finite set
l null l is Relation-like NAT -defined l \/ (dom l) -defined l \/ (rng l) -valued Function-like finite len l -element FinSequence-like FinSubsequence-like finite-support set
dom l is non empty finite set
l \/ (dom l) is non empty finite set
l \typed/ l is Relation-like NAT -defined finite Element of bool (l \/ l)
l \/ l is non empty Relation-like NAT -defined finite set
bool (l \/ l) is non empty finite finite-membered set
(u,S) -SymbolSubstIn (l null l) is Relation-like NAT -defined Function-like finite len l -element FinSequence-like FinSubsequence-like finite-support set
(l null l) +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
II is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal l -termal Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,II) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
II +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
u SubstWith S is non empty Relation-like (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
U -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf U) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):]
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
[:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial non finite V166() set
(U -termsOfMaxDepth) . l is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
[:((U -termsOfMaxDepth) . l),((U -termsOfMaxDepth) . l):] is non empty Relation-like set
bool [:((U -termsOfMaxDepth) . l),((U -termsOfMaxDepth) . l):] is non empty set
(u SubstWith S) | ((U -termsOfMaxDepth) . l) is Relation-like (AllSymbolsOf U) * -defined (U -termsOfMaxDepth) . l -defined (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
III is non empty Relation-like non empty-yielding (U -termsOfMaxDepth) . l -defined (U -termsOfMaxDepth) . l -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((U -termsOfMaxDepth) . l),((U -termsOfMaxDepth) . l):]
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (U -termsOfMaxDepth) . l
III . X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (U -termsOfMaxDepth) . l
(u SubstWith S) . X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(III . X) \+\ ((u SubstWith S) . X) is Relation-like finite set
(III . X) \ ((u SubstWith S) . X) is Relation-like NAT -defined finite set
(III . X) typed\ ((u SubstWith S) . X) is Relation-like NAT -defined Function-like finite finite-support Element of bool (III . X)
bool (III . X) is non empty finite finite-membered set
(III . X) \ ((u SubstWith S) . X) is Relation-like NAT -defined Function-like finite finite-support Element of bool (III . X)
((u SubstWith S) . X) \ (III . X) is Relation-like NAT -defined finite set
((u SubstWith S) . X) typed\ (III . X) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((u SubstWith S) . X)
bool ((u SubstWith S) . X) is non empty finite finite-membered set
((u SubstWith S) . X) \ (III . X) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((u SubstWith S) . X)
((III . X) \ ((u SubstWith S) . X)) \/ (((u SubstWith S) . X) \ (III . X)) is Relation-like NAT -defined finite set
(u SubstWith S) . II is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
UU is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(U -termsOfMaxDepth) . UU is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
TermSymbolsOf U is non empty set
the U1 of U is set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllSymbolsOf U is non empty non trivial non finite V166() set
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
l is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
u is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
(U,S,l,u) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
u +~ (S,l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
U -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf U) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial non finite V166() set
x is Relation-like Function-like set
O is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
x . O is set
UU is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal O -termal Element of ((AllSymbolsOf U) *) \ {{}}
(U,S,l,UU) is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal O -termal Element of ((AllSymbolsOf U) *) \ {{}}
UU +~ (S,l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
III is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
[:(AllTermsOf U),(AllTermsOf U):] is non empty Relation-like set
bool [:(AllTermsOf U),(AllTermsOf U):] is non empty set
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
u SubstWith S is non empty Relation-like (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(u SubstWith S) | (AllTermsOf U) is Relation-like (AllSymbolsOf U) * -defined AllTermsOf U -defined (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(AllTermsOf U) /\ (((AllSymbolsOf U) *) \ {{}}) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(AllTermsOf U) typed/\ (((AllSymbolsOf U) *) \ {{}}) is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf U)
bool (AllTermsOf U) is non empty set
(AllTermsOf U) /\ (((AllSymbolsOf U) *) \ {{}}) is functional set
(AllTermsOf U) /\typed (((AllSymbolsOf U) *) \ {{}}) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf U) *) \ {{}})
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
(AllTermsOf U) null (((AllSymbolsOf U) *) \ {{}}) is set
(((AllSymbolsOf U) *) \ {{}}) /\ (AllTermsOf U) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf U) *) \ {{}})
(((AllSymbolsOf U) *) \ {{}}) typed/\ (AllTermsOf U) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf U) *) \ {{}})
(((AllSymbolsOf U) *) \ {{}}) /\ (AllTermsOf U) is functional set
(((AllSymbolsOf U) *) \ {{}}) /\typed (AllTermsOf U) is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf U)
(AllTermsOf U) \typed/ (((AllSymbolsOf U) *) \ {{}}) is functional finite-membered V165() Element of bool ((AllTermsOf U) \/ (((AllSymbolsOf U) *) \ {{}}))
(AllTermsOf U) \/ (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial functional non finite finite-membered V165() V166() set
bool ((AllTermsOf U) \/ (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
i is non empty functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(u SubstWith S) | i is Relation-like (AllSymbolsOf U) * -defined i -defined (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
dom ((u SubstWith S) | i) is functional finite-membered FinSequence-membered Element of bool i
bool i is non empty set
O is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
III is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of i
((u SubstWith S) | i) . III is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u SubstWith S) . III is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
(((u SubstWith S) | i) . III) \+\ ((u SubstWith S) . III) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((u SubstWith S) | i) . III) \ ((u SubstWith S) . III) is Relation-like NAT -defined finite set
(((u SubstWith S) | i) . III) typed\ ((u SubstWith S) . III) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((u SubstWith S) | i) . III)
bool (((u SubstWith S) | i) . III) is non empty finite finite-membered set
(((u SubstWith S) | i) . III) \ ((u SubstWith S) . III) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((u SubstWith S) | i) . III)
((u SubstWith S) . III) \ (((u SubstWith S) | i) . III) is Relation-like NAT -defined AllSymbolsOf U -valued finite set
((u SubstWith S) . III) typed\ (((u SubstWith S) | i) . III) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite finite-support Element of bool ((u SubstWith S) . III)
bool ((u SubstWith S) . III) is non empty finite finite-membered set
((u SubstWith S) . III) \ (((u SubstWith S) | i) . III) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite finite-support Element of bool ((u SubstWith S) . III)
((((u SubstWith S) | i) . III) \ ((u SubstWith S) . III)) \/ (((u SubstWith S) . III) \ (((u SubstWith S) | i) . III)) is Relation-like NAT -defined finite set
UU is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,UU) is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
UU +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((u SubstWith S) | i) . O is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AtomicFormulaSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
TheNorSymbOf U is set
the U3 of U is Element of the U1 of U
{(TheNorSymbOf U)} is non empty trivial finite 1 -element set
(AllSymbolsOf U) \ {(TheNorSymbOf U)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
(AllSymbolsOf U) typed\ {(TheNorSymbOf U)} is Element of bool (AllSymbolsOf U)
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
l is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,l) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
l +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
u SubstWith S is non empty Relation-like (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(AllTermsOf U) /\ (((AllSymbolsOf U) *) \ {{}}) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(AllTermsOf U) typed/\ (((AllSymbolsOf U) *) \ {{}}) is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf U)
bool (AllTermsOf U) is non empty set
(AllTermsOf U) /\ (((AllSymbolsOf U) *) \ {{}}) is functional set
(AllTermsOf U) /\typed (((AllSymbolsOf U) *) \ {{}}) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf U) *) \ {{}})
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
(AllTermsOf U) null (((AllSymbolsOf U) *) \ {{}}) is set
(((AllSymbolsOf U) *) \ {{}}) /\ (AllTermsOf U) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf U) *) \ {{}})
(((AllSymbolsOf U) *) \ {{}}) typed/\ (AllTermsOf U) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf U) *) \ {{}})
(((AllSymbolsOf U) *) \ {{}}) /\ (AllTermsOf U) is functional set
(((AllSymbolsOf U) *) \ {{}}) /\typed (AllTermsOf U) is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf U)
(AllTermsOf U) \typed/ (((AllSymbolsOf U) *) \ {{}}) is functional finite-membered V165() Element of bool ((AllTermsOf U) \/ (((AllSymbolsOf U) *) \ {{}}))
(AllTermsOf U) \/ (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial functional non finite finite-membered V165() V166() set
bool ((AllTermsOf U) \/ (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
[:(AllTermsOf U),(AllTermsOf U):] is non empty Relation-like set
bool [:(AllTermsOf U),(AllTermsOf U):] is non empty set
(u SubstWith S) | (AllTermsOf U) is Relation-like (AllSymbolsOf U) * -defined AllTermsOf U -defined (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
I is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
ar I is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . I is set
abs (ar I) 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 trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,I] is non empty set
{[1,I]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
j is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar I) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
(U -multiCat) . j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*I*> ^ ((U -multiCat) . j) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
jJ is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar I) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf U
X is non empty Relation-like non empty-yielding AllTermsOf U -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf U),(AllTermsOf U):]
X * jJ is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar I) -element len jJ -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf U
len jJ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
III is non empty functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
III * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
rng j is finite set
dom X is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf U)
(u SubstWith S) . l is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
(u SubstWith S) . <*I*> is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
g is Relation-like NAT -defined (AllSymbolsOf U) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of ((AllSymbolsOf U) *) *
(U -multiCat) . g is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
(u SubstWith S) . ((U -multiCat) . g) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
((u SubstWith S) . <*I*>) ^ ((u SubstWith S) . ((U -multiCat) . g)) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*I*> ^ ((u SubstWith S) . ((U -multiCat) . g)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u SubstWith S) * g is Relation-like NAT -defined (AllSymbolsOf U) * -valued Function-like finite len g -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of (AllSymbolsOf U) *
len g is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(U -multiCat) . ((u SubstWith S) * g) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*I*> ^ ((U -multiCat) . ((u SubstWith S) * g)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
jJ is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar I) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
(U -multiCat) . jJ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*I*> ^ ((U -multiCat) . jJ) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U is V51() V53() eligible Language-like
u 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support u -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l is set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
u SubstWith S is non empty Relation-like (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u SubstWith S) . l is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
TheNorSymbOf U is non literal non low-compounding non relational non own Element of AllSymbolsOf U
the U3 of U is Element of the U1 of U
LettersOf U is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
{0} is non empty trivial functional finite finite-membered 1 -element V166() Element of bool NAT
0 * is non empty functional finite-membered FinSequence-membered FinSequenceSet of 0
{0} is non empty trivial functional finite finite-membered 1 -element V166() set
the adicity of U " {0} is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
x is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth x is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u SubstWith S) . x is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
AtomicFormulaSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
TheNorSymbOf U is set
{(TheNorSymbOf U)} is non empty trivial finite 1 -element set
(AllSymbolsOf U) \ {(TheNorSymbOf U)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
(AllSymbolsOf U) typed\ {(TheNorSymbOf U)} is Element of bool (AllSymbolsOf U)
UU is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,UU) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
UU +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
III is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth III 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support 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
U -formulasOfMaxDepth x is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
UU is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth UU is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u SubstWith S) . UU is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
AtomicFormulaSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
TheNorSymbOf U is set
{(TheNorSymbOf U)} is non empty trivial finite 1 -element set
(AllSymbolsOf U) \ {(TheNorSymbOf U)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
(AllSymbolsOf U) typed\ {(TheNorSymbOf U)} is Element of bool (AllSymbolsOf U)
X is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,X) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
X +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
I is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support 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
X -ExFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) \ {{}})
U -formulasOfMaxDepth X is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
{ (<*b₁*> ^ b₂) where b₁ is literal Element of LettersOf U, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of U -formulasOfMaxDepth X : verum } is set
I is literal Element of LettersOf U
<*I*> is non empty trivial Relation-like NAT -defined TermSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf U) *) \ {{}}
TermSymbolsOf U is non empty set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
[1,I] is non empty set
{[1,I]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
j is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of U -formulasOfMaxDepth X
<*I*> ^ j is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff exal Element of ((AllSymbolsOf U) *) \ {{}}
jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support X -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth jJ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth jJ) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(u SubstWith S) . jJ is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth g is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
Jj is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
<*Jj*> is non empty trivial Relation-like NAT -defined TermSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf U) *) \ {{}}
[1,Jj] is non empty set
{[1,Jj]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(u SubstWith S) . <*Jj*> is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*S*> is non empty trivial Relation-like NAT -defined TermSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf U) *) \ {{}}
[1,S] is non empty set
{[1,S]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
h is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
<*h*> is non empty trivial Relation-like NAT -defined TermSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf U) *) \ {{}}
[1,h] is non empty set
{[1,h]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
1 + (Depth g) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
<*h*> ^ g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff 1 + (Depth g) -wff non Depth g -wff wff exal Element of ((AllSymbolsOf U) *) \ {{}}
G is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non Depth g -wff 1 + (Depth g) -wff wff exal Element of ((AllSymbolsOf U) *) \ {{}}
Depth G is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(Depth g) + 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
X -NorFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) \ {{}})
U -formulasOfMaxDepth X is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
<*(TheNorSymbOf U)*> is non empty trivial Relation-like NAT -defined AllSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support FinSequence of AllSymbolsOf U
[1,(TheNorSymbOf U)] is non empty set
{[1,(TheNorSymbOf U)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
{ ((<*(TheNorSymbOf U)*> ^ b₁) ^ b₂) where b₁, b₂ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of U -formulasOfMaxDepth X : verum } is set
<*(TheNorSymbOf U)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of U -formulasOfMaxDepth X
<*(TheNorSymbOf U)*> ^ I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non exal Element of ((AllSymbolsOf U) *) \ {{}}
j is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of U -formulasOfMaxDepth X
(<*(TheNorSymbOf U)*> ^ I) ^ j is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non exal Element of ((AllSymbolsOf U) *) \ {{}}
Jj is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support X -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth Jj is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support X -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth jJ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((Depth Jj),(Depth jJ)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 + (Depth Jj) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(max ((Depth Jj),(Depth jJ))) - (Depth Jj) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
((max ((Depth Jj),(Depth jJ))) - (Depth Jj)) + (Depth Jj) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 + (Depth jJ) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(max ((Depth Jj),(Depth jJ))) - (Depth jJ) is finite complex ext-real V40() V41() set
((max ((Depth Jj),(Depth jJ))) - (Depth jJ)) + (Depth jJ) is finite complex ext-real V40() V41() set
(max ((Depth Jj),(Depth jJ))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(u SubstWith S) . Jj is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
(u SubstWith S) . jJ is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
G is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth G 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 finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth n is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
G is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth G 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 finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth n is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((Depth G),(Depth n)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
<*(TheNorSymbOf U)*> ^ G is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non exal Element of ((AllSymbolsOf U) *) \ {{}}
(<*(TheNorSymbOf U)*> ^ G) ^ n is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non max ((Depth G),(Depth n)) -wff wff non exal Element of ((AllSymbolsOf U) *) \ {{}}
Enn is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non max ((Depth G),(Depth n)) -wff wff non exal Element of ((AllSymbolsOf U) *) \ {{}}
Depth Enn is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
<*(TheNorSymbOf U)*> ^ Jj is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non exal Element of ((AllSymbolsOf U) *) \ {{}}
(u SubstWith S) . (<*(TheNorSymbOf U)*> ^ Jj) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
((u SubstWith S) . (<*(TheNorSymbOf U)*> ^ Jj)) ^ ((u SubstWith S) . jJ) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u SubstWith S) . <*(TheNorSymbOf U)*> is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
((u SubstWith S) . <*(TheNorSymbOf U)*>) ^ ((u SubstWith S) . Jj) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((u SubstWith S) . <*(TheNorSymbOf U)*>) ^ ((u SubstWith S) . Jj)) ^ n is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
S null u is Relation-like NAT -defined u \/ (dom S) -defined u \/ (rng S) -valued Function-like finite len S -element FinSequence-like FinSubsequence-like finite-support set
dom S is non empty finite set
u \/ (dom S) is non empty finite set
rng S is non empty finite set
u \/ (rng S) is non empty finite set
len S is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
S \typed/ u is finite Element of bool (S \/ u)
S \/ u is non empty finite set
bool (S \/ u) is non empty finite finite-membered set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,S,u) is non empty Relation-like NAT -defined S \/ (dom u) -defined S \/ (rng u) -valued Function-like finite len u -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
dom u is non empty finite set
S \/ (dom u) is non empty finite set
rng u is non empty finite set
S \/ (rng u) is non empty finite set
len u is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
u \typed/ S is finite Element of bool (u \/ S)
u \/ S is non empty finite set
bool (u \/ S) is non empty finite finite-membered set
u null S is Relation-like NAT -defined S \/ (dom u) -defined S \/ (rng u) -valued Function-like finite len u -element FinSequence-like FinSubsequence-like finite-support set
Depth u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth u) + S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(Depth u) + (0 * S) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
u is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support u -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u - (Depth S) is finite complex ext-real V40() V41() set
(Depth S) - (Depth S) is finite complex ext-real V40() V41() set
II is ext-real set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support l -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,II) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
II +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
Depth II is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u SubstWith S is non empty Relation-like (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
l - (Depth II) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u SubstWith S) . II is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
O is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth O 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
(Depth O) + x is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(U,x,O) is non empty Relation-like NAT -defined x \/ (dom O) -defined x \/ (rng O) -valued Function-like finite len O -element FinSequence-like FinSubsequence-like finite-support (Depth O) + x -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
dom O is non empty finite set
x \/ (dom O) is non empty finite set
rng O is non empty finite set
x \/ (rng O) is non empty finite set
len O is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
O \typed/ x is finite Element of bool (O \/ x)
O \/ x is non empty finite set
bool (O \/ x) is non empty finite finite-membered set
O null x is Relation-like NAT -defined x \/ (dom O) -defined x \/ (rng O) -valued Function-like finite len O -element FinSequence-like FinSubsequence-like finite-support set
III is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,l) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
l +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
E is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
i is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(U,u,S,l) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
l +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
Depth (U,u,S,l) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u SubstWith S is non empty Relation-like (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(u SubstWith S) . l is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
i is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth i is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,l) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
l +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
Depth (U,u,S,l) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
Depth l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth (U,u,S,l)) \+\ (Depth l) is finite set
(Depth (U,u,S,l)) \ (Depth l) is finite set
(Depth (U,u,S,l)) typed\ (Depth l) is finite Element of bool (Depth (U,u,S,l))
bool (Depth (U,u,S,l)) is non empty finite finite-membered set
(Depth (U,u,S,l)) \ (Depth l) is finite Element of bool (Depth (U,u,S,l))
(Depth l) \ (Depth (U,u,S,l)) is finite set
(Depth l) typed\ (Depth (U,u,S,l)) is finite Element of bool (Depth l)
bool (Depth l) is non empty finite finite-membered set
(Depth l) \ (Depth (U,u,S,l)) is finite Element of bool (Depth l)
((Depth (U,u,S,l)) \ (Depth l)) \/ ((Depth l) \ (Depth (U,u,S,l))) is finite set
II is set
U is set
u is V51() V53() eligible Language-like
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
AllSymbolsOf u is non empty non trivial non finite V166() set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
(((AllSymbolsOf u) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf u) *) \ {{}}
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf u) *) \ {{}}) *)
bool ((((AllSymbolsOf u) *) \ {{}}) *) is non empty non trivial non finite V166() set
AtomicFormulasOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of bool (((AllSymbolsOf u) *) \ {{}})
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}} : b₁ is 0wff } is set
chi (U,(AtomicFormulasOf u)) is non empty Relation-like AtomicFormulasOf u -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(AtomicFormulasOf u),BOOLEAN:]
[:(AtomicFormulasOf u),BOOLEAN:] is non empty Relation-like set
bool [:(AtomicFormulasOf u),BOOLEAN:] is non empty set
S is ofAtomicFormula Element of AllSymbolsOf u
ar S is finite complex ext-real V40() V41() Element of INT
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
the U3 of u is Element of the U1 of u
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
the adicity of u . 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
(u,S,U) is non empty Relation-like (abs (ar S)) -tuples_on (AllTermsOf u) -defined (AllTermsOf u) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of S, AllTermsOf u
(abs (ar S)) -tuples_on (AllTermsOf u) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf u
(AllTermsOf u) \/ BOOLEAN is non empty set
(u,S) is non empty Relation-like non empty-yielding (((AllSymbolsOf u) *) \ {{}}) * -defined ((AllSymbolsOf u) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf u) *) \ {{}}) *),(((AllSymbolsOf u) *) \ {{}}):]
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
(((AllSymbolsOf u) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf u) *) *)
((AllSymbolsOf u) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf u) *
bool (((AllSymbolsOf u) *) *) is non empty non trivial non finite V166() set
[:((((AllSymbolsOf u) *) \ {{}}) *),(((AllSymbolsOf u) *) \ {{}}):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf u) *) \ {{}}) *),(((AllSymbolsOf u) *) \ {{}}):] is non empty non trivial non finite V166() set
(u,S) | ((abs (ar S)) -tuples_on (AllTermsOf u)) is Relation-like (abs (ar S)) -tuples_on (AllTermsOf u) -defined (((AllSymbolsOf u) *) \ {{}}) * -defined ((AllSymbolsOf u) *) \ {{}} -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf u) *) \ {{}}) *),(((AllSymbolsOf u) *) \ {{}}):]
X is Relation-like NAT -defined AllTermsOf u -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
(u,S,U) . X is set
(u,S,X) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
<*S*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
[1,S] is non empty set
{[1,S]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
u -multiCat is non empty Relation-like ((AllSymbolsOf u) *) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):]
((AllSymbolsOf u) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf u) *
[:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -multiCat is non empty Relation-like ((AllSymbolsOf u) *) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):]
(AllSymbolsOf u) -concatenation is non empty Relation-like [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf u) * ) Element of bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):]
[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf u) -concatenation) is non empty Relation-like (((AllSymbolsOf u) *) *) \ {{}} -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):]
(((AllSymbolsOf u) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf u) *) *)
bool (((AllSymbolsOf u) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf u) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf u) *) *)
[:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf u) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
(u -multiCat) . X is Relation-like NAT -defined AllSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf u) *
<*S*> ^ ((u -multiCat) . X) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(chi (U,(AtomicFormulasOf u))) . (u,S,X) is boolean set
dom (u,S) is non empty functional finite-membered FinSequence-membered Element of bool ((((AllSymbolsOf u) *) \ {{}}) *)
bool ((((AllSymbolsOf u) *) \ {{}}) *) is non empty non trivial non finite V166() set
((u,S) | ((abs (ar S)) -tuples_on (AllTermsOf u))) . X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,S) . X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
(chi (U,(AtomicFormulasOf u))) * ((u,S) | ((abs (ar S)) -tuples_on (AllTermsOf u))) is Relation-like (abs (ar S)) -tuples_on (AllTermsOf u) -defined (((AllSymbolsOf u) *) \ {{}}) * -defined BOOLEAN -valued Function-like Element of bool [:((((AllSymbolsOf u) *) \ {{}}) *),BOOLEAN:]
[:((((AllSymbolsOf u) *) \ {{}}) *),BOOLEAN:] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf u) *) \ {{}}) *),BOOLEAN:] is non empty non trivial non finite V166() set
(chi (U,(AtomicFormulasOf u))) * (u,S) is Relation-like (((AllSymbolsOf u) *) \ {{}}) * -defined BOOLEAN -valued Function-like Element of bool [:((((AllSymbolsOf u) *) \ {{}}) *),BOOLEAN:]
((chi (U,(AtomicFormulasOf u))) * (u,S)) | ((abs (ar S)) -tuples_on (AllTermsOf u)) is Relation-like (abs (ar S)) -tuples_on (AllTermsOf u) -defined (((AllSymbolsOf u) *) \ {{}}) * -defined BOOLEAN -valued Function-like Element of bool [:((((AllSymbolsOf u) *) \ {{}}) *),BOOLEAN:]
((chi (U,(AtomicFormulasOf u))) * (u,S)) . X is set
(chi (U,(AtomicFormulasOf u))) . ((u,S) . X) is boolean set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
<* the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U*> is non empty trivial Relation-like NAT -defined TermSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf U) *) \ {{}}
[1, the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U] is non empty set
{[1, the literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
u is non empty trivial Relation-like NAT -defined TermSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf U) *) \ {{}}
AtomicFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : b₁ is 0wff } is set
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff Element of AtomicFormulasOf U is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff Element of AtomicFormulasOf U
U is set
u is non empty set
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l is V51() V53() eligible Language-like
AllSymbolsOf l is non empty non trivial non finite V166() set
the U1 of l is set
AllSymbolsOf l is non empty non trivial non finite V166() set
(AllSymbolsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf l
((AllSymbolsOf l) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf l) *)
bool ((AllSymbolsOf l) *) is non empty non trivial non finite V166() set
((AllSymbolsOf l) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
AllTermsOf l is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
bool (((AllSymbolsOf l) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf l) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf l) *) \ {{}}))
bool (bool (((AllSymbolsOf l) *) \ {{}})) is non empty non trivial non finite V166() set
l -termsOfMaxDepth is Relation-like Function-like set
rng (l -termsOfMaxDepth) is set
union (rng (l -termsOfMaxDepth)) is set
Funcs ((AllTermsOf l),(AllTermsOf l)) is non empty functional FUNCTION_DOMAIN of AllTermsOf l, AllTermsOf l
(l,U) is Relation-like OwnSymbolsOf l -defined Function-like total Function-yielding V164() l, AllTermsOf l -interpreter-like Element of (AllTermsOf l) -InterpretersOf l
OwnSymbolsOf l is non empty Element of bool (AllSymbolsOf l)
bool (AllSymbolsOf l) is non empty non trivial non finite V166() set
the U2 of l is Element of the U1 of l
the U3 of l is Element of the U1 of l
{ the U2 of l, the U3 of l} is non empty finite set
the U1 of l \ { the U2 of l, the U3 of l} is Element of bool the U1 of l
bool the U1 of l is non empty set
the U1 of l typed\ { the U2 of l, the U3 of l} is Element of bool the U1 of l
(AllTermsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf l
(AllTermsOf l) \/ BOOLEAN is non empty set
K546(((AllTermsOf l) *),((AllTermsOf l) \/ BOOLEAN)) is non empty functional M31((AllTermsOf l) * ,(AllTermsOf l) \/ BOOLEAN)
Funcs ((OwnSymbolsOf l),K546(((AllTermsOf l) *),((AllTermsOf l) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf l,K546(((AllTermsOf l) *),((AllTermsOf l) \/ BOOLEAN))
(AllTermsOf l) -InterpretersOf l is non empty functional Element of bool (Funcs ((OwnSymbolsOf l),K546(((AllTermsOf l) *),((AllTermsOf l) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf l),K546(((AllTermsOf l) *),((AllTermsOf l) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf l -defined K546(((AllTermsOf l) *),((AllTermsOf l) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf l),K546(((AllTermsOf l) *),((AllTermsOf l) \/ BOOLEAN))) : b₁ is l, AllTermsOf l -interpreter-like } is set
l -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf l) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf l) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf l) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf l) *) \ {{}})):] is non empty non trivial non finite V166() set
(l -termsOfMaxDepth) . S is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
Funcs ((AllTermsOf l),u) is non empty functional FUNCTION_DOMAIN of AllTermsOf l,u
II is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
E is Relation-like Function-like Function-yielding V164() l,u -interpreter-like set
E -TermEval is non empty Relation-like AllTermsOf l -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),u:]
[:(AllTermsOf l),u:] is non empty Relation-like set
bool [:(AllTermsOf l),u:] is non empty set
i is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf l
(II,i) ReassignIn (l,U) is Relation-like OwnSymbolsOf l -defined Function-like total Function-yielding V164() l, AllTermsOf l -interpreter-like Element of (AllTermsOf l) -InterpretersOf l
{} .--> i is trivial Relation-like {{}} -defined AllTermsOf l -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> i is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf l -valued {i} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{i}:]
{i} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{i}:] is non empty Relation-like finite set
bool [:{{}},{i}:] is non empty finite finite-membered set
II .--> ({} .--> i) is trivial Relation-like AllSymbolsOf l -defined {II} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{II} is non empty trivial finite 1 -element set
{II} --> ({} .--> i) is non empty Relation-like {II} -defined {({} .--> i)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{II},{({} .--> i)}:]
{({} .--> i)} is non empty trivial functional finite finite-membered 1 -element set
[:{II},{({} .--> i)}:] is non empty Relation-like finite set
bool [:{II},{({} .--> i)}:] is non empty finite finite-membered set
(l,U) +* (II .--> ({} .--> i)) is Relation-like Function-like Function-yielding V164() set
(((II,i) ReassignIn (l,U)),i) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf l),(AllTermsOf l)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf l),(AllTermsOf l))):]
[:NAT,(Funcs ((AllTermsOf l),(AllTermsOf l))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllTermsOf l),(AllTermsOf l))):] is non empty non trivial non finite V166() set
((((II,i) ReassignIn (l,U)),i) -TermEval) . S is Relation-like Function-like Element of Funcs ((AllTermsOf l),(AllTermsOf l))
(E -TermEval) (*) (((((II,i) ReassignIn (l,U)),i) -TermEval) . S) is Relation-like u -valued Function-like set
((E -TermEval) (*) (((((II,i) ReassignIn (l,U)),i) -TermEval) . S)) | ((l -termsOfMaxDepth) . S) is Relation-like (l -termsOfMaxDepth) . S -defined u -valued Function-like set
(E -TermEval) . i is Element of u
(II,((E -TermEval) . i)) ReassignIn E is Relation-like Function-like Function-yielding V164() l,u -interpreter-like set
{} .--> ((E -TermEval) . i) is trivial Relation-like {{}} -defined u -valued Function-like one-to-one constant finite finite-support set
{{}} --> ((E -TermEval) . i) is non empty Relation-like {{}} -defined u -valued {((E -TermEval) . i)} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{((E -TermEval) . i)}:]
{((E -TermEval) . i)} is non empty trivial finite 1 -element set
[:{{}},{((E -TermEval) . i)}:] is non empty Relation-like finite set
bool [:{{}},{((E -TermEval) . i)}:] is non empty finite finite-membered set
II .--> ({} .--> ((E -TermEval) . i)) is trivial Relation-like AllSymbolsOf l -defined {II} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{II} --> ({} .--> ((E -TermEval) . i)) is non empty Relation-like {II} -defined {({} .--> ((E -TermEval) . i))} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{II},{({} .--> ((E -TermEval) . i))}:]
{({} .--> ((E -TermEval) . i))} is non empty trivial functional finite finite-membered 1 -element set
[:{II},{({} .--> ((E -TermEval) . i))}:] is non empty Relation-like finite set
bool [:{II},{({} .--> ((E -TermEval) . i))}:] is non empty finite finite-membered set
E +* (II .--> ({} .--> ((E -TermEval) . i))) is Relation-like Function-like Function-yielding V164() set
(((II,((E -TermEval) . i)) ReassignIn E),((E -TermEval) . i)) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf l),u) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf l),u)):]
[:NAT,(Funcs ((AllTermsOf l),u)):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllTermsOf l),u)):] is non empty non trivial non finite V166() set
((((II,((E -TermEval) . i)) ReassignIn E),((E -TermEval) . i)) -TermEval) . S is Relation-like Function-like Element of Funcs ((AllTermsOf l),u)
(((((II,((E -TermEval) . i)) ReassignIn E),((E -TermEval) . i)) -TermEval) . S) | ((l -termsOfMaxDepth) . S) is Relation-like (l -termsOfMaxDepth) . S -defined Function-like set
u -InterpretersOf l is non empty functional Element of bool (Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN))))
u * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of u
u \/ BOOLEAN is non empty set
K546((u *),(u \/ BOOLEAN)) is non empty functional M31(u * ,u \/ BOOLEAN)
Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf l,K546((u *),(u \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf l -defined K546((u *),(u \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN))) : b₁ is l,u -interpreter-like } is set
l -firstChar is non empty Relation-like ((AllSymbolsOf l) *) \ {{}} -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):]
[:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):] is non empty non trivial non finite V166() set
(AllSymbolsOf l) -firstChar is non empty Relation-like ((AllSymbolsOf l) *) \ {{}} -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):]
(AllSymbolsOf l) -pr1 is non empty Relation-like [:(AllSymbolsOf l),(AllSymbolsOf l):] -defined AllSymbolsOf l -valued Function-like total quasi_total V233( AllSymbolsOf l) Element of bool [:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):]
[:(AllSymbolsOf l),(AllSymbolsOf l):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf l),(AllSymbolsOf l)) is non empty Relation-like [:(AllSymbolsOf l),(AllSymbolsOf l):] -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):]
MultPlace ((AllSymbolsOf l) -pr1) is non empty Relation-like ((AllSymbolsOf l) *) \ {{}} -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):]
O is Element of u
(E,O) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf l),u) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf l),u)):]
((l,U),i) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf l),(AllTermsOf l)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf l),(AllTermsOf l))):]
(((II,((E -TermEval) . i)) ReassignIn E),O) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf l),u) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf l),u)):]
l -multiCat is non empty Relation-like ((AllSymbolsOf l) *) * -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf l) *) *),((AllSymbolsOf l) *):]
((AllSymbolsOf l) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf l) *
[:(((AllSymbolsOf l) *) *),((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf l) *) *),((AllSymbolsOf l) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf l) -multiCat is non empty Relation-like ((AllSymbolsOf l) *) * -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf l) *) *),((AllSymbolsOf l) *):]
(AllSymbolsOf l) -concatenation is non empty Relation-like [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):] -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf l) * ) Element of bool [:[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):],((AllSymbolsOf l) *):]
[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):],((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):],((AllSymbolsOf l) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf l) -concatenation) is non empty Relation-like (((AllSymbolsOf l) *) *) \ {{}} -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf l) *) *) \ {{}}),((AllSymbolsOf l) *):]
(((AllSymbolsOf l) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf l) *) *)
bool (((AllSymbolsOf l) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf l) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf l) *) *)
[:((((AllSymbolsOf l) *) *) \ {{}}),((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf l) *) *) \ {{}}),((AllSymbolsOf l) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf l) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
TermSymbolsOf l is non empty set
{ the U3 of l} is non empty trivial finite 1 -element set
the U1 of l \ { the U3 of l} is non empty Element of bool the U1 of l
the U1 of l typed\ { the U3 of l} is Element of bool the U1 of l
the adicity of l is non empty Relation-like the U1 of l \ { the U3 of l} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of l \ { the U3 of l}),INT:]
[:( the U1 of l \ { the U3 of l}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of l \ { the U3 of l}),INT:] is non empty non trivial non finite V166() set
the adicity of l " NAT is Element of bool ( the U1 of l \ { the U3 of l})
bool ( the U1 of l \ { the U3 of l}) is non empty set
En is non empty Relation-like NAT -defined TermSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf l) *) \ {{}}
Depth En is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
{II} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf l)
bool (AllSymbolsOf l) is non empty non trivial non finite V166() set
dom (II .--> ({} .--> i)) is trivial finite Element of bool {II}
bool {II} is non empty finite finite-membered set
dom (II .--> ({} .--> ((E -TermEval) . i))) is trivial finite Element of bool {II}
((II,i) ReassignIn (l,U)) . II is non empty Relation-like (abs (ar II)) -tuples_on (AllTermsOf l) -defined (AllTermsOf l) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of II, AllTermsOf l
ar II 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of l . II is set
abs (ar II) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(abs (ar II)) -tuples_on (AllTermsOf l) is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf l
(II .--> ({} .--> i)) . II is Relation-like Function-like set
((II,((E -TermEval) . i)) ReassignIn E) . II is non empty Relation-like (abs (ar II)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of II,u
(abs (ar II)) -tuples_on u is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of u
(II .--> ({} .--> ((E -TermEval) . i))) . II is Relation-like Function-like set
((((II,i) ReassignIn (l,U)),i) -TermEval) . 0 is Relation-like Function-like Element of Funcs ((AllTermsOf l),(AllTermsOf l))
(E -TermEval) (*) (((((II,i) ReassignIn (l,U)),i) -TermEval) . 0) is Relation-like u -valued Function-like set
(l -termsOfMaxDepth) . 0 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
((E -TermEval) (*) (((((II,i) ReassignIn (l,U)),i) -TermEval) . 0)) | ((l -termsOfMaxDepth) . 0) is Relation-like (l -termsOfMaxDepth) . 0 -defined u -valued Function-like set
((((II,((E -TermEval) . i)) ReassignIn E),O) -TermEval) . 0 is Relation-like Function-like Element of Funcs ((AllTermsOf l),u)
(((((II,((E -TermEval) . i)) ReassignIn E),O) -TermEval) . 0) | ((l -termsOfMaxDepth) . 0) is Relation-like (l -termsOfMaxDepth) . 0 -defined Function-like set
(AllTermsOf l) --> O is non empty Relation-like AllTermsOf l -defined u -valued Function-like constant total quasi_total Element of bool [:(AllTermsOf l),u:]
{O} is non empty trivial finite 1 -element set
[:(AllTermsOf l),{O}:] is non empty Relation-like set
dom ((AllTermsOf l) --> O) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf l)
bool (AllTermsOf l) is non empty set
(AllTermsOf l) --> i is non empty Relation-like non-empty non empty-yielding AllTermsOf l -defined AllTermsOf l -valued Function-like constant total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf l),(AllTermsOf l):]
[:(AllTermsOf l),(AllTermsOf l):] is non empty Relation-like set
bool [:(AllTermsOf l),(AllTermsOf l):] is non empty set
[:(AllTermsOf l),{i}:] is non empty Relation-like set
dom ((AllTermsOf l) --> i) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf l)
dom (E -TermEval) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf l)
((E,O) -TermEval) . 0 is Relation-like Function-like Element of Funcs ((AllTermsOf l),u)
(AllTermsOf l) --> ((E -TermEval) . i) is non empty Relation-like AllTermsOf l -defined u -valued Function-like constant total quasi_total Element of bool [:(AllTermsOf l),u:]
[:(AllTermsOf l),{((E -TermEval) . i)}:] is non empty Relation-like set
hhh is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
((((II,i) ReassignIn (l,U)),i) -TermEval) . hhh is Relation-like Function-like Element of Funcs ((AllTermsOf l),(AllTermsOf l))
(E -TermEval) (*) (((((II,i) ReassignIn (l,U)),i) -TermEval) . hhh) is Relation-like u -valued Function-like set
(l -termsOfMaxDepth) . hhh is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
((E -TermEval) (*) (((((II,i) ReassignIn (l,U)),i) -TermEval) . hhh)) | ((l -termsOfMaxDepth) . hhh) is Relation-like (l -termsOfMaxDepth) . hhh -defined u -valued Function-like set
((((II,((E -TermEval) . i)) ReassignIn E),O) -TermEval) . hhh is Relation-like Function-like Element of Funcs ((AllTermsOf l),u)
(((((II,((E -TermEval) . i)) ReassignIn E),O) -TermEval) . hhh) | ((l -termsOfMaxDepth) . hhh) is Relation-like (l -termsOfMaxDepth) . hhh -defined Function-like set
hhh + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
((((II,i) ReassignIn (l,U)),i) -TermEval) . (hhh + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf l),(AllTermsOf l))
(E -TermEval) (*) (((((II,i) ReassignIn (l,U)),i) -TermEval) . (hhh + 1)) is Relation-like u -valued Function-like set
(l -termsOfMaxDepth) . (hhh + 1) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
((E -TermEval) (*) (((((II,i) ReassignIn (l,U)),i) -TermEval) . (hhh + 1))) | ((l -termsOfMaxDepth) . (hhh + 1)) is Relation-like (l -termsOfMaxDepth) . (hhh + 1) -defined u -valued Function-like set
((((II,((E -TermEval) . i)) ReassignIn E),O) -TermEval) . (hhh + 1) is Relation-like Function-like Element of Funcs ((AllTermsOf l),u)
(((((II,((E -TermEval) . i)) ReassignIn E),O) -TermEval) . (hhh + 1)) | ((l -termsOfMaxDepth) . (hhh + 1)) is Relation-like (l -termsOfMaxDepth) . (hhh + 1) -defined Function-like set
bool (AllTermsOf l) is non empty set
ss is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(l -termsOfMaxDepth) . ss is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
s is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(l -termsOfMaxDepth) . s is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
((((II,((E -TermEval) . i)) ReassignIn E),O) -TermEval) . s is Relation-like Function-like Element of Funcs ((AllTermsOf l),u)
((E,O) -TermEval) . ss is Relation-like Function-like Element of Funcs ((AllTermsOf l),u)
((((II,((E -TermEval) . i)) ReassignIn E),O) -TermEval) . ss is Relation-like Function-like Element of Funcs ((AllTermsOf l),u)
((E,O) -TermEval) . s is Relation-like Function-like Element of Funcs ((AllTermsOf l),u)
((((II,i) ReassignIn (l,U)),i) -TermEval) . s is Relation-like Function-like Element of Funcs ((AllTermsOf l),(AllTermsOf l))
((((II,i) ReassignIn (l,U)),i) -TermEval) . ss is Relation-like Function-like Element of Funcs ((AllTermsOf l),(AllTermsOf l))
[:(AllTermsOf l),(AllTermsOf l):] is non empty Relation-like set
bool [:(AllTermsOf l),(AllTermsOf l):] is non empty set
A1 is non empty Relation-like non empty-yielding AllTermsOf l -defined AllTermsOf l -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf l),(AllTermsOf l):]
(E -TermEval) * A1 is non empty Relation-like AllTermsOf l -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),u:]
phi22 is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf l)
((E -TermEval) * A1) | phi22 is Relation-like AllTermsOf l -defined phi22 -defined AllTermsOf l -defined u -valued Function-like total Element of bool [:(AllTermsOf l),u:]
b1 is non empty Relation-like AllTermsOf l -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),u:]
b1 | phi22 is Relation-like AllTermsOf l -defined phi22 -defined AllTermsOf l -defined u -valued Function-like total Element of bool [:(AllTermsOf l),u:]
dom (((E -TermEval) * A1) | phi22) is functional finite-membered FinSequence-membered V165() Element of bool phi22
bool phi22 is non empty set
dom (b1 | phi22) is functional finite-membered FinSequence-membered V165() Element of bool phi22
t2 is set
dom ((E -TermEval) * A1) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf l)
s + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
E11 is non empty Relation-like NAT -defined TermSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal s + 1 -termal Element of ((AllSymbolsOf l) *) \ {{}}
SubTerms E11 is Relation-like NAT -defined (l -termsOfMaxDepth) . s -valued (rng E11) * -valued AllTermsOf l -valued Function-like finite abs (ar E11) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf l) *
K335(((AllSymbolsOf l) *)) is non empty non trivial non finite V166() Element of bool (bool ((AllSymbolsOf l) *))
bool (bool ((AllSymbolsOf l) *)) is non empty non trivial non finite V166() set
l -termsOfMaxDepth is non empty Relation-like NAT -defined K335(((AllSymbolsOf l) *)) -valued Function-like total quasi_total Element of bool [:NAT,K335(((AllSymbolsOf l) *)):]
[:NAT,K335(((AllSymbolsOf l) *)):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335(((AllSymbolsOf l) *)):] is non empty non trivial non finite V166() set
(l -termsOfMaxDepth) . s is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335(((AllSymbolsOf l) *))
rng E11 is non empty finite set
(rng E11) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng E11
AllTermsOf l is non empty functional finite-membered FinSequence-membered AllSymbolsOf l -prefix l -prefix Element of bool ((AllSymbolsOf l) *)
ar E11 is finite complex ext-real V40() V41() Element of INT
(l -firstChar) . E11 is non relational termal own ofAtomicFormula Element of AllSymbolsOf l
ar ((l -firstChar) . E11) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of l . ((l -firstChar) . E11) is set
abs (ar E11) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(AllTermsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf l) *) *)
abs (ar ((l -firstChar) . E11)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
c1 is non empty Relation-like AllTermsOf l -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),u:]
c1 * A1 is non empty Relation-like AllTermsOf l -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),u:]
(c1 * A1) | phi22 is Relation-like AllTermsOf l -defined phi22 -defined AllTermsOf l -defined u -valued Function-like total Element of bool [:(AllTermsOf l),u:]
EE1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of phi22
((c1 * A1) | phi22) . EE1 is set
(c1 * A1) . EE1 is set
(((c1 * A1) | phi22) . EE1) \+\ ((c1 * A1) . EE1) is set
(((c1 * A1) | phi22) . EE1) \ ((c1 * A1) . EE1) is set
(((c1 * A1) | phi22) . EE1) typed\ ((c1 * A1) . EE1) is Element of bool (((c1 * A1) | phi22) . EE1)
bool (((c1 * A1) | phi22) . EE1) is non empty set
(((c1 * A1) | phi22) . EE1) \ ((c1 * A1) . EE1) is Element of bool (((c1 * A1) | phi22) . EE1)
((c1 * A1) . EE1) \ (((c1 * A1) | phi22) . EE1) is set
((c1 * A1) . EE1) typed\ (((c1 * A1) | phi22) . EE1) is Element of bool ((c1 * A1) . EE1)
bool ((c1 * A1) . EE1) is non empty set
((c1 * A1) . EE1) \ (((c1 * A1) | phi22) . EE1) is Element of bool ((c1 * A1) . EE1)
((((c1 * A1) | phi22) . EE1) \ ((c1 * A1) . EE1)) \/ (((c1 * A1) . EE1) \ (((c1 * A1) | phi22) . EE1)) is set
(b1 | phi22) . EE1 is set
b1 . EE1 is set
((b1 | phi22) . EE1) \+\ (b1 . EE1) is set
((b1 | phi22) . EE1) \ (b1 . EE1) is set
((b1 | phi22) . EE1) typed\ (b1 . EE1) is Element of bool ((b1 | phi22) . EE1)
bool ((b1 | phi22) . EE1) is non empty set
((b1 | phi22) . EE1) \ (b1 . EE1) is Element of bool ((b1 | phi22) . EE1)
(b1 . EE1) \ ((b1 | phi22) . EE1) is set
(b1 . EE1) typed\ ((b1 | phi22) . EE1) is Element of bool (b1 . EE1)
bool (b1 . EE1) is non empty set
(b1 . EE1) \ ((b1 | phi22) . EE1) is Element of bool (b1 . EE1)
(((b1 | phi22) . EE1) \ (b1 . EE1)) \/ ((b1 . EE1) \ ((b1 | phi22) . EE1)) is set
(((E -TermEval) * A1) | phi22) . EE1 is set
((E -TermEval) * A1) . EE1 is set
((((E -TermEval) * A1) | phi22) . EE1) \+\ (((E -TermEval) * A1) . EE1) is set
((((E -TermEval) * A1) | phi22) . EE1) \ (((E -TermEval) * A1) . EE1) is set
((((E -TermEval) * A1) | phi22) . EE1) typed\ (((E -TermEval) * A1) . EE1) is Element of bool ((((E -TermEval) * A1) | phi22) . EE1)
bool ((((E -TermEval) * A1) | phi22) . EE1) is non empty set
((((E -TermEval) * A1) | phi22) . EE1) \ (((E -TermEval) * A1) . EE1) is Element of bool ((((E -TermEval) * A1) | phi22) . EE1)
(((E -TermEval) * A1) . EE1) \ ((((E -TermEval) * A1) | phi22) . EE1) is set
(((E -TermEval) * A1) . EE1) typed\ ((((E -TermEval) * A1) | phi22) . EE1) is Element of bool (((E -TermEval) * A1) . EE1)
bool (((E -TermEval) * A1) . EE1) is non empty set
(((E -TermEval) * A1) . EE1) \ ((((E -TermEval) * A1) | phi22) . EE1) is Element of bool (((E -TermEval) * A1) . EE1)
(((((E -TermEval) * A1) | phi22) . EE1) \ (((E -TermEval) * A1) . EE1)) \/ ((((E -TermEval) * A1) . EE1) \ ((((E -TermEval) * A1) | phi22) . EE1)) is set
((c1 * A1) | phi22) . t2 is set
(c1 * A1) . t2 is set
(b1 | phi22) . t2 is set
b1 . t2 is set
(((E -TermEval) * A1) | phi22) . t2 is set
((E -TermEval) * A1) . t2 is set
tt2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf l
(c1 * A1) . tt2 is Element of u
A1 . tt2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf l
c1 . (A1 . tt2) is Element of u
((c1 * A1) . tt2) \+\ (c1 . (A1 . tt2)) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
((c1 * A1) . tt2) \ (c1 . (A1 . tt2)) is set
((c1 * A1) . tt2) typed\ (c1 . (A1 . tt2)) is Element of bool ((c1 * A1) . tt2)
bool ((c1 * A1) . tt2) is non empty set
((c1 * A1) . tt2) \ (c1 . (A1 . tt2)) is Element of bool ((c1 * A1) . tt2)
(c1 . (A1 . tt2)) \ ((c1 * A1) . tt2) is set
(c1 . (A1 . tt2)) typed\ ((c1 * A1) . tt2) is Element of bool (c1 . (A1 . tt2))
bool (c1 . (A1 . tt2)) is non empty set
(c1 . (A1 . tt2)) \ ((c1 * A1) . tt2) is Element of bool (c1 . (A1 . tt2))
(((c1 * A1) . tt2) \ (c1 . (A1 . tt2))) \/ ((c1 . (A1 . tt2)) \ ((c1 * A1) . tt2)) is set
((E -TermEval) * A1) . tt2 is Element of u
(E -TermEval) . (A1 . tt2) is Element of u
(((E -TermEval) * A1) . tt2) \+\ ((E -TermEval) . (A1 . tt2)) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((E -TermEval) * A1) . tt2) \ ((E -TermEval) . (A1 . tt2)) is set
(((E -TermEval) * A1) . tt2) typed\ ((E -TermEval) . (A1 . tt2)) is Element of bool (((E -TermEval) * A1) . tt2)
bool (((E -TermEval) * A1) . tt2) is non empty set
(((E -TermEval) * A1) . tt2) \ ((E -TermEval) . (A1 . tt2)) is Element of bool (((E -TermEval) * A1) . tt2)
((E -TermEval) . (A1 . tt2)) \ (((E -TermEval) * A1) . tt2) is set
((E -TermEval) . (A1 . tt2)) typed\ (((E -TermEval) * A1) . tt2) is Element of bool ((E -TermEval) . (A1 . tt2))
bool ((E -TermEval) . (A1 . tt2)) is non empty set
((E -TermEval) . (A1 . tt2)) \ (((E -TermEval) * A1) . tt2) is Element of bool ((E -TermEval) . (A1 . tt2))
((((E -TermEval) * A1) . tt2) \ ((E -TermEval) . (A1 . tt2))) \/ (((E -TermEval) . (A1 . tt2)) \ (((E -TermEval) * A1) . tt2)) is set
(c1 * A1) . E11 is set
A1 . E11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
c1 . (A1 . E11) is set
c2 is non empty Relation-like non empty-yielding AllTermsOf l -defined AllTermsOf l -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf l),(AllTermsOf l):]
c2 (*) (SubTerms E11) is Relation-like NAT -defined AllTermsOf l -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l) is non empty functional finite-membered FinSequence-membered FinSequenceSet of AllTermsOf l
Y2 is Relation-like NAT -defined AllTermsOf l -valued Function-like finite abs (ar ((l -firstChar) . E11)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf l
(AllSymbolsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf l
((AllSymbolsOf l) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf l) *)
bool ((AllSymbolsOf l) *) is non empty non trivial non finite V166() set
((AllSymbolsOf l) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
(((AllSymbolsOf l) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf l) *) *)
((AllSymbolsOf l) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf l) *
bool (((AllSymbolsOf l) *) *) is non empty non trivial non finite V166() set
(l,((l -firstChar) . E11)) is non empty Relation-like non empty-yielding (((AllSymbolsOf l) *) \ {{}}) * -defined ((AllSymbolsOf l) *) \ {{}} -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf l) *) \ {{}}) *),(((AllSymbolsOf l) *) \ {{}}):]
[:((((AllSymbolsOf l) *) \ {{}}) *),(((AllSymbolsOf l) *) \ {{}}):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf l) *) \ {{}}) *),(((AllSymbolsOf l) *) \ {{}}):] is non empty non trivial non finite V166() set
(l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l)) is Relation-like (abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l) -defined (((AllSymbolsOf l) *) \ {{}}) * -defined (abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l) -defined (((AllSymbolsOf l) *) \ {{}}) * -defined ((AllSymbolsOf l) *) \ {{}} -valued ((AllSymbolsOf l) *) \ {{}} -valued AllTermsOf l -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf l) *) \ {{}}) *),(((AllSymbolsOf l) *) \ {{}}):]
f1 is Relation-like NAT -defined AllTermsOf l -valued Function-like finite abs (ar ((l -firstChar) . E11)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l)
((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(l,((l -firstChar) . E11)) . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1) \+\ ((l,((l -firstChar) . E11)) . f1) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1) \ ((l,((l -firstChar) . E11)) . f1) is Relation-like NAT -defined finite set
(((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1) typed\ ((l,((l -firstChar) . E11)) . f1) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1)
bool (((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1) is non empty finite finite-membered set
(((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1) \ ((l,((l -firstChar) . E11)) . f1) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1)
((l,((l -firstChar) . E11)) . f1) \ (((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1) is Relation-like NAT -defined finite set
((l,((l -firstChar) . E11)) . f1) typed\ (((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((l,((l -firstChar) . E11)) . f1)
bool ((l,((l -firstChar) . E11)) . f1) is non empty finite finite-membered set
((l,((l -firstChar) . E11)) . f1) \ (((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((l,((l -firstChar) . E11)) . f1)
((((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1) \ ((l,((l -firstChar) . E11)) . f1)) \/ (((l,((l -firstChar) . E11)) . f1) \ (((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . f1)) is Relation-like NAT -defined finite set
((l,((l -firstChar) . E11)) | ((abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l))) . Y2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(l,((l -firstChar) . E11)) . Y2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((E -TermEval) * A1) . E11 is set
({} .--> i) . {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(E -TermEval) . (({} .--> i) . {}) is set
b1 . E11 is set
({} .--> ((E -TermEval) . i)) . {} is set
(l,U) . ((l -firstChar) . E11) is non empty Relation-like (abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l) -defined (AllTermsOf l) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (l -firstChar) . E11, AllTermsOf l
((II,i) ReassignIn (l,U)) . ((l -firstChar) . E11) is non empty Relation-like (abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l) -defined (AllTermsOf l) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (l -firstChar) . E11, AllTermsOf l
(l,((l -firstChar) . E11),U) is non empty Relation-like (abs (ar ((l -firstChar) . E11))) -tuples_on (AllTermsOf l) -defined (AllTermsOf l) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (l -firstChar) . E11, AllTermsOf l
(((AllSymbolsOf l) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf l) *) \ {{}}
(AllTermsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf l) *) \ {{}}) *)
bool ((((AllSymbolsOf l) *) \ {{}}) *) is non empty non trivial non finite V166() set
(((II,i) ReassignIn (l,U)) . ((l -firstChar) . E11)) . Y2 is set
r2 is Relation-like NAT -defined AllTermsOf l -valued Function-like finite abs (ar ((l -firstChar) . E11)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf l) *
(l,((l -firstChar) . E11),r2) is non empty Relation-like NAT -defined TermSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf l) *) \ {{}}
<*((l -firstChar) . E11)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf l) *) \ {{}}
[1,((l -firstChar) . E11)] is non empty set
{[1,((l -firstChar) . E11)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(l -multiCat) . r2 is Relation-like NAT -defined AllSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf l) *
<*((l -firstChar) . E11)*> ^ ((l -multiCat) . r2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
r2 is non empty Relation-like NAT -defined TermSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf l) *) \ {{}}
Depth r2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
tt22 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
((E,O) -TermEval) . tt22 is Relation-like Function-like Element of Funcs ((AllTermsOf l),u)
(l -firstChar) . r2 is non relational termal own ofAtomicFormula Element of AllSymbolsOf l
r2 . 1 is set
SubTerms r2 is Relation-like NAT -defined (rng r2) * -valued AllTermsOf l -valued Function-like finite abs (ar r2) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf l) *
rng r2 is non empty finite set
(rng r2) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng r2
ar r2 is finite complex ext-real V40() V41() Element of INT
ar ((l -firstChar) . r2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of l . ((l -firstChar) . r2) is set
abs (ar r2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
c₃₀ is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf l)
c2 | c₃₀ is Relation-like AllTermsOf l -defined c₃₀ -defined AllTermsOf l -defined AllTermsOf l -valued Function-like total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf l),(AllTermsOf l):]
dom (c2 | c₃₀) is functional finite-membered FinSequence-membered V165() Element of bool c₃₀
bool c₃₀ is non empty set
phi2 is non empty Relation-like AllTermsOf l -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),u:]
phi2 | c₃₀ is Relation-like AllTermsOf l -defined c₃₀ -defined AllTermsOf l -defined u -valued Function-like total Element of bool [:(AllTermsOf l),u:]
dom (phi2 | c₃₀) is functional finite-membered FinSequence-membered V165() Element of bool c₃₀
rng (SubTerms E11) is finite set
((E -TermEval) * A1) . E11 is set
(E -TermEval) . r2 is set
E . ((l -firstChar) . E11) is non empty Relation-like (abs (ar ((l -firstChar) . E11))) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (l -firstChar) . E11,u
(abs (ar ((l -firstChar) . E11))) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
(E -TermEval) (*) (SubTerms r2) is Relation-like NAT -defined u -valued Function-like finite abs (ar r2) -element len (SubTerms r2) -element FinSequence-like FinSubsequence-like finite-support set
len (SubTerms r2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(E . ((l -firstChar) . E11)) . ((E -TermEval) (*) (SubTerms r2)) is set
(c2 | c₃₀) (*) (SubTerms E11) is Relation-like NAT -defined AllTermsOf l -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(E -TermEval) (*) ((c2 | c₃₀) (*) (SubTerms E11)) is Relation-like NAT -defined u -valued Function-like finite finite-support set
(E . ((l -firstChar) . E11)) . ((E -TermEval) (*) ((c2 | c₃₀) (*) (SubTerms E11))) is set
(E -TermEval) * (c2 | c₃₀) is Relation-like AllTermsOf l -defined u -valued Function-like Element of bool [:(AllTermsOf l),u:]
((E -TermEval) * (c2 | c₃₀)) (*) (SubTerms E11) is Relation-like NAT -defined u -valued Function-like finite finite-support set
(E . ((l -firstChar) . E11)) . (((E -TermEval) * (c2 | c₃₀)) (*) (SubTerms E11)) is set
(E -TermEval) * c2 is non empty Relation-like AllTermsOf l -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),u:]
((E -TermEval) * c2) | c₃₀ is Relation-like AllTermsOf l -defined c₃₀ -defined AllTermsOf l -defined u -valued Function-like total Element of bool [:(AllTermsOf l),u:]
(((E -TermEval) * c2) | c₃₀) (*) (SubTerms E11) is Relation-like NAT -defined u -valued Function-like finite finite-support set
(E . ((l -firstChar) . E11)) . ((((E -TermEval) * c2) | c₃₀) (*) (SubTerms E11)) is set
phi2 (*) (SubTerms E11) is Relation-like NAT -defined u -valued Function-like finite finite-support set
(E . ((l -firstChar) . E11)) . (phi2 (*) (SubTerms E11)) is set
((II,((E -TermEval) . i)) ReassignIn E) . ((l -firstChar) . E11) is non empty Relation-like (abs (ar ((l -firstChar) . E11))) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (l -firstChar) . E11,u
(((II,((E -TermEval) . i)) ReassignIn E) . ((l -firstChar) . E11)) . (phi2 (*) (SubTerms E11)) is set
b1 . E11 is set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
AtomicFormulaSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
TheNorSymbOf U is set
the U3 of U is Element of the U1 of U
{(TheNorSymbOf U)} is non empty trivial finite 1 -element set
(AllSymbolsOf U) \ {(TheNorSymbOf U)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
(AllSymbolsOf U) typed\ {(TheNorSymbOf U)} is Element of bool (AllSymbolsOf U)
U -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
[:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(AllSymbolsOf U) -pr1 is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total V233( AllSymbolsOf U) Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
[:(AllSymbolsOf U),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf U),(AllSymbolsOf U)) is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
MultPlace ((AllSymbolsOf U) -pr1) is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
l is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
(U -firstChar) . l is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
<*((U -firstChar) . l)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,((U -firstChar) . l)] is non empty set
{[1,((U -firstChar) . l)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
SubTerms l is Relation-like NAT -defined (rng l) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . l)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
ar ((U -firstChar) . l) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . ((U -firstChar) . l) is set
abs (ar ((U -firstChar) . l)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng l is non empty finite set
(rng l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng l
TermSymbolsOf U is non empty set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
(TermSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf U
AllTermsOf U is non empty functional finite-membered FinSequence-membered AllSymbolsOf U -prefix U -prefix Element of bool ((AllSymbolsOf U) *)
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
(U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
the U2 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) is non empty functional M31((AllTermsOf U) * ,(AllTermsOf U) \/ BOOLEAN)
Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U,K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))
(AllTermsOf U) -InterpretersOf U is non empty functional Element of bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf U -defined K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) : b₁ is U, AllTermsOf U -interpreter-like } is set
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf U
(u,S) ReassignIn (U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
{} .--> S is trivial Relation-like {{}} -defined AllTermsOf U -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> S is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf U -valued {S} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{S}:]
{S} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{S}:] is non empty Relation-like finite set
bool [:{{}},{S}:] is non empty finite finite-membered set
u .--> ({} .--> S) is trivial Relation-like AllSymbolsOf U -defined {u} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{u} is non empty trivial finite 1 -element set
{u} --> ({} .--> S) is non empty Relation-like {u} -defined {({} .--> S)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{u},{({} .--> S)}:]
{({} .--> S)} is non empty trivial functional finite finite-membered 1 -element set
[:{u},{({} .--> S)}:] is non empty Relation-like finite set
bool [:{u},{({} .--> S)}:] is non empty finite finite-membered set
(U,{}) +* (u .--> ({} .--> S)) is Relation-like Function-like Function-yielding V164() set
((u,S) ReassignIn (U,{})) -TermEval is non empty Relation-like non empty-yielding AllTermsOf U -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf U),(AllTermsOf U):]
[:(AllTermsOf U),(AllTermsOf U):] is non empty Relation-like set
bool [:(AllTermsOf U),(AllTermsOf U):] is non empty set
(((u,S) ReassignIn (U,{})) -TermEval) (*) (SubTerms l) is Relation-like NAT -defined AllTermsOf U -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(U -multiCat) . ((((u,S) ReassignIn (U,{})) -TermEval) (*) (SubTerms l)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((U -firstChar) . l)*> ^ ((U -multiCat) . ((((u,S) ReassignIn (U,{})) -TermEval) (*) (SubTerms l))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AtomicFormulaSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
TheNorSymbOf U is set
the U3 of U is Element of the U1 of U
{(TheNorSymbOf U)} is non empty trivial finite 1 -element set
(AllSymbolsOf U) \ {(TheNorSymbOf U)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
(AllSymbolsOf U) typed\ {(TheNorSymbOf U)} is Element of bool (AllSymbolsOf U)
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf U
(U,u,l,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
[:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(AllSymbolsOf U) -pr1 is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total V233( AllSymbolsOf U) Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
[:(AllSymbolsOf U),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf U),(AllSymbolsOf U)) is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
MultPlace ((AllSymbolsOf U) -pr1) is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(U -firstChar) . S is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
<*((U -firstChar) . S)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,((U -firstChar) . S)] is non empty set
{[1,((U -firstChar) . S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
SubTerms S is Relation-like NAT -defined (rng S) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . S)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
ar ((U -firstChar) . S) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . ((U -firstChar) . S) is set
abs (ar ((U -firstChar) . S)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng S is non empty finite set
(rng S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng S
TermSymbolsOf U is non empty set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
(TermSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf U
AllTermsOf U is non empty functional finite-membered FinSequence-membered AllSymbolsOf U -prefix U -prefix Element of bool ((AllSymbolsOf U) *)
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
(U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
the U2 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) is non empty functional M31((AllTermsOf U) * ,(AllTermsOf U) \/ BOOLEAN)
Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U,K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))
(AllTermsOf U) -InterpretersOf U is non empty functional Element of bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf U -defined K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) : b₁ is U, AllTermsOf U -interpreter-like } is set
(u,l) ReassignIn (U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
{} .--> l is trivial Relation-like {{}} -defined AllTermsOf U -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> l is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf U -valued {l} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{l}:]
{l} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{l}:] is non empty Relation-like finite set
bool [:{{}},{l}:] is non empty finite finite-membered set
u .--> ({} .--> l) is trivial Relation-like AllSymbolsOf U -defined {u} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{u} is non empty trivial finite 1 -element set
{u} --> ({} .--> l) is non empty Relation-like {u} -defined {({} .--> l)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{u},{({} .--> l)}:]
{({} .--> l)} is non empty trivial functional finite finite-membered 1 -element set
[:{u},{({} .--> l)}:] is non empty Relation-like finite set
bool [:{u},{({} .--> l)}:] is non empty finite finite-membered set
(U,{}) +* (u .--> ({} .--> l)) is Relation-like Function-like Function-yielding V164() set
((u,l) ReassignIn (U,{})) -TermEval is non empty Relation-like non empty-yielding AllTermsOf U -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf U),(AllTermsOf U):]
[:(AllTermsOf U),(AllTermsOf U):] is non empty Relation-like set
bool [:(AllTermsOf U),(AllTermsOf U):] is non empty set
(((u,l) ReassignIn (U,{})) -TermEval) (*) (SubTerms S) is Relation-like NAT -defined AllTermsOf U -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(U -multiCat) . ((((u,l) ReassignIn (U,{})) -TermEval) (*) (SubTerms S)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((U -firstChar) . S)*> ^ ((U -multiCat) . ((((u,l) ReassignIn (U,{})) -TermEval) (*) (SubTerms S))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
Jj is Relation-like NAT -defined AllTermsOf U -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf U
(((u,l) ReassignIn (U,{})) -TermEval) * Jj is Relation-like NAT -defined AllTermsOf U -valued Function-like finite len Jj -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf U
len Jj is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
jJ is Relation-like NAT -defined AllTermsOf U -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf U
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
jJ is Relation-like NAT -defined (AllSymbolsOf U) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of ((AllSymbolsOf U) *) *
(U -multiCat) . jJ is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*((U -firstChar) . S)*> ^ ((U -multiCat) . jJ) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
AtomicFormulaSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
TheNorSymbOf U is set
the U3 of U is Element of the U1 of U
{(TheNorSymbOf U)} is non empty trivial finite 1 -element set
(AllSymbolsOf U) \ {(TheNorSymbOf U)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
(AllSymbolsOf U) typed\ {(TheNorSymbOf U)} is Element of bool (AllSymbolsOf U)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf U
l is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
[:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(AllSymbolsOf U) -pr1 is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total V233( AllSymbolsOf U) Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
[:(AllSymbolsOf U),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf U),(AllSymbolsOf U)) is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
MultPlace ((AllSymbolsOf U) -pr1) is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(U -firstChar) . l is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
<*((U -firstChar) . l)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,((U -firstChar) . l)] is non empty set
{[1,((U -firstChar) . l)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
SubTerms l is Relation-like NAT -defined (rng l) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . l)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
ar ((U -firstChar) . l) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . ((U -firstChar) . l) is set
abs (ar ((U -firstChar) . l)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng l is non empty finite set
(rng l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng l
TermSymbolsOf U is non empty set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
(TermSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf U
AllTermsOf U is non empty functional finite-membered FinSequence-membered AllSymbolsOf U -prefix U -prefix Element of bool ((AllSymbolsOf U) *)
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
(U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
the U2 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) is non empty functional M31((AllTermsOf U) * ,(AllTermsOf U) \/ BOOLEAN)
Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U,K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))
(AllTermsOf U) -InterpretersOf U is non empty functional Element of bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf U -defined K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) : b₁ is U, AllTermsOf U -interpreter-like } is set
(u,S) ReassignIn (U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
{} .--> S is trivial Relation-like {{}} -defined AllTermsOf U -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> S is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf U -valued {S} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{S}:]
{S} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{S}:] is non empty Relation-like finite set
bool [:{{}},{S}:] is non empty finite finite-membered set
u .--> ({} .--> S) is trivial Relation-like AllSymbolsOf U -defined {u} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{u} is non empty trivial finite 1 -element set
{u} --> ({} .--> S) is non empty Relation-like {u} -defined {({} .--> S)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{u},{({} .--> S)}:]
{({} .--> S)} is non empty trivial functional finite finite-membered 1 -element set
[:{u},{({} .--> S)}:] is non empty Relation-like finite set
bool [:{u},{({} .--> S)}:] is non empty finite finite-membered set
(U,{}) +* (u .--> ({} .--> S)) is Relation-like Function-like Function-yielding V164() set
((u,S) ReassignIn (U,{})) -TermEval is non empty Relation-like non empty-yielding AllTermsOf U -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf U),(AllTermsOf U):]
[:(AllTermsOf U),(AllTermsOf U):] is non empty Relation-like set
bool [:(AllTermsOf U),(AllTermsOf U):] is non empty set
(((u,S) ReassignIn (U,{})) -TermEval) (*) (SubTerms l) is Relation-like NAT -defined AllTermsOf U -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(U -multiCat) . ((((u,S) ReassignIn (U,{})) -TermEval) (*) (SubTerms l)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((U -firstChar) . l)*> ^ ((U -multiCat) . ((((u,S) ReassignIn (U,{})) -TermEval) (*) (SubTerms l))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
AtomicFormulaSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
TheNorSymbOf U is set
the U3 of U is Element of the U1 of U
{(TheNorSymbOf U)} is non empty trivial finite 1 -element set
(AllSymbolsOf U) \ {(TheNorSymbOf U)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
(AllSymbolsOf U) typed\ {(TheNorSymbOf U)} is Element of bool (AllSymbolsOf U)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf U
l is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,l) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
[:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(AllSymbolsOf U) -pr1 is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total V233( AllSymbolsOf U) Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
[:(AllSymbolsOf U),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf U),(AllSymbolsOf U)) is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
MultPlace ((AllSymbolsOf U) -pr1) is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(U -firstChar) . l is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
<*((U -firstChar) . l)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,((U -firstChar) . l)] is non empty set
{[1,((U -firstChar) . l)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
SubTerms l is Relation-like NAT -defined (rng l) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . l)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
ar ((U -firstChar) . l) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . ((U -firstChar) . l) is set
abs (ar ((U -firstChar) . l)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng l is non empty finite set
(rng l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng l
TermSymbolsOf U is non empty set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
(TermSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf U
AllTermsOf U is non empty functional finite-membered FinSequence-membered AllSymbolsOf U -prefix U -prefix Element of bool ((AllSymbolsOf U) *)
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
(U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
the U2 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) is non empty functional M31((AllTermsOf U) * ,(AllTermsOf U) \/ BOOLEAN)
Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U,K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))
(AllTermsOf U) -InterpretersOf U is non empty functional Element of bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf U -defined K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) : b₁ is U, AllTermsOf U -interpreter-like } is set
(u,S) ReassignIn (U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
{} .--> S is trivial Relation-like {{}} -defined AllTermsOf U -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> S is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf U -valued {S} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{S}:]
{S} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{S}:] is non empty Relation-like finite set
bool [:{{}},{S}:] is non empty finite finite-membered set
u .--> ({} .--> S) is trivial Relation-like AllSymbolsOf U -defined {u} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{u} is non empty trivial finite 1 -element set
{u} --> ({} .--> S) is non empty Relation-like {u} -defined {({} .--> S)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{u},{({} .--> S)}:]
{({} .--> S)} is non empty trivial functional finite finite-membered 1 -element set
[:{u},{({} .--> S)}:] is non empty Relation-like finite set
bool [:{u},{({} .--> S)}:] is non empty finite finite-membered set
(U,{}) +* (u .--> ({} .--> S)) is Relation-like Function-like Function-yielding V164() set
((u,S) ReassignIn (U,{})) -TermEval is non empty Relation-like non empty-yielding AllTermsOf U -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf U),(AllTermsOf U):]
[:(AllTermsOf U),(AllTermsOf U):] is non empty Relation-like set
bool [:(AllTermsOf U),(AllTermsOf U):] is non empty set
(((u,S) ReassignIn (U,{})) -TermEval) (*) (SubTerms l) is Relation-like NAT -defined AllTermsOf U -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(U -multiCat) . ((((u,S) ReassignIn (U,{})) -TermEval) (*) (SubTerms l)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((U -firstChar) . l)*> ^ ((U -multiCat) . ((((u,S) ReassignIn (U,{})) -TermEval) (*) (SubTerms l))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AtomicFormulaSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
TheNorSymbOf U is set
the U3 of U is Element of the U1 of U
{(TheNorSymbOf U)} is non empty trivial finite 1 -element set
(AllSymbolsOf U) \ {(TheNorSymbOf U)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
(AllSymbolsOf U) typed\ {(TheNorSymbOf U)} is Element of bool (AllSymbolsOf U)
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
U -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
[:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(AllSymbolsOf U) -pr1 is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total V233( AllSymbolsOf U) Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
[:(AllSymbolsOf U),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf U),(AllSymbolsOf U)) is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
MultPlace ((AllSymbolsOf U) -pr1) is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
the U2 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) is non empty functional M31((AllTermsOf U) * ,(AllTermsOf U) \/ BOOLEAN)
Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U,K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))
(AllTermsOf U) -InterpretersOf U is non empty functional Element of bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf U -defined K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) : b₁ is U, AllTermsOf U -interpreter-like } is set
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
(U -firstChar) . S is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
SubTerms S is Relation-like NAT -defined (rng S) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . S)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
ar ((U -firstChar) . S) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . ((U -firstChar) . S) is set
abs (ar ((U -firstChar) . S)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng S is non empty finite set
(rng S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng S
TermSymbolsOf U is non empty set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
(TermSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf U
AllTermsOf U is non empty functional finite-membered FinSequence-membered AllSymbolsOf U -prefix U -prefix Element of bool ((AllSymbolsOf U) *)
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf U
(U,u,l,S) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
<*((U -firstChar) . S)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,((U -firstChar) . S)] is non empty set
{[1,((U -firstChar) . S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
(u,l) ReassignIn (U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
{} .--> l is trivial Relation-like {{}} -defined AllTermsOf U -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> l is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf U -valued {l} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{l}:]
{l} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{l}:] is non empty Relation-like finite set
bool [:{{}},{l}:] is non empty finite finite-membered set
u .--> ({} .--> l) is trivial Relation-like AllSymbolsOf U -defined {u} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{u} is non empty trivial finite 1 -element set
{u} --> ({} .--> l) is non empty Relation-like {u} -defined {({} .--> l)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{u},{({} .--> l)}:]
{({} .--> l)} is non empty trivial functional finite finite-membered 1 -element set
[:{u},{({} .--> l)}:] is non empty Relation-like finite set
bool [:{u},{({} .--> l)}:] is non empty finite finite-membered set
(U,{}) +* (u .--> ({} .--> l)) is Relation-like Function-like Function-yielding V164() set
((u,l) ReassignIn (U,{})) -TermEval is non empty Relation-like non empty-yielding AllTermsOf U -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf U),(AllTermsOf U):]
[:(AllTermsOf U),(AllTermsOf U):] is non empty Relation-like set
bool [:(AllTermsOf U),(AllTermsOf U):] is non empty set
(((u,l) ReassignIn (U,{})) -TermEval) (*) (SubTerms S) is Relation-like NAT -defined AllTermsOf U -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(U -multiCat) . ((((u,l) ReassignIn (U,{})) -TermEval) (*) (SubTerms S)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((U -firstChar) . S)*> ^ ((U -multiCat) . ((((u,l) ReassignIn (U,{})) -TermEval) (*) (SubTerms S))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(U -firstChar) . (U,u,l,S) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
SubTerms (U,u,l,S) is Relation-like NAT -defined (rng (U,u,l,S)) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . (U,u,l,S))) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
ar ((U -firstChar) . (U,u,l,S)) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U . ((U -firstChar) . (U,u,l,S)) is set
abs (ar ((U -firstChar) . (U,u,l,S))) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng (U,u,l,S) is non empty finite set
(rng (U,u,l,S)) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng (U,u,l,S)
(U,u,l,S) . 1 is set
Jj is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . S)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf U
(((u,l) ReassignIn (U,{})) -TermEval) * Jj is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . S)) -element len Jj -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf U
len Jj is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
jJ is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . (U,u,l,S))) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf U
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
U is set
u is non empty set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V166() set
the U1 of S is set
AllSymbolsOf S is non empty non trivial non finite V166() set
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
AllTermsOf S is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() set
S -termsOfMaxDepth is Relation-like Function-like set
rng (S -termsOfMaxDepth) is set
union (rng (S -termsOfMaxDepth)) is set
(S,U) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S, AllTermsOf S -interpreter-like Element of (AllTermsOf S) -InterpretersOf S
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V166() 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
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf S
(AllTermsOf S) \/ BOOLEAN is non empty set
K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN)) is non empty functional M31((AllTermsOf S) * ,(AllTermsOf S) \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S,K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN))
(AllTermsOf S) -InterpretersOf S is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf S),K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),K546(((AllTermsOf S) *),((AllTermsOf S) \/ BOOLEAN))) : b₁ is S, AllTermsOf S -interpreter-like } is set
l is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
II is Relation-like Function-like Function-yielding V164() S,u -interpreter-like set
II -TermEval is non empty Relation-like AllTermsOf S -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),u:]
[:(AllTermsOf S),u:] is non empty Relation-like set
bool [:(AllTermsOf S),u:] is non empty set
E is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf S
(l,E) ReassignIn (S,U) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S, AllTermsOf S -interpreter-like Element of (AllTermsOf S) -InterpretersOf S
{} .--> E is trivial Relation-like {{}} -defined AllTermsOf S -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> E is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf S -valued {E} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{E}:]
{E} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{E}:] is non empty Relation-like finite set
bool [:{{}},{E}:] is non empty finite finite-membered set
l .--> ({} .--> E) is trivial Relation-like AllSymbolsOf S -defined {l} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} is non empty trivial finite 1 -element set
{l} --> ({} .--> E) is non empty Relation-like {l} -defined {({} .--> E)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({} .--> E)}:]
{({} .--> E)} is non empty trivial functional finite finite-membered 1 -element set
[:{l},{({} .--> E)}:] is non empty Relation-like finite set
bool [:{l},{({} .--> E)}:] is non empty finite finite-membered set
(S,U) +* (l .--> ({} .--> E)) is Relation-like Function-like Function-yielding V164() set
((l,E) ReassignIn (S,U)) -TermEval is non empty Relation-like non empty-yielding AllTermsOf S -defined AllTermsOf S -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf S),(AllTermsOf S):]
[:(AllTermsOf S),(AllTermsOf S):] is non empty Relation-like set
bool [:(AllTermsOf S),(AllTermsOf S):] is non empty set
(II -TermEval) * (((l,E) ReassignIn (S,U)) -TermEval) is non empty Relation-like AllTermsOf S -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),u:]
(II -TermEval) . E is Element of u
(l,((II -TermEval) . E)) ReassignIn II is Relation-like Function-like Function-yielding V164() S,u -interpreter-like set
{} .--> ((II -TermEval) . E) is trivial Relation-like {{}} -defined u -valued Function-like one-to-one constant finite finite-support set
{{}} --> ((II -TermEval) . E) is non empty Relation-like {{}} -defined u -valued {((II -TermEval) . E)} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{((II -TermEval) . E)}:]
{((II -TermEval) . E)} is non empty trivial finite 1 -element set
[:{{}},{((II -TermEval) . E)}:] is non empty Relation-like finite set
bool [:{{}},{((II -TermEval) . E)}:] is non empty finite finite-membered set
l .--> ({} .--> ((II -TermEval) . E)) is trivial Relation-like AllSymbolsOf S -defined {l} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} --> ({} .--> ((II -TermEval) . E)) is non empty Relation-like {l} -defined {({} .--> ((II -TermEval) . E))} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({} .--> ((II -TermEval) . E))}:]
{({} .--> ((II -TermEval) . E))} is non empty trivial functional finite finite-membered 1 -element set
[:{l},{({} .--> ((II -TermEval) . E))}:] is non empty Relation-like finite set
bool [:{l},{({} .--> ((II -TermEval) . E))}:] is non empty finite finite-membered set
II +* (l .--> ({} .--> ((II -TermEval) . E))) is Relation-like Function-like Function-yielding V164() set
((l,((II -TermEval) . E)) ReassignIn II) -TermEval is non empty Relation-like AllTermsOf S -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),u:]
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 V166() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V166() 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 V233( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V166() set
K415((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() FinSequence-yielding Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
((AllSymbolsOf S) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf S) *
[:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf S) -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
(AllSymbolsOf S) -concatenation is non empty Relation-like [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf S) * ) Element of bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):]
[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf S) -concatenation) is non empty Relation-like (((AllSymbolsOf S) *) *) \ {{}} -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):]
(((AllSymbolsOf S) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf S) *) *)
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf S) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf S) *) *)
[:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf S) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
S -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf S) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf S) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial non finite V166() set
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 V166() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V166() 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
G is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf S
n is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf S) *) \ {{}}
Depth n is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth n) + 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(Depth n) + (0 * 1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
hh is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Depth n -termal Element of ((AllSymbolsOf S) *) \ {{}}
nE is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
bool (AllTermsOf S) is non empty set
(S -termsOfMaxDepth) . nE is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
En is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S -termsOfMaxDepth) . En is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
ss is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
s is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
hhh is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal nE -termal Element of ((AllSymbolsOf S) *) \ {{}}
Funcs ((AllTermsOf S),(AllTermsOf S)) is non empty functional FUNCTION_DOMAIN of AllTermsOf S, AllTermsOf S
(((l,E) ReassignIn (S,U)),E) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf S),(AllTermsOf S)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf S),(AllTermsOf S))):]
[:NAT,(Funcs ((AllTermsOf S),(AllTermsOf S))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllTermsOf S),(AllTermsOf S))):] is non empty non trivial non finite V166() set
((((l,E) ReassignIn (S,U)),E) -TermEval) . nE is Relation-like Function-like Element of Funcs ((AllTermsOf S),(AllTermsOf S))
Funcs ((AllTermsOf S),u) is non empty functional FUNCTION_DOMAIN of AllTermsOf S,u
(((l,((II -TermEval) . E)) ReassignIn II),((II -TermEval) . E)) -TermEval is non empty Relation-like NAT -defined Funcs ((AllTermsOf S),u) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllTermsOf S),u)):]
[:NAT,(Funcs ((AllTermsOf S),u)):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllTermsOf S),u)):] is non empty non trivial non finite V166() set
((((l,((II -TermEval) . E)) ReassignIn II),((II -TermEval) . E)) -TermEval) . nE is Relation-like Function-like Element of Funcs ((AllTermsOf S),u)
phi2 is non empty Relation-like non empty-yielding AllTermsOf S -defined AllTermsOf S -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf S),(AllTermsOf S):]
phi2 . G is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf S
(II -TermEval) . (phi2 . G) is Element of u
(II -TermEval) * phi2 is non empty Relation-like AllTermsOf S -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),u:]
((II -TermEval) * phi2) . G is Element of u
((II -TermEval) . (phi2 . G)) \+\ (((II -TermEval) * phi2) . G) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
((II -TermEval) . (phi2 . G)) \ (((II -TermEval) * phi2) . G) is set
((II -TermEval) . (phi2 . G)) typed\ (((II -TermEval) * phi2) . G) is Element of bool ((II -TermEval) . (phi2 . G))
bool ((II -TermEval) . (phi2 . G)) is non empty set
((II -TermEval) . (phi2 . G)) \ (((II -TermEval) * phi2) . G) is Element of bool ((II -TermEval) . (phi2 . G))
(((II -TermEval) * phi2) . G) \ ((II -TermEval) . (phi2 . G)) is set
(((II -TermEval) * phi2) . G) typed\ ((II -TermEval) . (phi2 . G)) is Element of bool (((II -TermEval) * phi2) . G)
bool (((II -TermEval) * phi2) . G) is non empty set
(((II -TermEval) * phi2) . G) \ ((II -TermEval) . (phi2 . G)) is Element of bool (((II -TermEval) * phi2) . G)
(((II -TermEval) . (phi2 . G)) \ (((II -TermEval) * phi2) . G)) \/ ((((II -TermEval) * phi2) . G) \ ((II -TermEval) . (phi2 . G))) is set
((II -TermEval) * phi2) | s is Relation-like AllTermsOf S -defined s -defined AllTermsOf S -defined u -valued Function-like total Element of bool [:(AllTermsOf S),u:]
c₃₀ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of s
(((II -TermEval) * phi2) | s) . c₃₀ is set
((II -TermEval) * phi2) . c₃₀ is set
((((II -TermEval) * phi2) | s) . c₃₀) \+\ (((II -TermEval) * phi2) . c₃₀) is set
((((II -TermEval) * phi2) | s) . c₃₀) \ (((II -TermEval) * phi2) . c₃₀) is set
((((II -TermEval) * phi2) | s) . c₃₀) typed\ (((II -TermEval) * phi2) . c₃₀) is Element of bool ((((II -TermEval) * phi2) | s) . c₃₀)
bool ((((II -TermEval) * phi2) | s) . c₃₀) is non empty set
((((II -TermEval) * phi2) | s) . c₃₀) \ (((II -TermEval) * phi2) . c₃₀) is Element of bool ((((II -TermEval) * phi2) | s) . c₃₀)
(((II -TermEval) * phi2) . c₃₀) \ ((((II -TermEval) * phi2) | s) . c₃₀) is set
(((II -TermEval) * phi2) . c₃₀) typed\ ((((II -TermEval) * phi2) | s) . c₃₀) is Element of bool (((II -TermEval) * phi2) . c₃₀)
bool (((II -TermEval) * phi2) . c₃₀) is non empty set
(((II -TermEval) * phi2) . c₃₀) \ ((((II -TermEval) * phi2) | s) . c₃₀) is Element of bool (((II -TermEval) * phi2) . c₃₀)
(((((II -TermEval) * phi2) | s) . c₃₀) \ (((II -TermEval) * phi2) . c₃₀)) \/ ((((II -TermEval) * phi2) . c₃₀) \ ((((II -TermEval) * phi2) | s) . c₃₀)) is set
b1 is non empty Relation-like AllTermsOf S -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),u:]
b1 | s is Relation-like AllTermsOf S -defined s -defined AllTermsOf S -defined u -valued Function-like total Element of bool [:(AllTermsOf S),u:]
(b1 | s) . c₃₀ is set
b1 . c₃₀ is set
((b1 | s) . c₃₀) \+\ (b1 . c₃₀) is set
((b1 | s) . c₃₀) \ (b1 . c₃₀) is set
((b1 | s) . c₃₀) typed\ (b1 . c₃₀) is Element of bool ((b1 | s) . c₃₀)
bool ((b1 | s) . c₃₀) is non empty set
((b1 | s) . c₃₀) \ (b1 . c₃₀) is Element of bool ((b1 | s) . c₃₀)
(b1 . c₃₀) \ ((b1 | s) . c₃₀) is set
(b1 . c₃₀) typed\ ((b1 | s) . c₃₀) is Element of bool (b1 . c₃₀)
bool (b1 . c₃₀) is non empty set
(b1 . c₃₀) \ ((b1 | s) . c₃₀) is Element of bool (b1 . c₃₀)
(((b1 | s) . c₃₀) \ (b1 . c₃₀)) \/ ((b1 . c₃₀) \ ((b1 | s) . c₃₀)) is set
(((II -TermEval) * phi2) | s) . G is set
(b1 | s) . G is set
b1 . G is Element of u
g is non empty Relation-like AllTermsOf S -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),u:]
g . G is Element of u
(((l,E) ReassignIn (S,U)) -TermEval) . G is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf S
(II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G) is Element of u
(g . G) \+\ ((II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G)) is set
(g . G) \ ((II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G)) is set
(g . G) typed\ ((II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G)) is Element of bool (g . G)
bool (g . G) is non empty set
(g . G) \ ((II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G)) is Element of bool (g . G)
((II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G)) \ (g . G) is set
((II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G)) typed\ (g . G) is Element of bool ((II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G))
bool ((II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G)) is non empty set
((II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G)) \ (g . G) is Element of bool ((II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G))
((g . G) \ ((II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G))) \/ (((II -TermEval) . ((((l,E) ReassignIn (S,U)) -TermEval) . G)) \ (g . G)) is set
((l,E) ReassignIn (S,U)) -TermEval G is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf S
(II -TermEval) . (((l,E) ReassignIn (S,U)) -TermEval G) is Element of u
phi22 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ss
phi2 . phi22 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(II -TermEval) . (phi2 . phi22) is set
(((((l,((II -TermEval) . E)) ReassignIn II),((II -TermEval) . E)) -TermEval) . nE) . phi22 is set
((l,((II -TermEval) . E)) ReassignIn II) -TermEval G is Element of u
(((l,((II -TermEval) . E)) ReassignIn II) -TermEval) . G is Element of u
h is non empty Relation-like AllTermsOf S -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),u:]
h . G is Element of u
U is non empty set
u is V51() V53() eligible Language-like
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
AtomicFormulaSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
AllSymbolsOf u is non empty non trivial non finite V166() set
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
TheNorSymbOf u is set
the U3 of u is Element of the U1 of u
{(TheNorSymbOf u)} is non empty trivial finite 1 -element set
(AllSymbolsOf u) \ {(TheNorSymbOf u)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
(AllSymbolsOf u) typed\ {(TheNorSymbOf u)} is Element of bool (AllSymbolsOf u)
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
l is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
II is Relation-like Function-like Function-yielding V164() u,U -interpreter-like set
II -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
E is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u
(u,S,E,l) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
u -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
[:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(AllSymbolsOf u) -pr1 is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total V233( AllSymbolsOf u) Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
[:(AllSymbolsOf u),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf u),(AllSymbolsOf u)) is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
MultPlace ((AllSymbolsOf u) -pr1) is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(u -firstChar) . l is low-compounding relational ofAtomicFormula Element of AllSymbolsOf u
<*((u -firstChar) . l)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
[1,((u -firstChar) . l)] is non empty set
{[1,((u -firstChar) . l)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
u -multiCat is non empty Relation-like ((AllSymbolsOf u) *) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):]
((AllSymbolsOf u) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf u) *
[:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -multiCat is non empty Relation-like ((AllSymbolsOf u) *) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):]
(AllSymbolsOf u) -concatenation is non empty Relation-like [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf u) * ) Element of bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):]
[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf u) -concatenation) is non empty Relation-like (((AllSymbolsOf u) *) *) \ {{}} -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):]
(((AllSymbolsOf u) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf u) *) *)
bool (((AllSymbolsOf u) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf u) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf u) *) *)
[:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf u) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
SubTerms l is Relation-like NAT -defined (rng l) * -valued (TermSymbolsOf u) * -valued AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . l)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
ar ((u -firstChar) . l) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
the adicity of u . ((u -firstChar) . l) is set
abs (ar ((u -firstChar) . l)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng l is non empty finite set
(rng l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng l
TermSymbolsOf u is non empty set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
(TermSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf u
AllTermsOf u is non empty functional finite-membered FinSequence-membered AllSymbolsOf u -prefix u -prefix Element of bool ((AllSymbolsOf u) *)
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf u) *) *)
(u,{}) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u, AllTermsOf u -interpreter-like Element of (AllTermsOf u) -InterpretersOf u
OwnSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
the U2 of u is Element of the U1 of u
{ the U2 of u, the U3 of u} is non empty finite set
the U1 of u \ { the U2 of u, the U3 of u} is Element of bool the U1 of u
the U1 of u typed\ { the U2 of u, the U3 of u} is Element of bool the U1 of u
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf u
(AllTermsOf u) \/ BOOLEAN is non empty set
K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN)) is non empty functional M31((AllTermsOf u) * ,(AllTermsOf u) \/ BOOLEAN)
Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf u,K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))
(AllTermsOf u) -InterpretersOf u is non empty functional Element of bool (Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf u -defined K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))) : b₁ is u, AllTermsOf u -interpreter-like } is set
(S,E) ReassignIn (u,{}) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u, AllTermsOf u -interpreter-like Element of (AllTermsOf u) -InterpretersOf u
{} .--> E is trivial Relation-like {{}} -defined AllTermsOf u -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> E is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf u -valued {E} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{E}:]
{E} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{E}:] is non empty Relation-like finite set
bool [:{{}},{E}:] is non empty finite finite-membered set
S .--> ({} .--> E) is trivial Relation-like AllSymbolsOf u -defined {S} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{S} is non empty trivial finite 1 -element set
{S} --> ({} .--> E) is non empty Relation-like {S} -defined {({} .--> E)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{S},{({} .--> E)}:]
{({} .--> E)} is non empty trivial functional finite finite-membered 1 -element set
[:{S},{({} .--> E)}:] is non empty Relation-like finite set
bool [:{S},{({} .--> E)}:] is non empty finite finite-membered set
(u,{}) +* (S .--> ({} .--> E)) is Relation-like Function-like Function-yielding V164() set
((S,E) ReassignIn (u,{})) -TermEval is non empty Relation-like non empty-yielding AllTermsOf u -defined AllTermsOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf u),(AllTermsOf u):]
[:(AllTermsOf u),(AllTermsOf u):] is non empty Relation-like set
bool [:(AllTermsOf u),(AllTermsOf u):] is non empty set
(((S,E) ReassignIn (u,{})) -TermEval) (*) (SubTerms l) is Relation-like NAT -defined AllTermsOf u -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(u -multiCat) . ((((S,E) ReassignIn (u,{})) -TermEval) (*) (SubTerms l)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((u -firstChar) . l)*> ^ ((u -multiCat) . ((((S,E) ReassignIn (u,{})) -TermEval) (*) (SubTerms l))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
II -AtomicEval (u,S,E,l) is boolean Element of BOOLEAN
II === is Relation-like Function-like Function-yielding V164() u,U -interpreter-like II -extension set
TheEqSymbOf u is Element of AtomicFormulaSymbolsOf u
U -deltaInterpreter is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
2 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
[:(2 -tuples_on U),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on U),BOOLEAN:] is non empty set
U * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of U
[:(U *),(U *):] is non empty non trivial Relation-like non finite V166() set
U -concatenation is non empty Relation-like [:(U *),(U *):] -defined U * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233(U * ) Element of bool [:[:(U *),(U *):],(U *):]
[:[:(U *),(U *):],(U *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(U *),(U *):],(U *):] is non empty non trivial non finite V166() set
1 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
id (1 -tuples_on U) is non empty Relation-like non empty-yielding 1 -tuples_on U -defined 1 -tuples_on U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(1 -tuples_on U),(1 -tuples_on U):]
[:(1 -tuples_on U),(1 -tuples_on U):] is non empty Relation-like set
bool [:(1 -tuples_on U),(1 -tuples_on U):] is non empty set
(U -concatenation) .: (id (1 -tuples_on U)) is functional finite-membered FinSequence-membered Element of bool (U *)
bool (U *) is non empty non trivial non finite V166() set
chi (((U -concatenation) .: (id (1 -tuples_on U))),(2 -tuples_on U)) is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
(TheEqSymbOf u) .--> (U -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf u -defined {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf u)} is non empty trivial finite 1 -element set
{(TheEqSymbOf u)} --> (U -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued {(U -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:]
{(U -deltaInterpreter)} is non empty trivial functional finite 1 -element V165() V166() set
[:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty finite finite-membered set
II +* ((TheEqSymbOf u) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(u -firstChar) . (u,S,E,l) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf u
(II ===) . ((u -firstChar) . (u,S,E,l)) is non empty Relation-like (abs (ar ((u -firstChar) . (u,S,E,l)))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . (u,S,E,l),U
ar ((u -firstChar) . (u,S,E,l)) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of u . ((u -firstChar) . (u,S,E,l)) is set
abs (ar ((u -firstChar) . (u,S,E,l))) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((u -firstChar) . (u,S,E,l)))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
U \/ BOOLEAN is non empty set
SubTerms (u,S,E,l) is Relation-like NAT -defined (rng (u,S,E,l)) * -valued (TermSymbolsOf u) * -valued AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . (u,S,E,l))) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
rng (u,S,E,l) is non empty finite set
(rng (u,S,E,l)) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng (u,S,E,l)
(II -TermEval) (*) (SubTerms (u,S,E,l)) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((II ===) . ((u -firstChar) . (u,S,E,l))) . ((II -TermEval) (*) (SubTerms (u,S,E,l))) is set
(II -TermEval) . E is Element of U
(S,((II -TermEval) . E)) ReassignIn II is Relation-like Function-like Function-yielding V164() u,U -interpreter-like set
{} .--> ((II -TermEval) . E) is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> ((II -TermEval) . E) is non empty Relation-like {{}} -defined U -valued {((II -TermEval) . E)} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{((II -TermEval) . E)}:]
{((II -TermEval) . E)} is non empty trivial finite 1 -element set
[:{{}},{((II -TermEval) . E)}:] is non empty Relation-like finite set
bool [:{{}},{((II -TermEval) . E)}:] is non empty finite finite-membered set
S .--> ({} .--> ((II -TermEval) . E)) is trivial Relation-like AllSymbolsOf u -defined {S} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{S} --> ({} .--> ((II -TermEval) . E)) is non empty Relation-like {S} -defined {({} .--> ((II -TermEval) . E))} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{S},{({} .--> ((II -TermEval) . E))}:]
{({} .--> ((II -TermEval) . E))} is non empty trivial functional finite finite-membered 1 -element set
[:{S},{({} .--> ((II -TermEval) . E))}:] is non empty Relation-like finite set
bool [:{S},{({} .--> ((II -TermEval) . E))}:] is non empty finite finite-membered set
II +* (S .--> ({} .--> ((II -TermEval) . E))) is Relation-like Function-like Function-yielding V164() set
((S,((II -TermEval) . E)) ReassignIn II) -AtomicEval l is boolean Element of BOOLEAN
((S,((II -TermEval) . E)) ReassignIn II) === is Relation-like Function-like Function-yielding V164() u,U -interpreter-like (S,((II -TermEval) . E)) ReassignIn II -extension set
((S,((II -TermEval) . E)) ReassignIn II) +* ((TheEqSymbOf u) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(((S,((II -TermEval) . E)) ReassignIn II) ===) . ((u -firstChar) . l) is non empty Relation-like (abs (ar ((u -firstChar) . l))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . l,U
(abs (ar ((u -firstChar) . l))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
((S,((II -TermEval) . E)) ReassignIn II) -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
(((S,((II -TermEval) . E)) ReassignIn II) -TermEval) (*) (SubTerms l) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((((S,((II -TermEval) . E)) ReassignIn II) ===) . ((u -firstChar) . l)) . ((((S,((II -TermEval) . E)) ReassignIn II) -TermEval) (*) (SubTerms l)) is set
TheEqSymbOf u is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf u
dom (S .--> ({} .--> ((II -TermEval) . E))) is trivial finite Element of bool {S}
bool {S} is non empty finite finite-membered set
((S,((II -TermEval) . E)) ReassignIn II) . ((u -firstChar) . l) is Relation-like Function-like set
II . ((u -firstChar) . l) is Relation-like Function-like set
(II -TermEval) (*) ((((S,E) ReassignIn (u,{})) -TermEval) (*) (SubTerms l)) is Relation-like NAT -defined U -valued Function-like finite finite-support set
(II -TermEval) * (((S,E) ReassignIn (u,{})) -TermEval) is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
((II -TermEval) * (((S,E) ReassignIn (u,{})) -TermEval)) (*) (SubTerms l) is Relation-like NAT -defined U -valued Function-like finite finite-support set
(((S,((II -TermEval) . E)) ReassignIn II) . ((u -firstChar) . l)) . ((((S,((II -TermEval) . E)) ReassignIn II) -TermEval) (*) (SubTerms l)) is set
(U -deltaInterpreter) . ((II -TermEval) (*) (SubTerms (u,S,E,l))) is boolean set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
u SubstWith S is non empty Relation-like (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf U) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf U) *) \ {{}})):] is non empty non trivial non finite V166() set
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(U -termsOfMaxDepth) . l is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
(u SubstWith S) | ((U -termsOfMaxDepth) . l) is Relation-like (AllSymbolsOf U) * -defined (U -termsOfMaxDepth) . l -defined (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
x is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(u SubstWith S) | x is Relation-like (AllSymbolsOf U) * -defined x -defined (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
dom ((u SubstWith S) | x) is functional finite-membered FinSequence-membered Element of bool x
bool x is non empty set
UU is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
III is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of x
((u SubstWith S) | x) . III is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u SubstWith S) . III is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((u SubstWith S) | x) . III) \+\ ((u SubstWith S) . III) is Relation-like finite set
(((u SubstWith S) | x) . III) \ ((u SubstWith S) . III) is Relation-like NAT -defined finite set
(((u SubstWith S) | x) . III) typed\ ((u SubstWith S) . III) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((u SubstWith S) | x) . III)
bool (((u SubstWith S) | x) . III) is non empty finite finite-membered set
(((u SubstWith S) | x) . III) \ ((u SubstWith S) . III) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((u SubstWith S) | x) . III)
((u SubstWith S) . III) \ (((u SubstWith S) | x) . III) is Relation-like NAT -defined finite set
((u SubstWith S) . III) typed\ (((u SubstWith S) | x) . III) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((u SubstWith S) . III)
bool ((u SubstWith S) . III) is non empty finite finite-membered set
((u SubstWith S) . III) \ (((u SubstWith S) | x) . III) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((u SubstWith S) . III)
((((u SubstWith S) | x) . III) \ ((u SubstWith S) . III)) \/ (((u SubstWith S) . III) \ (((u SubstWith S) | x) . III)) is Relation-like NAT -defined finite set
((u SubstWith S) | x) . UU is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
X is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal l -termal Element of ((AllSymbolsOf U) *) \ {{}}
(u SubstWith S) . X is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
(U,u,S,X) is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal l -termal Element of ((AllSymbolsOf U) *) \ {{}}
X +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
UU is Relation-like set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
u SubstWith S is non empty Relation-like (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
(u SubstWith S) | (AllTermsOf U) is Relation-like (AllSymbolsOf U) * -defined AllTermsOf U -defined (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
i is non empty functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(u SubstWith S) | i is Relation-like (AllSymbolsOf U) * -defined i -defined (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
dom ((u SubstWith S) | i) is functional finite-membered FinSequence-membered Element of bool i
bool i is non empty set
x is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
O is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of i
((u SubstWith S) | i) . O is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u SubstWith S) . O is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
(((u SubstWith S) | i) . O) \+\ ((u SubstWith S) . O) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((u SubstWith S) | i) . O) \ ((u SubstWith S) . O) is Relation-like NAT -defined finite set
(((u SubstWith S) | i) . O) typed\ ((u SubstWith S) . O) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((u SubstWith S) | i) . O)
bool (((u SubstWith S) | i) . O) is non empty finite finite-membered set
(((u SubstWith S) | i) . O) \ ((u SubstWith S) . O) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((u SubstWith S) | i) . O)
((u SubstWith S) . O) \ (((u SubstWith S) | i) . O) is Relation-like NAT -defined AllSymbolsOf U -valued finite set
((u SubstWith S) . O) typed\ (((u SubstWith S) | i) . O) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite finite-support Element of bool ((u SubstWith S) . O)
bool ((u SubstWith S) . O) is non empty finite finite-membered set
((u SubstWith S) . O) \ (((u SubstWith S) | i) . O) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite finite-support Element of bool ((u SubstWith S) . O)
((((u SubstWith S) | i) . O) \ ((u SubstWith S) . O)) \/ (((u SubstWith S) . O) \ (((u SubstWith S) | i) . O)) is Relation-like NAT -defined finite set
((u SubstWith S) | i) . x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
UU is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
(u SubstWith S) . UU is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
(U,u,S,UU) is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
UU +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
x is Relation-like set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
u SubstWith S is non empty Relation-like (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
l is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,l) is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
l +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
SubTerms (U,u,S,l) is Relation-like NAT -defined (rng (U,u,S,l)) * -valued AllTermsOf U -valued Function-like finite abs (ar (U,u,S,l)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
rng (U,u,S,l) is non empty finite set
(rng (U,u,S,l)) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng (U,u,S,l)
AllTermsOf U is non empty functional finite-membered FinSequence-membered AllSymbolsOf U -prefix U -prefix Element of bool ((AllSymbolsOf U) *)
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
ar (U,u,S,l) is finite complex ext-real V40() V41() Element of INT
U -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
[:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(AllSymbolsOf U) -pr1 is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total V233( AllSymbolsOf U) Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
[:(AllSymbolsOf U),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf U),(AllSymbolsOf U)) is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
MultPlace ((AllSymbolsOf U) -pr1) is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(U -firstChar) . (U,u,S,l) is non relational termal own ofAtomicFormula Element of AllSymbolsOf U
ar ((U -firstChar) . (U,u,S,l)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of U . ((U -firstChar) . (U,u,S,l)) is set
abs (ar (U,u,S,l)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
SubTerms l is Relation-like NAT -defined (rng l) * -valued AllTermsOf U -valued Function-like finite abs (ar l) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
rng l is non empty finite set
(rng l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng l
ar l is finite complex ext-real V40() V41() Element of INT
(U -firstChar) . l is non relational termal own ofAtomicFormula Element of AllSymbolsOf U
ar ((U -firstChar) . l) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of U . ((U -firstChar) . l) is set
abs (ar l) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(u SubstWith S) (*) (SubTerms l) is Relation-like NAT -defined (AllSymbolsOf U) * -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
rng (SubTerms l) is finite set
I is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(u SubstWith S) | I is Relation-like (AllSymbolsOf U) * -defined I -defined (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
dom ((u SubstWith S) | I) is functional finite-membered FinSequence-membered Element of bool I
bool I is non empty set
(u SubstWith S) | (AllTermsOf U) is Relation-like (AllSymbolsOf U) * -defined AllTermsOf U -defined (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued AllTermsOf U -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
rng ((u SubstWith S) | (AllTermsOf U)) is set
[:(AllTermsOf U),(AllTermsOf U):] is non empty Relation-like set
bool [:(AllTermsOf U),(AllTermsOf U):] is non empty set
Jj is non literal ofAtomicFormula Element of AllSymbolsOf U
<*Jj*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,Jj] is non empty set
{[1,Jj]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(U,u,S,<*Jj*>) is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
<*Jj*> +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
ar Jj is finite complex ext-real V40() V41() Element of INT
the adicity of U . Jj is set
abs (ar Jj) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
abs (ar ((U -firstChar) . (U,u,S,l))) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
j is non empty Relation-like non empty-yielding AllTermsOf U -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf U),(AllTermsOf U):]
j (*) (SubTerms l) is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar l) -element len (SubTerms l) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support set
len (SubTerms l) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
<*((U -firstChar) . (U,u,S,l))*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,((U -firstChar) . (U,u,S,l))] is non empty set
{[1,((U -firstChar) . (U,u,S,l))]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(U -multiCat) . (SubTerms (U,u,S,l)) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*((U -firstChar) . (U,u,S,l))*> ^ ((U -multiCat) . (SubTerms (U,u,S,l))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(U -multiCat) . (SubTerms l) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*Jj*> ^ ((U -multiCat) . (SubTerms l)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u SubstWith S) . l is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
(u SubstWith S) . <*Jj*> is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
(u SubstWith S) . ((U -multiCat) . (SubTerms l)) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
((u SubstWith S) . <*Jj*>) ^ ((u SubstWith S) . ((U -multiCat) . (SubTerms l))) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support set
jJ is non empty trivial Relation-like NAT -defined AllSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
jJ ^ ((u SubstWith S) . ((U -multiCat) . (SubTerms l))) is non empty Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support set
(U -multiCat) . ((u SubstWith S) (*) (SubTerms l)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
jJ ^ ((U -multiCat) . ((u SubstWith S) (*) (SubTerms l))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
G is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar Jj) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf U
(U -multiCat) . G is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
jJ ^ ((U -multiCat) . G) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
jJ . 1 is set
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
n is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . (U,u,S,l))) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
(U -multiCat) . n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((U -firstChar) . (U,u,S,l))*> ^ ((U -multiCat) . n) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
Jj is non empty trivial Relation-like NAT -defined TermSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,Jj) is non empty trivial Relation-like NAT -defined TermSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf U) *) \ {{}}
Jj +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
jJ is non empty trivial Relation-like NAT -defined TermSymbolsOf U -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf U) *) \ {{}}
SubTerms jJ is empty trivial Relation-like non-empty empty-yielding NAT -defined (rng jJ) * -valued AllTermsOf U -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element abs (ar jJ) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllTermsOf U) *
rng jJ is non empty trivial finite 1 -element set
(rng jJ) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng jJ
ar jJ is finite complex ext-real V40() V41() Element of INT
(U -firstChar) . jJ is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
ar ((U -firstChar) . jJ) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of U . ((U -firstChar) . jJ) is set
abs (ar jJ) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
SubTerms Jj is empty trivial Relation-like non-empty empty-yielding NAT -defined (rng Jj) * -valued AllTermsOf U -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element abs (ar Jj) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllTermsOf U) *
rng Jj is non empty trivial finite 1 -element set
(rng Jj) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng Jj
ar Jj is finite complex ext-real V40() V41() Element of INT
(U -firstChar) . Jj is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
ar ((U -firstChar) . Jj) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of U . ((U -firstChar) . Jj) is set
abs (ar Jj) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AtomicFormulaSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
AllSymbolsOf U is non empty non trivial non finite V166() set
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
TheNorSymbOf U is set
the U3 of U is Element of the U1 of U
{(TheNorSymbOf U)} is non empty trivial finite 1 -element set
(AllSymbolsOf U) \ {(TheNorSymbOf U)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
(AllSymbolsOf U) typed\ {(TheNorSymbOf U)} is Element of bool (AllSymbolsOf U)
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
u SubstWith S is non empty Relation-like (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
l is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,l) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
l +~ (u,S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
SubTerms (U,u,S,l) is Relation-like NAT -defined (rng (U,u,S,l)) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . (U,u,S,l))) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
U -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
[:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(AllSymbolsOf U) -pr1 is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total V233( AllSymbolsOf U) Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
[:(AllSymbolsOf U),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf U),(AllSymbolsOf U)) is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
MultPlace ((AllSymbolsOf U) -pr1) is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(U -firstChar) . (U,u,S,l) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
ar ((U -firstChar) . (U,u,S,l)) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . ((U -firstChar) . (U,u,S,l)) is set
abs (ar ((U -firstChar) . (U,u,S,l))) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng (U,u,S,l) is non empty finite set
(rng (U,u,S,l)) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng (U,u,S,l)
TermSymbolsOf U is non empty set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
(TermSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf U
AllTermsOf U is non empty functional finite-membered FinSequence-membered AllSymbolsOf U -prefix U -prefix Element of bool ((AllSymbolsOf U) *)
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
SubTerms l is Relation-like NAT -defined (rng l) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . l)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
(U -firstChar) . l is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
ar ((U -firstChar) . l) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U . ((U -firstChar) . l) is set
abs (ar ((U -firstChar) . l)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng l is non empty finite set
(rng l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng l
(u SubstWith S) (*) (SubTerms l) is Relation-like NAT -defined (AllSymbolsOf U) * -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
rng (SubTerms l) is finite set
I is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
(u SubstWith S) | I is Relation-like (AllSymbolsOf U) * -defined I -defined (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued Function-like total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
dom ((u SubstWith S) | I) is functional finite-membered FinSequence-membered Element of bool I
bool I is non empty set
(u SubstWith S) | (AllTermsOf U) is Relation-like (AllSymbolsOf U) * -defined AllTermsOf U -defined (AllSymbolsOf U) * -defined (AllSymbolsOf U) * -valued AllTermsOf U -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):]
rng ((u SubstWith S) | (AllTermsOf U)) is set
[:(AllTermsOf U),(AllTermsOf U):] is non empty Relation-like set
bool [:(AllTermsOf U),(AllTermsOf U):] is non empty set
l . 1 is set
Jj is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
(U,u,S,l) . 1 is set
jJ is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
ar Jj is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U . Jj is set
abs (ar Jj) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
ar jJ is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U . jJ is set
abs (ar jJ) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
j is non empty Relation-like non empty-yielding AllTermsOf U -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf U),(AllTermsOf U):]
j (*) (SubTerms l) is Relation-like NAT -defined AllTermsOf U -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(((AllSymbolsOf U) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf U) *) \ {{}}
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf U) *) \ {{}}) *)
bool ((((AllSymbolsOf U) *) \ {{}}) *) is non empty non trivial non finite V166() set
<*Jj*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,Jj] is non empty set
{[1,Jj]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(U -multiCat) . (SubTerms l) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
<*Jj*> ^ ((U -multiCat) . (SubTerms l)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u SubstWith S) . l is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
(u SubstWith S) . <*Jj*> is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
(u SubstWith S) . ((U -multiCat) . (SubTerms l)) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
((u SubstWith S) . <*Jj*>) ^ ((u SubstWith S) . ((U -multiCat) . (SubTerms l))) is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*Jj*> ^ ((u SubstWith S) . ((U -multiCat) . (SubTerms l))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*jJ*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,jJ] is non empty set
{[1,jJ]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
h is Relation-like NAT -defined AllTermsOf U -valued Function-like finite abs (ar jJ) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
(U -multiCat) . h is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*jJ*> ^ ((U -multiCat) . h) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U is non empty set
u is Element of U
S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l is V51() V53() eligible Language-like
AllSymbolsOf l is non empty non trivial non finite V166() set
the U1 of l is set
AllTermsOf l is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
AllSymbolsOf l is non empty non trivial non finite V166() set
(AllSymbolsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf l
((AllSymbolsOf l) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf l) *)
bool ((AllSymbolsOf l) *) is non empty non trivial non finite V166() set
((AllSymbolsOf l) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
bool (((AllSymbolsOf l) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf l) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf l) *) \ {{}}))
bool (bool (((AllSymbolsOf l) *) \ {{}})) is non empty non trivial non finite V166() set
l -termsOfMaxDepth is Relation-like Function-like set
rng (l -termsOfMaxDepth) is set
union (rng (l -termsOfMaxDepth)) is set
l -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf l) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf l) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf l) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf l) *) \ {{}})):] is non empty non trivial non finite V166() set
(l -termsOfMaxDepth) . S is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
(AllSymbolsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf l
II is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
E is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
{E} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf l)
bool (AllSymbolsOf l) is non empty non trivial non finite V166() set
(AllSymbolsOf l) \ {E} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf l)
(AllSymbolsOf l) typed\ {E} is Element of bool (AllSymbolsOf l)
((AllSymbolsOf l) \ {E}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((AllSymbolsOf l) *)
bool ((AllSymbolsOf l) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf l) \ {E}) *) /\ ((l -termsOfMaxDepth) . S) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf l) *) \ {{}})
(((AllSymbolsOf l) \ {E}) *) typed/\ ((l -termsOfMaxDepth) . S) is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf l) \ {E}) *)
bool (((AllSymbolsOf l) \ {E}) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf l) \ {E}) *) /\ ((l -termsOfMaxDepth) . S) is functional set
(((AllSymbolsOf l) \ {E}) *) /\typed ((l -termsOfMaxDepth) . S) is functional finite-membered FinSequence-membered V165() Element of bool ((l -termsOfMaxDepth) . S)
bool ((l -termsOfMaxDepth) . S) is non empty set
II SubstWith E is non empty Relation-like (AllSymbolsOf l) * -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):]
[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):] is non empty non trivial non finite V166() set
i is Relation-like Function-like Function-yielding V164() l,U -interpreter-like set
(II,u) ReassignIn i is Relation-like Function-like Function-yielding V164() l,U -interpreter-like set
{} .--> u is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> u is non empty Relation-like {{}} -defined U -valued {u} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{u}:]
{u} is non empty trivial finite 1 -element set
[:{{}},{u}:] is non empty Relation-like finite set
bool [:{{}},{u}:] is non empty finite finite-membered set
II .--> ({} .--> u) is trivial Relation-like AllSymbolsOf l -defined {II} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{II} is non empty trivial finite 1 -element set
{II} --> ({} .--> u) is non empty Relation-like {II} -defined {({} .--> u)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{II},{({} .--> u)}:]
{({} .--> u)} is non empty trivial functional finite finite-membered 1 -element set
[:{II},{({} .--> u)}:] is non empty Relation-like finite set
bool [:{II},{({} .--> u)}:] is non empty finite finite-membered set
i +* (II .--> ({} .--> u)) is Relation-like Function-like Function-yielding V164() set
((II,u) ReassignIn i) -TermEval is non empty Relation-like AllTermsOf l -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),U:]
[:(AllTermsOf l),U:] is non empty Relation-like set
bool [:(AllTermsOf l),U:] is non empty set
(((II,u) ReassignIn i) -TermEval) | ((((AllSymbolsOf l) \ {E}) *) /\ ((l -termsOfMaxDepth) . S)) is Relation-like AllTermsOf l -defined (((AllSymbolsOf l) \ {E}) *) /\ ((l -termsOfMaxDepth) . S) -defined AllTermsOf l -defined U -valued Function-like Element of bool [:(AllTermsOf l),U:]
(E,u) ReassignIn i is Relation-like Function-like Function-yielding V164() l,U -interpreter-like set
E .--> ({} .--> u) is trivial Relation-like AllSymbolsOf l -defined {E} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{E} is non empty trivial finite 1 -element set
{E} --> ({} .--> u) is non empty Relation-like {E} -defined {({} .--> u)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{E},{({} .--> u)}:]
[:{E},{({} .--> u)}:] is non empty Relation-like finite set
bool [:{E},{({} .--> u)}:] is non empty finite finite-membered set
i +* (E .--> ({} .--> u)) is Relation-like Function-like Function-yielding V164() set
((E,u) ReassignIn i) -TermEval is non empty Relation-like AllTermsOf l -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),U:]
(((E,u) ReassignIn i) -TermEval) * (II SubstWith E) is Relation-like (AllSymbolsOf l) * -defined U -valued Function-like Element of bool [:((AllSymbolsOf l) *),U:]
[:((AllSymbolsOf l) *),U:] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf l) *),U:] is non empty non trivial non finite V166() set
((((E,u) ReassignIn i) -TermEval) * (II SubstWith E)) | ((((AllSymbolsOf l) \ {E}) *) /\ ((l -termsOfMaxDepth) . S)) is Relation-like (AllSymbolsOf l) * -defined (((AllSymbolsOf l) \ {E}) *) /\ ((l -termsOfMaxDepth) . S) -defined (AllSymbolsOf l) * -defined U -valued Function-like Element of bool [:((AllSymbolsOf l) *),U:]
l -firstChar is non empty Relation-like ((AllSymbolsOf l) *) \ {{}} -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):]
[:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):] is non empty non trivial non finite V166() set
(AllSymbolsOf l) -firstChar is non empty Relation-like ((AllSymbolsOf l) *) \ {{}} -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):]
(AllSymbolsOf l) -pr1 is non empty Relation-like [:(AllSymbolsOf l),(AllSymbolsOf l):] -defined AllSymbolsOf l -valued Function-like total quasi_total V233( AllSymbolsOf l) Element of bool [:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):]
[:(AllSymbolsOf l),(AllSymbolsOf l):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf l),(AllSymbolsOf l)) is non empty Relation-like [:(AllSymbolsOf l),(AllSymbolsOf l):] -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):]
MultPlace ((AllSymbolsOf l) -pr1) is non empty Relation-like ((AllSymbolsOf l) *) \ {{}} -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):]
l -multiCat is non empty Relation-like ((AllSymbolsOf l) *) * -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf l) *) *),((AllSymbolsOf l) *):]
((AllSymbolsOf l) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf l) *
[:(((AllSymbolsOf l) *) *),((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf l) *) *),((AllSymbolsOf l) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf l) -multiCat is non empty Relation-like ((AllSymbolsOf l) *) * -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf l) *) *),((AllSymbolsOf l) *):]
(AllSymbolsOf l) -concatenation is non empty Relation-like [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):] -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf l) * ) Element of bool [:[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):],((AllSymbolsOf l) *):]
[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):],((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):],((AllSymbolsOf l) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf l) -concatenation) is non empty Relation-like (((AllSymbolsOf l) *) *) \ {{}} -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf l) *) *) \ {{}}),((AllSymbolsOf l) *):]
(((AllSymbolsOf l) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf l) *) *)
bool (((AllSymbolsOf l) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf l) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf l) *) *)
[:((((AllSymbolsOf l) *) *) \ {{}}),((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf l) *) *) \ {{}}),((AllSymbolsOf l) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf l) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
LettersOf l is non empty non trivial non finite V166() Element of bool (AllSymbolsOf l)
bool (AllSymbolsOf l) is non empty non trivial non finite V166() set
the U3 of l is Element of the U1 of l
{ the U3 of l} is non empty trivial finite 1 -element set
the U1 of l \ { the U3 of l} is non empty Element of bool the U1 of l
bool the U1 of l is non empty set
the U1 of l typed\ { the U3 of l} is Element of bool the U1 of l
the adicity of l is non empty Relation-like the U1 of l \ { the U3 of l} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of l \ { the U3 of l}),INT:]
[:( the U1 of l \ { the U3 of l}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of l \ { the U3 of l}),INT:] is non empty non trivial non finite V166() set
{0} is non empty trivial functional finite finite-membered 1 -element V166() Element of bool NAT
0 * is non empty functional finite-membered FinSequence-membered FinSequenceSet of 0
{0} is non empty trivial functional finite finite-membered 1 -element V166() set
the adicity of l " {0} is Element of bool ( the U1 of l \ { the U3 of l})
bool ( the U1 of l \ { the U3 of l}) is non empty set
n is non empty Element of bool (AllSymbolsOf l)
n * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((AllSymbolsOf l) *)
{II} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf l)
dom (II .--> ({} .--> u)) is trivial finite Element of bool {II}
bool {II} is non empty finite finite-membered set
dom (E .--> ({} .--> u)) is trivial finite Element of bool {E}
bool {E} is non empty finite finite-membered set
((II,u) ReassignIn i) . II is non empty Relation-like (abs (ar II)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of II,U
ar II 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of l . II is set
abs (ar II) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(abs (ar II)) -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
U \/ BOOLEAN is non empty set
(II .--> ({} .--> u)) . II is Relation-like Function-like set
((E,u) ReassignIn i) . E is non empty Relation-like (abs (ar E)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of E,U
ar E 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of l . E is set
abs (ar E) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(abs (ar E)) -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
(E .--> ({} .--> u)) . E is Relation-like Function-like set
(l -termsOfMaxDepth) . 0 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
((l -termsOfMaxDepth) . 0) /\ (n *) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
((l -termsOfMaxDepth) . 0) typed/\ (n *) is functional finite-membered FinSequence-membered V165() Element of bool ((l -termsOfMaxDepth) . 0)
bool ((l -termsOfMaxDepth) . 0) is non empty set
((l -termsOfMaxDepth) . 0) /\ (n *) is functional set
((l -termsOfMaxDepth) . 0) /\typed (n *) is functional finite-membered FinSequence-membered Element of bool (n *)
bool (n *) is non empty non trivial non finite V166() set
(((II,u) ReassignIn i) -TermEval) | (((l -termsOfMaxDepth) . 0) /\ (n *)) is Relation-like AllTermsOf l -defined ((l -termsOfMaxDepth) . 0) /\ (n *) -defined AllTermsOf l -defined U -valued Function-like Element of bool [:(AllTermsOf l),U:]
((((E,u) ReassignIn i) -TermEval) * (II SubstWith E)) | (((l -termsOfMaxDepth) . 0) /\ (n *)) is Relation-like (AllSymbolsOf l) * -defined ((l -termsOfMaxDepth) . 0) /\ (n *) -defined (AllSymbolsOf l) * -defined U -valued Function-like Element of bool [:((AllSymbolsOf l) *),U:]
bool (AllTermsOf l) is non empty set
En is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf l)
(II SubstWith E) | ((l -termsOfMaxDepth) . 0) is Relation-like (AllSymbolsOf l) * -defined (l -termsOfMaxDepth) . 0 -defined (AllSymbolsOf l) * -defined (AllSymbolsOf l) * -valued (l -termsOfMaxDepth) . 0 -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):]
bool En is non empty set
En /\ (n *) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
En typed/\ (n *) is functional finite-membered FinSequence-membered V165() Element of bool En
En /\ (n *) is functional set
En /\typed (n *) is functional finite-membered FinSequence-membered Element of bool (n *)
hh is Relation-like (l -termsOfMaxDepth) . 0 -valued Function-like Function-yielding V164() FinSequence-yielding set
hh | (n *) is Relation-like n * -defined (l -termsOfMaxDepth) . 0 -valued Function-like Function-yielding V164() FinSequence-yielding set
nE is non empty functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
(II SubstWith E) | (En /\ (n *)) is Relation-like (AllSymbolsOf l) * -defined En /\ (n *) -defined (AllSymbolsOf l) * -defined (AllSymbolsOf l) * -valued Function-like total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):]
ss is Relation-like nE -valued Function-like Function-yielding V164() FinSequence-yielding set
(((E,u) ReassignIn i) -TermEval) (*) ss is Relation-like U -valued Function-like set
dom ((((E,u) ReassignIn i) -TermEval) (*) ss) is set
s is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf l)
(((II,u) ReassignIn i) -TermEval) | s is Relation-like AllTermsOf l -defined s -defined AllTermsOf l -defined U -valued Function-like total Element of bool [:(AllTermsOf l),U:]
dom ((((II,u) ReassignIn i) -TermEval) | s) is functional finite-membered FinSequence-membered V165() Element of bool s
bool s is non empty set
rng ((((E,u) ReassignIn i) -TermEval) (*) ss) is set
rng ((((II,u) ReassignIn i) -TermEval) | s) is set
[:s,U:] is Relation-like set
bool [:s,U:] is non empty set
phi2 is set
hhh is functional finite-membered FinSequence-membered V165() Element of bool En
dom ss is set
rng ss is set
b1 is non empty functional finite-membered FinSequence-membered Element of bool (n *)
[:b1,En:] is non empty Relation-like set
bool [:b1,En:] is non empty set
b2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of b1
TermSymbolsOf l is non empty set
the adicity of l " NAT is Element of bool ( the U1 of l \ { the U3 of l})
A1 is non empty trivial Relation-like NAT -defined TermSymbolsOf l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf l) *) \ {{}}
AtomicTermsOf l is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
LettersOf l is non empty non trivial non finite V166() set
1 -tuples_on (LettersOf l) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of LettersOf l
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of En
bool (LettersOf l) is non empty non trivial non finite V166() set
(LettersOf l) \ {E} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf l)
(LettersOf l) typed\ {E} is Element of bool (LettersOf l)
(LettersOf l) \ {E} is non empty non trivial non finite V166() Element of bool (LettersOf l)
X1 is non empty trivial Relation-like NAT -defined LettersOf l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support FinSequence of LettersOf l
rng X1 is non empty trivial finite 1 -element set
c2 is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of n *
rng c2 is finite set
rng b2 is finite set
(LettersOf l) /\ ((AllSymbolsOf l) \ {E}) is Element of bool (AllSymbolsOf l)
(LettersOf l) typed/\ ((AllSymbolsOf l) \ {E}) is Element of bool (LettersOf l)
(LettersOf l) /\ ((AllSymbolsOf l) \ {E}) is set
(LettersOf l) /\typed ((AllSymbolsOf l) \ {E}) is Element of bool ((AllSymbolsOf l) \ {E})
bool ((AllSymbolsOf l) \ {E}) is non empty non trivial non finite V166() set
(LettersOf l) null (AllSymbolsOf l) is set
(AllSymbolsOf l) /\ (LettersOf l) is Element of bool (AllSymbolsOf l)
(AllSymbolsOf l) typed/\ (LettersOf l) is Element of bool (AllSymbolsOf l)
(AllSymbolsOf l) /\ (LettersOf l) is set
(AllSymbolsOf l) /\typed (LettersOf l) is Element of bool (LettersOf l)
(LettersOf l) \typed/ (AllSymbolsOf l) is Element of bool ((LettersOf l) \/ (AllSymbolsOf l))
(LettersOf l) \/ (AllSymbolsOf l) is non empty non trivial non finite V166() set
bool ((LettersOf l) \/ (AllSymbolsOf l)) is non empty non trivial non finite V166() set
((LettersOf l) null (AllSymbolsOf l)) \ {E} is Element of bool ((LettersOf l) null (AllSymbolsOf l))
bool ((LettersOf l) null (AllSymbolsOf l)) is non empty set
((LettersOf l) null (AllSymbolsOf l)) typed\ {E} is Element of bool ((LettersOf l) null (AllSymbolsOf l))
t2 is non empty Element of bool (LettersOf l)
tt2 is non empty trivial Relation-like NAT -defined t2 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
tt2 . 1 is set
{(tt2 . 1)} is non empty trivial finite 1 -element set
{(tt2 . 1)} \ t2 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of bool {(tt2 . 1)}
bool {(tt2 . 1)} is non empty finite finite-membered set
{(tt2 . 1)} typed\ t2 is trivial finite Element of bool {(tt2 . 1)}
E11 is Element of t2
len tt2 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(l,II,E,A1) is non empty trivial Relation-like NAT -defined TermSymbolsOf l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf l) *) \ {{}}
A1 +~ (II,E) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(l -firstChar) . A1 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
EE1 is non empty trivial Relation-like NAT -defined TermSymbolsOf l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf l) *) \ {{}}
(l -firstChar) . EE1 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
E22 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
EE2 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
EE1 . 1 is set
c1 is non empty Relation-like non empty-yielding b1 -defined En -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:b1,En:]
(((E,u) ReassignIn i) -TermEval) * c1 is Relation-like b1 -defined U -valued Function-like Element of bool [:b1,U:]
[:b1,U:] is non empty Relation-like set
bool [:b1,U:] is non empty set
((((E,u) ReassignIn i) -TermEval) * c1) . b2 is set
c1 . b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of En
(((E,u) ReassignIn i) -TermEval) . (c1 . b2) is set
(((((E,u) ReassignIn i) -TermEval) * c1) . b2) \+\ ((((E,u) ReassignIn i) -TermEval) . (c1 . b2)) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((((E,u) ReassignIn i) -TermEval) * c1) . b2) \ ((((E,u) ReassignIn i) -TermEval) . (c1 . b2)) is set
(((((E,u) ReassignIn i) -TermEval) * c1) . b2) typed\ ((((E,u) ReassignIn i) -TermEval) . (c1 . b2)) is Element of bool (((((E,u) ReassignIn i) -TermEval) * c1) . b2)
bool (((((E,u) ReassignIn i) -TermEval) * c1) . b2) is non empty set
(((((E,u) ReassignIn i) -TermEval) * c1) . b2) \ ((((E,u) ReassignIn i) -TermEval) . (c1 . b2)) is Element of bool (((((E,u) ReassignIn i) -TermEval) * c1) . b2)
((((E,u) ReassignIn i) -TermEval) . (c1 . b2)) \ (((((E,u) ReassignIn i) -TermEval) * c1) . b2) is set
((((E,u) ReassignIn i) -TermEval) . (c1 . b2)) typed\ (((((E,u) ReassignIn i) -TermEval) * c1) . b2) is Element of bool ((((E,u) ReassignIn i) -TermEval) . (c1 . b2))
bool ((((E,u) ReassignIn i) -TermEval) . (c1 . b2)) is non empty set
((((E,u) ReassignIn i) -TermEval) . (c1 . b2)) \ (((((E,u) ReassignIn i) -TermEval) * c1) . b2) is Element of bool ((((E,u) ReassignIn i) -TermEval) . (c1 . b2))
((((((E,u) ReassignIn i) -TermEval) * c1) . b2) \ ((((E,u) ReassignIn i) -TermEval) . (c1 . b2))) \/ (((((E,u) ReassignIn i) -TermEval) . (c1 . b2)) \ (((((E,u) ReassignIn i) -TermEval) * c1) . b2)) is set
ss . b2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(II SubstWith E) . b2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(ss . b2) \+\ ((II SubstWith E) . b2) is Relation-like finite set
(ss . b2) \ ((II SubstWith E) . b2) is Relation-like NAT -defined finite set
(ss . b2) typed\ ((II SubstWith E) . b2) is Relation-like NAT -defined Function-like finite finite-support Element of bool (ss . b2)
bool (ss . b2) is non empty finite finite-membered set
(ss . b2) \ ((II SubstWith E) . b2) is Relation-like NAT -defined Function-like finite finite-support Element of bool (ss . b2)
((II SubstWith E) . b2) \ (ss . b2) is Relation-like NAT -defined finite set
((II SubstWith E) . b2) typed\ (ss . b2) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((II SubstWith E) . b2)
bool ((II SubstWith E) . b2) is non empty finite finite-membered set
((II SubstWith E) . b2) \ (ss . b2) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((II SubstWith E) . b2)
((ss . b2) \ ((II SubstWith E) . b2)) \/ (((II SubstWith E) . b2) \ (ss . b2)) is Relation-like NAT -defined finite set
phi22 is Relation-like s -defined U -valued Function-like total quasi_total Element of bool [:s,U:]
phi22 . b2 is set
(((II,u) ReassignIn i) -TermEval) . b2 is set
(phi22 . b2) \+\ ((((II,u) ReassignIn i) -TermEval) . b2) is set
(phi22 . b2) \ ((((II,u) ReassignIn i) -TermEval) . b2) is set
(phi22 . b2) typed\ ((((II,u) ReassignIn i) -TermEval) . b2) is Element of bool (phi22 . b2)
bool (phi22 . b2) is non empty set
(phi22 . b2) \ ((((II,u) ReassignIn i) -TermEval) . b2) is Element of bool (phi22 . b2)
((((II,u) ReassignIn i) -TermEval) . b2) \ (phi22 . b2) is set
((((II,u) ReassignIn i) -TermEval) . b2) typed\ (phi22 . b2) is Element of bool ((((II,u) ReassignIn i) -TermEval) . b2)
bool ((((II,u) ReassignIn i) -TermEval) . b2) is non empty set
((((II,u) ReassignIn i) -TermEval) . b2) \ (phi22 . b2) is Element of bool ((((II,u) ReassignIn i) -TermEval) . b2)
((phi22 . b2) \ ((((II,u) ReassignIn i) -TermEval) . b2)) \/ (((((II,u) ReassignIn i) -TermEval) . b2) \ (phi22 . b2)) is set
((((E,u) ReassignIn i) -TermEval) (*) ss) . phi2 is set
ss . phi2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((E,u) ReassignIn i) -TermEval) . (ss . phi2) is set
(II SubstWith E) . phi2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
phi22 . phi2 is set
(((II,u) ReassignIn i) -TermEval) . phi2 is set
c₃₀ is Relation-like s -defined U -valued Function-like total quasi_total Element of bool [:s,U:]
c₃₀ . phi2 is set
(((E,u) ReassignIn i) -TermEval) . EE1 is set
((E,u) ReassignIn i) . EE2 is non empty Relation-like (abs (ar EE2)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of EE2,U
ar EE2 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of l . EE2 is set
abs (ar EE2) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(abs (ar EE2)) -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
SubTerms EE1 is empty trivial Relation-like non-empty empty-yielding NAT -defined (rng EE1) * -valued AllTermsOf l -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element abs (ar EE1) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllTermsOf l) *
rng EE1 is non empty trivial finite 1 -element set
(rng EE1) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng EE1
AllTermsOf l is non empty functional finite-membered FinSequence-membered AllSymbolsOf l -prefix l -prefix Element of bool ((AllSymbolsOf l) *)
ar EE1 is finite complex ext-real V40() V41() Element of INT
ar ((l -firstChar) . EE1) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of l . ((l -firstChar) . EE1) is set
abs (ar EE1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(AllTermsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf l) *) *)
(((E,u) ReassignIn i) -TermEval) (*) (SubTerms EE1) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued U -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element len (SubTerms EE1) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
len (SubTerms EE1) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(((E,u) ReassignIn i) . EE2) . ((((E,u) ReassignIn i) -TermEval) (*) (SubTerms EE1)) is set
(((E,u) ReassignIn i) . EE2) . {} is set
((II,u) ReassignIn i) . E22 is non empty Relation-like (abs (ar E22)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of E22,U
ar E22 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of l . E22 is set
abs (ar E22) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(abs (ar E22)) -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
SubTerms A1 is empty trivial Relation-like non-empty empty-yielding NAT -defined (rng A1) * -valued AllTermsOf l -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element abs (ar A1) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllTermsOf l) *
rng A1 is non empty trivial finite 1 -element set
(rng A1) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng A1
ar A1 is finite complex ext-real V40() V41() Element of INT
ar ((l -firstChar) . 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of l . ((l -firstChar) . 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
(((II,u) ReassignIn i) -TermEval) (*) (SubTerms A1) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued U -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element len (SubTerms A1) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
len (SubTerms 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(((II,u) ReassignIn i) . E22) . ((((II,u) ReassignIn i) -TermEval) (*) (SubTerms A1)) is set
(((II,u) ReassignIn i) . E22) . {} is set
<*II*> is non empty trivial Relation-like NAT -defined TermSymbolsOf l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf l) *) \ {{}}
[1,II] is non empty set
{[1,II]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
<*E*> is non empty trivial Relation-like NAT -defined TermSymbolsOf l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf l) *) \ {{}}
[1,E] is non empty set
{[1,E]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
i . E11 is Relation-like Function-like set
(i . E11) . {} is set
En is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(l -termsOfMaxDepth) . En is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
((l -termsOfMaxDepth) . En) /\ (n *) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
((l -termsOfMaxDepth) . En) typed/\ (n *) is functional finite-membered FinSequence-membered V165() Element of bool ((l -termsOfMaxDepth) . En)
bool ((l -termsOfMaxDepth) . En) is non empty set
((l -termsOfMaxDepth) . En) /\ (n *) is functional set
((l -termsOfMaxDepth) . En) /\typed (n *) is functional finite-membered FinSequence-membered Element of bool (n *)
(((II,u) ReassignIn i) -TermEval) | (((l -termsOfMaxDepth) . En) /\ (n *)) is Relation-like AllTermsOf l -defined ((l -termsOfMaxDepth) . En) /\ (n *) -defined AllTermsOf l -defined U -valued Function-like Element of bool [:(AllTermsOf l),U:]
((((E,u) ReassignIn i) -TermEval) * (II SubstWith E)) | (((l -termsOfMaxDepth) . En) /\ (n *)) is Relation-like (AllSymbolsOf l) * -defined ((l -termsOfMaxDepth) . En) /\ (n *) -defined (AllSymbolsOf l) * -defined U -valued Function-like Element of bool [:((AllSymbolsOf l) *),U:]
En + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(l -termsOfMaxDepth) . (En + 1) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
((l -termsOfMaxDepth) . (En + 1)) /\ (n *) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
((l -termsOfMaxDepth) . (En + 1)) typed/\ (n *) is functional finite-membered FinSequence-membered V165() Element of bool ((l -termsOfMaxDepth) . (En + 1))
bool ((l -termsOfMaxDepth) . (En + 1)) is non empty set
((l -termsOfMaxDepth) . (En + 1)) /\ (n *) is functional set
((l -termsOfMaxDepth) . (En + 1)) /\typed (n *) is functional finite-membered FinSequence-membered Element of bool (n *)
(((II,u) ReassignIn i) -TermEval) | (((l -termsOfMaxDepth) . (En + 1)) /\ (n *)) is Relation-like AllTermsOf l -defined ((l -termsOfMaxDepth) . (En + 1)) /\ (n *) -defined AllTermsOf l -defined U -valued Function-like Element of bool [:(AllTermsOf l),U:]
((((E,u) ReassignIn i) -TermEval) * (II SubstWith E)) | (((l -termsOfMaxDepth) . (En + 1)) /\ (n *)) is Relation-like (AllSymbolsOf l) * -defined ((l -termsOfMaxDepth) . (En + 1)) /\ (n *) -defined (AllSymbolsOf l) * -defined U -valued Function-like Element of bool [:((AllSymbolsOf l) *),U:]
bool (AllTermsOf l) is non empty set
nE is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(l -termsOfMaxDepth) . nE is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
hh is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(l -termsOfMaxDepth) . hh is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
hhh is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf l)
hhh /\ (n *) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
hhh typed/\ (n *) is functional finite-membered FinSequence-membered V165() Element of bool hhh
bool hhh is non empty set
hhh /\ (n *) is functional set
hhh /\typed (n *) is functional finite-membered FinSequence-membered Element of bool (n *)
s is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf l)
s /\ (n *) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
s typed/\ (n *) is functional finite-membered FinSequence-membered V165() Element of bool s
bool s is non empty set
s /\ (n *) is functional set
s /\typed (n *) is functional finite-membered FinSequence-membered Element of bool (n *)
(II SubstWith E) | ((l -termsOfMaxDepth) . hh) is Relation-like (AllSymbolsOf l) * -defined (l -termsOfMaxDepth) . hh -defined (AllSymbolsOf l) * -defined (AllSymbolsOf l) * -valued (l -termsOfMaxDepth) . hh -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):]
((II SubstWith E) | ((l -termsOfMaxDepth) . hh)) | (n *) is Relation-like (AllSymbolsOf l) * -defined n * -defined (AllSymbolsOf l) * -defined (AllSymbolsOf l) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):]
phi22 is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf l)
(II SubstWith E) | phi22 is Relation-like (AllSymbolsOf l) * -defined phi22 -defined (AllSymbolsOf l) * -defined (AllSymbolsOf l) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):]
dom ((II SubstWith E) | phi22) is functional finite-membered FinSequence-membered V165() Element of bool phi22
bool phi22 is non empty set
c₃₀ is Relation-like AllTermsOf l -valued Function-like Function-yielding V164() FinSequence-yielding set
rng c₃₀ is set
[:phi22,(AllTermsOf l):] is Relation-like set
bool [:phi22,(AllTermsOf l):] is non empty set
(II SubstWith E) | ((l -termsOfMaxDepth) . nE) is Relation-like (AllSymbolsOf l) * -defined (l -termsOfMaxDepth) . nE -defined (AllSymbolsOf l) * -defined (AllSymbolsOf l) * -valued (l -termsOfMaxDepth) . nE -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):]
((II SubstWith E) | ((l -termsOfMaxDepth) . nE)) | (n *) is Relation-like (AllSymbolsOf l) * -defined n * -defined (AllSymbolsOf l) * -defined (AllSymbolsOf l) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):]
ss is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf l)
(II SubstWith E) | ss is Relation-like (AllSymbolsOf l) * -defined ss -defined (AllSymbolsOf l) * -defined (AllSymbolsOf l) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):]
(((II,u) ReassignIn i) -TermEval) | phi22 is Relation-like AllTermsOf l -defined phi22 -defined AllTermsOf l -defined U -valued Function-like total Element of bool [:(AllTermsOf l),U:]
dom ((((II,u) ReassignIn i) -TermEval) | phi22) is functional finite-membered FinSequence-membered V165() Element of bool phi22
(((E,u) ReassignIn i) -TermEval) (*) c₃₀ is Relation-like U -valued Function-like set
dom ((((E,u) ReassignIn i) -TermEval) (*) c₃₀) is set
b1 is Relation-like AllTermsOf l -valued Function-like Function-yielding V164() FinSequence-yielding set
(((E,u) ReassignIn i) -TermEval) (*) b1 is Relation-like U -valued Function-like set
dom ((((E,u) ReassignIn i) -TermEval) (*) b1) is set
rng ((((II,u) ReassignIn i) -TermEval) | phi22) is set
rng ((((E,u) ReassignIn i) -TermEval) (*) c₃₀) is set
[:phi22,U:] is Relation-like set
bool [:phi22,U:] is non empty set
c2 is set
A1 is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool s
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of A1
TermSymbolsOf l is non empty set
the adicity of l " NAT is Element of bool ( the U1 of l \ { the U3 of l})
t2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of s
tt2 is non empty Relation-like NAT -defined TermSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal hh -termal Element of ((AllSymbolsOf l) *) \ {{}}
Depth tt2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
bool ((AllSymbolsOf l) \ {E}) is non empty non trivial non finite V166() set
X1 is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of n *
rng X1 is finite set
E22 is Element of bool ((AllSymbolsOf l) \ {E})
E22 * is non empty functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf l) \ {E}) *)
((AllSymbolsOf l) \ {E}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf l) \ {E}
bool (((AllSymbolsOf l) \ {E}) *) is non empty non trivial non finite V166() set
SubTerms tt2 is Relation-like NAT -defined (rng tt2) * -valued AllTermsOf l -valued Function-like finite abs (ar tt2) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf l) *
rng tt2 is non empty finite set
(rng tt2) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng tt2
AllTermsOf l is non empty functional finite-membered FinSequence-membered AllSymbolsOf l -prefix l -prefix Element of bool ((AllSymbolsOf l) *)
ar tt2 is finite complex ext-real V40() V41() Element of INT
(l -firstChar) . tt2 is non relational termal own ofAtomicFormula Element of AllSymbolsOf l
ar ((l -firstChar) . tt2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of l . ((l -firstChar) . tt2) is set
abs (ar tt2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(AllTermsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf l) *) *)
rng (SubTerms tt2) is finite set
nE + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(l,II,E,tt2) is non empty Relation-like NAT -defined TermSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal hh -termal Element of ((AllSymbolsOf l) *) \ {{}}
tt2 +~ (II,E) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
EE2 is non empty Relation-like NAT -defined TermSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal nE + 1 -termal Element of ((AllSymbolsOf l) *) \ {{}}
SubTerms EE2 is Relation-like NAT -defined (l -termsOfMaxDepth) . nE -valued (rng EE2) * -valued AllTermsOf l -valued Function-like finite abs (ar EE2) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf l) *
K335(((AllSymbolsOf l) *)) is non empty non trivial non finite V166() Element of bool (bool ((AllSymbolsOf l) *))
bool (bool ((AllSymbolsOf l) *)) is non empty non trivial non finite V166() set
l -termsOfMaxDepth is non empty Relation-like NAT -defined K335(((AllSymbolsOf l) *)) -valued Function-like total quasi_total Element of bool [:NAT,K335(((AllSymbolsOf l) *)):]
[:NAT,K335(((AllSymbolsOf l) *)):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335(((AllSymbolsOf l) *)):] is non empty non trivial non finite V166() set
(l -termsOfMaxDepth) . nE is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335(((AllSymbolsOf l) *))
rng EE2 is non empty finite set
(rng EE2) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng EE2
ar EE2 is finite complex ext-real V40() V41() Element of INT
(l -firstChar) . EE2 is non relational termal own ofAtomicFormula Element of AllSymbolsOf l
ar ((l -firstChar) . EE2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of l . ((l -firstChar) . EE2) is set
abs (ar EE2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
rng (SubTerms EE2) is finite set
(((II,u) ReassignIn i) -TermEval) | ss is Relation-like AllTermsOf l -defined ss -defined AllTermsOf l -defined U -valued Function-like total Element of bool [:(AllTermsOf l),U:]
dom ((((II,u) ReassignIn i) -TermEval) | ss) is functional finite-membered FinSequence-membered V165() Element of bool ss
bool ss is non empty set
((((E,u) ReassignIn i) -TermEval) * (II SubstWith E)) | ss is Relation-like (AllSymbolsOf l) * -defined ss -defined (AllSymbolsOf l) * -defined U -valued Function-like Element of bool [:((AllSymbolsOf l) *),U:]
dom (((((E,u) ReassignIn i) -TermEval) * (II SubstWith E)) | ss) is functional finite-membered FinSequence-membered V165() Element of bool ss
c1 is Relation-like phi22 -defined U -valued Function-like total quasi_total Element of bool [:phi22,U:]
c1 . A2 is set
(((II,u) ReassignIn i) -TermEval) . A2 is set
(c1 . A2) \+\ ((((II,u) ReassignIn i) -TermEval) . A2) is set
(c1 . A2) \ ((((II,u) ReassignIn i) -TermEval) . A2) is set
(c1 . A2) typed\ ((((II,u) ReassignIn i) -TermEval) . A2) is Element of bool (c1 . A2)
bool (c1 . A2) is non empty set
(c1 . A2) \ ((((II,u) ReassignIn i) -TermEval) . A2) is Element of bool (c1 . A2)
((((II,u) ReassignIn i) -TermEval) . A2) \ (c1 . A2) is set
((((II,u) ReassignIn i) -TermEval) . A2) typed\ (c1 . A2) is Element of bool ((((II,u) ReassignIn i) -TermEval) . A2)
bool ((((II,u) ReassignIn i) -TermEval) . A2) is non empty set
((((II,u) ReassignIn i) -TermEval) . A2) \ (c1 . A2) is Element of bool ((((II,u) ReassignIn i) -TermEval) . A2)
((c1 . A2) \ ((((II,u) ReassignIn i) -TermEval) . A2)) \/ (((((II,u) ReassignIn i) -TermEval) . A2) \ (c1 . A2)) is set
(II SubstWith E) | A1 is Relation-like (AllSymbolsOf l) * -defined A1 -defined (AllSymbolsOf l) * -defined (AllSymbolsOf l) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):]
((II SubstWith E) | A1) . A2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(II SubstWith E) . A2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((II SubstWith E) | A1) . A2) \+\ ((II SubstWith E) . 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((II SubstWith E) | A1) . A2) \ ((II SubstWith E) . A2) is Relation-like NAT -defined finite set
(((II SubstWith E) | A1) . A2) typed\ ((II SubstWith E) . A2) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((II SubstWith E) | A1) . A2)
bool (((II SubstWith E) | A1) . A2) is non empty finite finite-membered set
(((II SubstWith E) | A1) . A2) \ ((II SubstWith E) . A2) is Relation-like NAT -defined Function-like finite finite-support Element of bool (((II SubstWith E) | A1) . A2)
((II SubstWith E) . A2) \ (((II SubstWith E) | A1) . A2) is Relation-like NAT -defined finite set
((II SubstWith E) . A2) typed\ (((II SubstWith E) | A1) . A2) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((II SubstWith E) . A2)
bool ((II SubstWith E) . A2) is non empty finite finite-membered set
((II SubstWith E) . A2) \ (((II SubstWith E) | A1) . A2) is Relation-like NAT -defined Function-like finite finite-support Element of bool ((II SubstWith E) . A2)
((((II SubstWith E) | A1) . A2) \ ((II SubstWith E) . A2)) \/ (((II SubstWith E) . A2) \ (((II SubstWith E) | A1) . A2)) is Relation-like NAT -defined finite set
phi2 is Relation-like phi22 -defined AllTermsOf l -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:phi22,(AllTermsOf l):]
(((E,u) ReassignIn i) -TermEval) * phi2 is Relation-like phi22 -defined U -valued Function-like total quasi_total Element of bool [:phi22,U:]
((((E,u) ReassignIn i) -TermEval) * phi2) . A2 is set
phi2 . A2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((E,u) ReassignIn i) -TermEval) . (phi2 . A2) is set
(((((E,u) ReassignIn i) -TermEval) * phi2) . A2) \+\ ((((E,u) ReassignIn i) -TermEval) . (phi2 . A2)) is set
(((((E,u) ReassignIn i) -TermEval) * phi2) . A2) \ ((((E,u) ReassignIn i) -TermEval) . (phi2 . A2)) is set
(((((E,u) ReassignIn i) -TermEval) * phi2) . A2) typed\ ((((E,u) ReassignIn i) -TermEval) . (phi2 . A2)) is Element of bool (((((E,u) ReassignIn i) -TermEval) * phi2) . A2)
bool (((((E,u) ReassignIn i) -TermEval) * phi2) . A2) is non empty set
(((((E,u) ReassignIn i) -TermEval) * phi2) . A2) \ ((((E,u) ReassignIn i) -TermEval) . (phi2 . A2)) is Element of bool (((((E,u) ReassignIn i) -TermEval) * phi2) . A2)
((((E,u) ReassignIn i) -TermEval) . (phi2 . A2)) \ (((((E,u) ReassignIn i) -TermEval) * phi2) . A2) is set
((((E,u) ReassignIn i) -TermEval) . (phi2 . A2)) typed\ (((((E,u) ReassignIn i) -TermEval) * phi2) . A2) is Element of bool ((((E,u) ReassignIn i) -TermEval) . (phi2 . A2))
bool ((((E,u) ReassignIn i) -TermEval) . (phi2 . A2)) is non empty set
((((E,u) ReassignIn i) -TermEval) . (phi2 . A2)) \ (((((E,u) ReassignIn i) -TermEval) * phi2) . A2) is Element of bool ((((E,u) ReassignIn i) -TermEval) . (phi2 . A2))
((((((E,u) ReassignIn i) -TermEval) * phi2) . A2) \ ((((E,u) ReassignIn i) -TermEval) . (phi2 . A2))) \/ (((((E,u) ReassignIn i) -TermEval) . (phi2 . A2)) \ (((((E,u) ReassignIn i) -TermEval) * phi2) . A2)) is set
c1 . c2 is set
(((II,u) ReassignIn i) -TermEval) . c2 is set
c₃₀ . c2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(II SubstWith E) . c2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
b2 is Relation-like phi22 -defined U -valued Function-like total quasi_total Element of bool [:phi22,U:]
b2 . c2 is set
(((E,u) ReassignIn i) -TermEval) . (c₃₀ . c2) is set
Y2 is non empty trivial Relation-like NAT -defined TermSymbolsOf l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf l) *) \ {{}}
(l -firstChar) . Y2 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
f1 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
<*f1*> is non empty trivial Relation-like NAT -defined TermSymbolsOf l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf l) *) \ {{}}
[1,f1] is non empty set
{[1,f1]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
SubTerms Y2 is empty trivial Relation-like non-empty empty-yielding NAT -defined (rng Y2) * -valued AllTermsOf l -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element abs (ar Y2) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllTermsOf l) *
rng Y2 is non empty trivial finite 1 -element set
(rng Y2) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng Y2
ar Y2 is finite complex ext-real V40() V41() Element of INT
ar ((l -firstChar) . Y2) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of l . ((l -firstChar) . Y2) is set
abs (ar Y2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(l -multiCat) . (SubTerms Y2) is Relation-like NAT -defined AllSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf l) *
<*f1*> ^ ((l -multiCat) . (SubTerms Y2)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(l,{},<*f1*>) is non empty Relation-like NAT -defined {} \/ (dom <*f1*>) -defined Seg (1 + {}) -defined {} \/ (rng <*f1*>) -valued TermSymbolsOf l -valued Function-like finite len <*f1*> -element total FinSequence-like FinSubsequence-like finite-support termal (Depth <*f1*>) + {} -termal Element of ((AllSymbolsOf l) *) \ {{}}
dom <*f1*> is non empty trivial finite 1 -element set
{} \/ (dom <*f1*>) is non empty finite set
1 + {} is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
Seg (1 + {}) is non empty 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
rng <*f1*> is non empty trivial finite 1 -element set
{} \/ (rng <*f1*>) is non empty finite set
len <*f1*> is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
Depth <*f1*> 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(Depth <*f1*>) + {} 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
<*f1*> \typed/ {} is Relation-like NAT -defined finite Element of bool (<*f1*> \/ {})
<*f1*> \/ {} is non empty Relation-like NAT -defined finite set
bool (<*f1*> \/ {}) is non empty finite finite-membered set
<*f1*> null {} is Relation-like NAT -defined {} \/ (dom <*f1*>) -defined Seg (1 + {}) -defined {} \/ (rng <*f1*>) -valued Function-like finite len <*f1*> -element total FinSequence-like FinSubsequence-like finite-support set
<*f1*> ^ {} is non empty Relation-like NAT -defined Function-like finite 1 + {} -element FinSequence-like FinSubsequence-like finite-support set
{} ^ <*f1*> is non empty Relation-like NAT -defined Function-like finite {} + 1 -element {} + 1 -element FinSequence-like FinSubsequence-like finite-support 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
X1 . 1 is set
{(X1 . 1)} is non empty trivial finite 1 -element set
{(X1 . 1)} \ n is trivial finite Element of bool {(X1 . 1)}
bool {(X1 . 1)} is non empty finite finite-membered set
{(X1 . 1)} typed\ n is trivial finite Element of bool {(X1 . 1)}
Y2 . 1 is set
ar f1 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of l . f1 is set
abs (ar f1) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(abs (ar f1)) -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
((E,u) ReassignIn i) . f1 is non empty Relation-like (abs (ar f1)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of f1,U
i . f1 is non empty Relation-like (abs (ar f1)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of f1,U
c1 . Y2 is set
((II,u) ReassignIn i) . f1 is non empty Relation-like (abs (ar f1)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of f1,U
(((II,u) ReassignIn i) -TermEval) (*) (SubTerms Y2) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued U -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element len (SubTerms Y2) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
len (SubTerms Y2) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(((II,u) ReassignIn i) . f1) . ((((II,u) ReassignIn i) -TermEval) (*) (SubTerms Y2)) is set
(((II,u) ReassignIn i) . f1) . {} is set
(((II,u) ReassignIn i) . II) . {} is set
(II SubstWith E) . Y2 is Relation-like NAT -defined AllSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf l) *
<*E*> is non empty trivial Relation-like NAT -defined TermSymbolsOf l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf l) *) \ {{}}
[1,E] is non empty set
{[1,E]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
b2 . Y2 is set
(l -firstChar) . <*E*> is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
((E,u) ReassignIn i) . ((l -firstChar) . <*E*>) is non empty Relation-like (abs (ar ((l -firstChar) . <*E*>))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (l -firstChar) . <*E*>,U
ar ((l -firstChar) . <*E*>) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of l . ((l -firstChar) . <*E*>) is set
abs (ar ((l -firstChar) . <*E*>)) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(abs (ar ((l -firstChar) . <*E*>))) -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
SubTerms <*E*> is empty trivial Relation-like non-empty empty-yielding NAT -defined (rng <*E*>) * -valued AllTermsOf l -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element abs (ar <*E*>) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllTermsOf l) *
rng <*E*> is non empty trivial finite 1 -element set
(rng <*E*>) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng <*E*>
ar <*E*> is finite complex ext-real V40() V41() Element of INT
abs (ar <*E*>) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(((E,u) ReassignIn i) -TermEval) (*) (SubTerms <*E*>) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued U -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element len (SubTerms <*E*>) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
len (SubTerms <*E*>) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(((E,u) ReassignIn i) . ((l -firstChar) . <*E*>)) . ((((E,u) ReassignIn i) -TermEval) (*) (SubTerms <*E*>)) is set
<*E*> . 1 is set
((E,u) ReassignIn i) . (<*E*> . 1) is Relation-like Function-like set
(((E,u) ReassignIn i) . (<*E*> . 1)) . {} is set
(((E,u) ReassignIn i) . E) . {} is set
(i . f1) . {} is set
(II SubstWith E) . Y2 is Relation-like NAT -defined AllSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf l) *
b2 . Y2 is set
(((E,u) ReassignIn i) -TermEval) (*) (SubTerms Y2) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued U -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element len (SubTerms Y2) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((E,u) ReassignIn i) . f1) . ((((E,u) ReassignIn i) -TermEval) (*) (SubTerms Y2)) is set
(((E,u) ReassignIn i) . f1) . {} is set
tt2 . 1 is set
Y1 is non empty Relation-like NAT -defined TermSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal hh -termal Element of ((AllSymbolsOf l) *) \ {{}}
Y1 . 1 is set
Y2 is non literal ofAtomicFormula Element of AllSymbolsOf l
(l -firstChar) . Y1 is non relational termal own ofAtomicFormula Element of AllSymbolsOf l
f1 is non literal ofAtomicFormula Element of AllSymbolsOf l
((II,u) ReassignIn i) . Y2 is Relation-like Function-like set
i . Y2 is Relation-like Function-like set
((E,u) ReassignIn i) . f1 is Relation-like Function-like set
i . f1 is Relation-like Function-like set
(((E,u) ReassignIn i) -TermEval) . Y1 is set
SubTerms Y1 is Relation-like NAT -defined (rng Y1) * -valued AllTermsOf l -valued Function-like finite abs (ar Y1) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf l) *
rng Y1 is non empty finite set
(rng Y1) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng Y1
ar Y1 is finite complex ext-real V40() V41() Element of INT
ar ((l -firstChar) . Y1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of l . ((l -firstChar) . Y1) is set
abs (ar Y1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(((E,u) ReassignIn i) -TermEval) (*) (SubTerms Y1) is Relation-like NAT -defined U -valued Function-like finite abs (ar Y1) -element len (SubTerms Y1) -element FinSequence-like FinSubsequence-like finite-support set
len (SubTerms Y1) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(((E,u) ReassignIn i) . f1) . ((((E,u) ReassignIn i) -TermEval) (*) (SubTerms Y1)) is set
(II SubstWith E) (*) (SubTerms tt2) is Relation-like NAT -defined (AllSymbolsOf l) * -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(((E,u) ReassignIn i) -TermEval) (*) ((II SubstWith E) (*) (SubTerms tt2)) is Relation-like NAT -defined U -valued Function-like finite finite-support set
(((E,u) ReassignIn i) . f1) . ((((E,u) ReassignIn i) -TermEval) (*) ((II SubstWith E) (*) (SubTerms tt2))) is set
((((E,u) ReassignIn i) -TermEval) * (II SubstWith E)) (*) (SubTerms tt2) is Relation-like NAT -defined U -valued Function-like finite finite-support set
(i . f1) . (((((E,u) ReassignIn i) -TermEval) * (II SubstWith E)) (*) (SubTerms tt2)) is set
(((((E,u) ReassignIn i) -TermEval) * (II SubstWith E)) | (((l -termsOfMaxDepth) . En) /\ (n *))) (*) (SubTerms tt2) is Relation-like NAT -defined U -valued Function-like finite finite-support set
(i . f1) . ((((((E,u) ReassignIn i) -TermEval) * (II SubstWith E)) | (((l -termsOfMaxDepth) . En) /\ (n *))) (*) (SubTerms tt2)) is set
(((II,u) ReassignIn i) -TermEval) (*) (SubTerms tt2) is Relation-like NAT -defined U -valued Function-like finite finite-support set
(i . f1) . ((((II,u) ReassignIn i) -TermEval) (*) (SubTerms tt2)) is set
U is non empty set
u is Element of U
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V166() set
the U1 of S is set
AtomicFormulaSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V166() set
bool (AllSymbolsOf S) is non empty non trivial non finite V166() set
TheNorSymbOf S is set
the U3 of S is Element of the U1 of S
{(TheNorSymbOf S)} is non empty trivial finite 1 -element set
(AllSymbolsOf S) \ {(TheNorSymbOf S)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V166() set
(AllSymbolsOf S) typed\ {(TheNorSymbOf S)} is Element of bool (AllSymbolsOf S)
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
l is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
{l} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf S)
(AllSymbolsOf S) \ {l} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf S)
(AllSymbolsOf S) typed\ {l} is Element of bool (AllSymbolsOf S)
II is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
E is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
(S,II,l,E) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
E +~ (II,l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
i is Relation-like Function-like Function-yielding V164() S,U -interpreter-like set
(II,u) ReassignIn i is Relation-like Function-like Function-yielding V164() S,U -interpreter-like set
{} .--> u is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> u is non empty Relation-like {{}} -defined U -valued {u} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{u}:]
{u} is non empty trivial finite 1 -element set
[:{{}},{u}:] is non empty Relation-like finite set
bool [:{{}},{u}:] is non empty finite finite-membered set
II .--> ({} .--> u) is trivial Relation-like AllSymbolsOf S -defined {II} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{II} is non empty trivial finite 1 -element set
{II} --> ({} .--> u) is non empty Relation-like {II} -defined {({} .--> u)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{II},{({} .--> u)}:]
{({} .--> u)} is non empty trivial functional finite finite-membered 1 -element set
[:{II},{({} .--> u)}:] is non empty Relation-like finite set
bool [:{II},{({} .--> u)}:] is non empty finite finite-membered set
i +* (II .--> ({} .--> u)) is Relation-like Function-like Function-yielding V164() set
((II,u) ReassignIn i) -AtomicEval E is boolean Element of BOOLEAN
((II,u) ReassignIn i) === is Relation-like Function-like Function-yielding V164() S,U -interpreter-like (II,u) ReassignIn i -extension set
TheEqSymbOf S is Element of AtomicFormulaSymbolsOf S
the U2 of S is Element of the U1 of S
U -deltaInterpreter is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
2 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
[:(2 -tuples_on U),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on U),BOOLEAN:] is non empty set
U * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of U
[:(U *),(U *):] is non empty non trivial Relation-like non finite V166() set
U -concatenation is non empty Relation-like [:(U *),(U *):] -defined U * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233(U * ) Element of bool [:[:(U *),(U *):],(U *):]
[:[:(U *),(U *):],(U *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(U *),(U *):],(U *):] is non empty non trivial non finite V166() set
1 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
id (1 -tuples_on U) is non empty Relation-like non empty-yielding 1 -tuples_on U -defined 1 -tuples_on U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(1 -tuples_on U),(1 -tuples_on U):]
[:(1 -tuples_on U),(1 -tuples_on U):] is non empty Relation-like set
bool [:(1 -tuples_on U),(1 -tuples_on U):] is non empty set
(U -concatenation) .: (id (1 -tuples_on U)) is functional finite-membered FinSequence-membered Element of bool (U *)
bool (U *) is non empty non trivial non finite V166() set
chi (((U -concatenation) .: (id (1 -tuples_on U))),(2 -tuples_on U)) is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
(TheEqSymbOf S) .--> (U -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf S -defined {(TheEqSymbOf S)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf S)} is non empty trivial finite 1 -element set
{(TheEqSymbOf S)} --> (U -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf S)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued {(U -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:]
{(U -deltaInterpreter)} is non empty trivial functional finite 1 -element V165() V166() set
[:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:] is non empty finite finite-membered set
((II,u) ReassignIn i) +* ((TheEqSymbOf S) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() 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 V166() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V166() 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 V233( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V166() set
K415((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) . E is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
(((II,u) ReassignIn i) ===) . ((S -firstChar) . E) is non empty Relation-like (abs (ar ((S -firstChar) . E))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . E,U
ar ((S -firstChar) . E) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
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
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 U1 of S \ { the U3 of S}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V166() set
the adicity of S . ((S -firstChar) . E) is set
abs (ar ((S -firstChar) . E)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((S -firstChar) . E))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
U \/ BOOLEAN is non empty set
SubTerms E is Relation-like NAT -defined (rng E) * -valued (TermSymbolsOf S) * -valued AllTermsOf S -valued Function-like finite abs (ar ((S -firstChar) . E)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
rng E is non empty finite set
(rng E) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng E
TermSymbolsOf S is non empty 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
(TermSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf S
AllTermsOf S is non empty functional finite-membered FinSequence-membered AllSymbolsOf S -prefix S -prefix Element of bool ((AllSymbolsOf S) *)
S -termsOfMaxDepth is Relation-like Function-like set
rng (S -termsOfMaxDepth) is set
union (rng (S -termsOfMaxDepth)) is set
((AllSymbolsOf S) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf S) *
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) *)
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V166() set
((II,u) ReassignIn i) -TermEval is non empty Relation-like AllTermsOf S -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),U:]
AllTermsOf S is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() set
[:(AllTermsOf S),U:] is non empty Relation-like set
bool [:(AllTermsOf S),U:] is non empty set
(((II,u) ReassignIn i) -TermEval) (*) (SubTerms E) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((((II,u) ReassignIn i) ===) . ((S -firstChar) . E)) . ((((II,u) ReassignIn i) -TermEval) (*) (SubTerms E)) is set
(l,u) ReassignIn i is Relation-like Function-like Function-yielding V164() S,U -interpreter-like set
l .--> ({} .--> u) is trivial Relation-like AllSymbolsOf S -defined {l} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} is non empty trivial finite 1 -element set
{l} --> ({} .--> u) is non empty Relation-like {l} -defined {({} .--> u)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({} .--> u)}:]
[:{l},{({} .--> u)}:] is non empty Relation-like finite set
bool [:{l},{({} .--> u)}:] is non empty finite finite-membered set
i +* (l .--> ({} .--> u)) is Relation-like Function-like Function-yielding V164() set
((l,u) ReassignIn i) -AtomicEval (S,II,l,E) is boolean Element of BOOLEAN
((l,u) ReassignIn i) === is Relation-like Function-like Function-yielding V164() S,U -interpreter-like (l,u) ReassignIn i -extension set
((l,u) ReassignIn i) +* ((TheEqSymbOf S) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(S -firstChar) . (S,II,l,E) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
(((l,u) ReassignIn i) ===) . ((S -firstChar) . (S,II,l,E)) is non empty Relation-like (abs (ar ((S -firstChar) . (S,II,l,E)))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . (S,II,l,E),U
ar ((S -firstChar) . (S,II,l,E)) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of S . ((S -firstChar) . (S,II,l,E)) is set
abs (ar ((S -firstChar) . (S,II,l,E))) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((S -firstChar) . (S,II,l,E)))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms (S,II,l,E) is Relation-like NAT -defined (rng (S,II,l,E)) * -valued (TermSymbolsOf S) * -valued AllTermsOf S -valued Function-like finite abs (ar ((S -firstChar) . (S,II,l,E))) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
rng (S,II,l,E) is non empty finite set
(rng (S,II,l,E)) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng (S,II,l,E)
((l,u) ReassignIn i) -TermEval is non empty Relation-like AllTermsOf S -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),U:]
(((l,u) ReassignIn i) -TermEval) (*) (SubTerms (S,II,l,E)) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((((l,u) ReassignIn i) ===) . ((S -firstChar) . (S,II,l,E))) . ((((l,u) ReassignIn i) -TermEval) (*) (SubTerms (S,II,l,E))) is set
II SubstWith l is non empty Relation-like (AllSymbolsOf S) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):]
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
S -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf S) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf S) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial non finite V166() set
S -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
[:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf S) -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
(AllSymbolsOf S) -concatenation is non empty Relation-like [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf S) * ) Element of bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):]
[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf S) -concatenation) is non empty Relation-like (((AllSymbolsOf S) *) *) \ {{}} -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):]
(((AllSymbolsOf S) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf S) *) *)
(((AllSymbolsOf S) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf S) *) *)
[:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf S) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
LettersOf S is non empty non trivial non finite V166() Element of bool (AllSymbolsOf S)
{0} is non empty trivial functional finite finite-membered 1 -element V166() Element of bool NAT
0 * is non empty functional finite-membered FinSequence-membered FinSequenceSet of 0
{0} is non empty trivial functional finite finite-membered 1 -element V166() set
the adicity of S " {0} is Element of bool ( the U1 of S \ { the U3 of S})
TheEqSymbOf S is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf S
hh is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
(S -firstChar) . hh is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
E . 1 is set
hhh is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
hh . 1 is set
s is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
dom (II .--> ({} .--> u)) is trivial finite Element of bool {II}
bool {II} is non empty finite finite-membered set
dom (l .--> ({} .--> u)) is trivial finite Element of bool {l}
bool {l} is non empty finite finite-membered set
((II,u) ReassignIn i) . hhh is Relation-like Function-like set
i . hhh is Relation-like Function-like set
((l,u) ReassignIn i) . hhh is Relation-like Function-like set
dom (((II,u) ReassignIn i) -TermEval) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf S)
bool (AllTermsOf S) is non empty set
dom (((l,u) ReassignIn i) -TermEval) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf S)
((AllSymbolsOf S) \ {l}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
(((II,u) ReassignIn i) -TermEval) | (((AllSymbolsOf S) \ {l}) *) is Relation-like AllTermsOf S -defined ((AllSymbolsOf S) \ {l}) * -defined AllTermsOf S -defined U -valued Function-like Element of bool [:(AllTermsOf S),U:]
dom ((((II,u) ReassignIn i) -TermEval) | (((AllSymbolsOf S) \ {l}) *)) is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf S) \ {l}) *)
bool (((AllSymbolsOf S) \ {l}) *) is non empty non trivial non finite V166() set
(AllTermsOf S) /\ (((AllSymbolsOf S) \ {l}) *) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(AllTermsOf S) typed/\ (((AllSymbolsOf S) \ {l}) *) is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
(AllTermsOf S) /\ (((AllSymbolsOf S) \ {l}) *) is functional set
(AllTermsOf S) /\typed (((AllSymbolsOf S) \ {l}) *) is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf S) \ {l}) *)
nE is non empty Element of bool (AllSymbolsOf S)
nE * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((AllSymbolsOf S) *)
(II SubstWith l) | (nE *) is Relation-like (AllSymbolsOf S) * -defined nE * -defined (AllSymbolsOf S) * -defined (AllSymbolsOf S) * -valued Function-like total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):]
dom ((II SubstWith l) | (nE *)) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(((AllSymbolsOf S) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf S) *) \ {{}}
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf S) *) \ {{}}) *)
bool ((((AllSymbolsOf S) *) \ {{}}) *) is non empty non trivial non finite V166() set
phi22 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S -termsOfMaxDepth) . phi22 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
((S -termsOfMaxDepth) . phi22) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf S) *) \ {{}}) *)
c₃₀ is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf S)
(((AllSymbolsOf S) \ {l}) *) /\ c₃₀ is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
(((AllSymbolsOf S) \ {l}) *) typed/\ c₃₀ is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf S) \ {l}) *)
(((AllSymbolsOf S) \ {l}) *) /\ c₃₀ is functional set
(((AllSymbolsOf S) \ {l}) *) /\typed c₃₀ is functional finite-membered FinSequence-membered V165() Element of bool c₃₀
bool c₃₀ is non empty set
(((II,u) ReassignIn i) -TermEval) | ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀) is Relation-like AllTermsOf S -defined (((AllSymbolsOf S) \ {l}) *) /\ c₃₀ -defined AllTermsOf S -defined U -valued Function-like total Element of bool [:(AllTermsOf S),U:]
dom ((((II,u) ReassignIn i) -TermEval) | ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀)) is functional finite-membered FinSequence-membered V165() Element of bool ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀)
bool ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀) is non empty set
((((II,u) ReassignIn i) -TermEval) | (((AllSymbolsOf S) \ {l}) *)) | c₃₀ is Relation-like AllTermsOf S -defined c₃₀ -defined AllTermsOf S -defined U -valued Function-like Element of bool [:(AllTermsOf S),U:]
dom (((((II,u) ReassignIn i) -TermEval) | (((AllSymbolsOf S) \ {l}) *)) | c₃₀) is functional finite-membered FinSequence-membered V165() Element of bool c₃₀
(dom ((((II,u) ReassignIn i) -TermEval) | (((AllSymbolsOf S) \ {l}) *))) /\ c₃₀ is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
(dom ((((II,u) ReassignIn i) -TermEval) | (((AllSymbolsOf S) \ {l}) *))) typed/\ c₃₀ is functional finite-membered FinSequence-membered Element of bool (dom ((((II,u) ReassignIn i) -TermEval) | (((AllSymbolsOf S) \ {l}) *)))
bool (dom ((((II,u) ReassignIn i) -TermEval) | (((AllSymbolsOf S) \ {l}) *))) is non empty set
(dom ((((II,u) ReassignIn i) -TermEval) | (((AllSymbolsOf S) \ {l}) *))) /\ c₃₀ is functional set
(dom ((((II,u) ReassignIn i) -TermEval) | (((AllSymbolsOf S) \ {l}) *))) /\typed c₃₀ is functional finite-membered FinSequence-membered V165() Element of bool c₃₀
c₃₀ null (AllTermsOf S) is set
(AllTermsOf S) /\ c₃₀ is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
(AllTermsOf S) typed/\ c₃₀ is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
(AllTermsOf S) /\ c₃₀ is functional set
(AllTermsOf S) /\typed c₃₀ is functional finite-membered FinSequence-membered V165() Element of bool c₃₀
c₃₀ \typed/ (AllTermsOf S) is functional finite-membered V165() Element of bool (c₃₀ \/ (AllTermsOf S))
c₃₀ \/ (AllTermsOf S) is non empty functional finite-membered V165() V166() set
bool (c₃₀ \/ (AllTermsOf S)) is non empty set
(c₃₀ null (AllTermsOf S)) /\ (((AllSymbolsOf S) \ {l}) *) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(c₃₀ null (AllTermsOf S)) typed/\ (((AllSymbolsOf S) \ {l}) *) is Element of bool (c₃₀ null (AllTermsOf S))
bool (c₃₀ null (AllTermsOf S)) is non empty set
(c₃₀ null (AllTermsOf S)) /\ (((AllSymbolsOf S) \ {l}) *) is functional set
(c₃₀ null (AllTermsOf S)) /\typed (((AllSymbolsOf S) \ {l}) *) is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf S) \ {l}) *)
(II SubstWith l) | ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀) is Relation-like (AllSymbolsOf S) * -defined (((AllSymbolsOf S) \ {l}) *) /\ c₃₀ -defined (AllSymbolsOf S) * -defined (AllSymbolsOf S) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):]
dom ((II SubstWith l) | ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀)) is functional finite-membered FinSequence-membered V165() Element of bool ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀)
(II SubstWith l) | (((AllSymbolsOf S) \ {l}) *) is Relation-like (AllSymbolsOf S) * -defined ((AllSymbolsOf S) \ {l}) * -defined (AllSymbolsOf S) * -defined (AllSymbolsOf S) * -valued Function-like total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):]
((II SubstWith l) | (((AllSymbolsOf S) \ {l}) *)) | c₃₀ is Relation-like (AllSymbolsOf S) * -defined c₃₀ -defined (AllSymbolsOf S) * -defined (AllSymbolsOf S) * -valued Function-like Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):]
dom (((II SubstWith l) | (((AllSymbolsOf S) \ {l}) *)) | c₃₀) is functional finite-membered FinSequence-membered V165() Element of bool c₃₀
bool nE is non empty set
rng (SubTerms E) is finite set
phi2 is non empty Element of bool nE
phi2 * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (nE *)
nE * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of nE
bool (nE *) is non empty non trivial non finite V166() set
((((II,u) ReassignIn i) -TermEval) | ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀)) (*) (SubTerms E) is Relation-like NAT -defined U -valued Function-like finite finite-support set
(((l,u) ReassignIn i) -TermEval) * (II SubstWith l) is Relation-like (AllSymbolsOf S) * -defined U -valued Function-like Element of bool [:((AllSymbolsOf S) *),U:]
[:((AllSymbolsOf S) *),U:] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf S) *),U:] is non empty non trivial non finite V166() set
((((l,u) ReassignIn i) -TermEval) * (II SubstWith l)) | ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀) is Relation-like (AllSymbolsOf S) * -defined (((AllSymbolsOf S) \ {l}) *) /\ c₃₀ -defined (AllSymbolsOf S) * -defined U -valued Function-like Element of bool [:((AllSymbolsOf S) *),U:]
(((((l,u) ReassignIn i) -TermEval) * (II SubstWith l)) | ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀)) (*) (SubTerms E) is Relation-like NAT -defined U -valued Function-like finite finite-support set
(((l,u) ReassignIn i) -TermEval) * ((II SubstWith l) | ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀)) is Relation-like (AllSymbolsOf S) * -defined U -valued Function-like Element of bool [:((AllSymbolsOf S) *),U:]
((((l,u) ReassignIn i) -TermEval) * ((II SubstWith l) | ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀))) (*) (SubTerms E) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((II SubstWith l) | ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀)) (*) (SubTerms E) is Relation-like NAT -defined (AllSymbolsOf S) * -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(((l,u) ReassignIn i) -TermEval) (*) (((II SubstWith l) | ((((AllSymbolsOf S) \ {l}) *) /\ c₃₀)) (*) (SubTerms E)) is Relation-like NAT -defined U -valued Function-like finite finite-support set
(II SubstWith l) (*) (SubTerms E) is Relation-like NAT -defined (AllSymbolsOf S) * -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(((l,u) ReassignIn i) -TermEval) (*) ((II SubstWith l) (*) (SubTerms E)) is Relation-like NAT -defined U -valued Function-like finite finite-support set
SubTerms hh is Relation-like NAT -defined (rng hh) * -valued (TermSymbolsOf S) * -valued AllTermsOf S -valued Function-like finite abs (ar ((S -firstChar) . hh)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
ar ((S -firstChar) . hh) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of S . ((S -firstChar) . hh) is set
abs (ar ((S -firstChar) . hh)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng hh is non empty finite set
(rng hh) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng hh
(((l,u) ReassignIn i) -TermEval) (*) (SubTerms hh) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((l,u) ReassignIn i) . s is Relation-like Function-like set
(((l,u) ReassignIn i) . s) . ((((l,u) ReassignIn i) -TermEval) (*) (SubTerms hh)) is set
((l,u) ReassignIn i) -AtomicEval hh is boolean Element of BOOLEAN
(((l,u) ReassignIn i) ===) . ((S -firstChar) . hh) is non empty Relation-like (abs (ar ((S -firstChar) . hh))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . hh,U
(abs (ar ((S -firstChar) . hh))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
((((l,u) ReassignIn i) ===) . ((S -firstChar) . hh)) . ((((l,u) ReassignIn i) -TermEval) (*) (SubTerms hh)) is set
(U -deltaInterpreter) . ((((II,u) ReassignIn i) -TermEval) (*) (SubTerms E)) is boolean set
((l,u) ReassignIn i) -AtomicEval hh is boolean Element of BOOLEAN
(((l,u) ReassignIn i) ===) . ((S -firstChar) . hh) is non empty Relation-like (abs (ar ((S -firstChar) . hh))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . hh,U
(abs (ar ((S -firstChar) . hh))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
((((l,u) ReassignIn i) ===) . ((S -firstChar) . hh)) . ((((l,u) ReassignIn i) -TermEval) (*) (SubTerms hh)) is set
U is non empty set
U * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of U
U \/ BOOLEAN is non empty set
K546((U *),(U \/ BOOLEAN)) is non empty functional M31(U * ,U \/ BOOLEAN)
u is Element of U
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V166() set
the U1 of S is set
AllSymbolsOf S is non empty non trivial non finite V166() set
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered 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 V166() 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
Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S,K546((U *),(U \/ BOOLEAN))
U -InterpretersOf S is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN))) : b₁ is S,U -interpreter-like } is set
l is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
II is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
E is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf S) *) \ {{}}
rng E is non empty finite set
(S,II,l,E) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf S) *) \ {{}}
E +~ (II,l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
II SubstWith l is non empty Relation-like (AllSymbolsOf S) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):]
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
{l} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V166() set
(AllSymbolsOf S) \ {l} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf S)
(AllSymbolsOf S) typed\ {l} is Element of bool (AllSymbolsOf S)
AllTermsOf S is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() set
S -termsOfMaxDepth is Relation-like Function-like set
rng (S -termsOfMaxDepth) is set
union (rng (S -termsOfMaxDepth)) is set
S -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf S) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf S) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial non finite V166() 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 V166() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V166() 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 V233( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V166() set
K415((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):]
TheNorSymbOf S is non literal non low-compounding non relational non own Element of AllSymbolsOf S
jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
jJ is Element of U
(II,jJ) ReassignIn jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
{} .--> jJ is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> jJ is non empty Relation-like {{}} -defined U -valued {jJ} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{jJ}:]
{jJ} is non empty trivial finite 1 -element set
[:{{}},{jJ}:] is non empty Relation-like finite set
bool [:{{}},{jJ}:] is non empty finite finite-membered set
II .--> ({} .--> jJ) is trivial Relation-like AllSymbolsOf S -defined {II} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{II} is non empty trivial finite 1 -element set
{II} --> ({} .--> jJ) is non empty Relation-like {II} -defined {({} .--> jJ)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{II},{({} .--> jJ)}:]
{({} .--> jJ)} is non empty trivial functional finite finite-membered 1 -element set
[:{II},{({} .--> jJ)}:] is non empty Relation-like finite set
bool [:{II},{({} .--> jJ)}:] is non empty finite finite-membered set
jJ +* (II .--> ({} .--> jJ)) is Relation-like Function-like Function-yielding V164() set
(l,jJ) ReassignIn jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
l .--> ({} .--> jJ) is trivial Relation-like AllSymbolsOf S -defined {l} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} is non empty trivial finite 1 -element set
{l} --> ({} .--> jJ) is non empty Relation-like {l} -defined {({} .--> jJ)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({} .--> jJ)}:]
[:{l},{({} .--> jJ)}:] is non empty Relation-like finite set
bool [:{l},{({} .--> jJ)}:] is non empty finite finite-membered set
jJ +* (l .--> ({} .--> jJ)) is Relation-like Function-like Function-yielding V164() set
g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf S) *) \ {{}}
((II,jJ) ReassignIn jJ) -TruthEval g is boolean Element of BOOLEAN
(S,II,l,g) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf S) *) \ {{}}
g +~ (II,l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((l,jJ) ReassignIn jJ) -TruthEval (S,II,l,g) is boolean Element of BOOLEAN
AtomicFormulaSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
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 V166() Element of bool (AllSymbolsOf S)
(AllSymbolsOf S) typed\ {(TheNorSymbOf S)} is Element of bool (AllSymbolsOf S)
n is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
((II,jJ) ReassignIn jJ) -TruthEval n is boolean Element of BOOLEAN
((II,jJ) ReassignIn jJ) -AtomicEval n is boolean Element of BOOLEAN
((II,jJ) ReassignIn jJ) === is Relation-like Function-like Function-yielding V164() S,U -interpreter-like (II,jJ) ReassignIn jJ -extension set
TheEqSymbOf S is Element of AtomicFormulaSymbolsOf S
U -deltaInterpreter is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
2 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
[:(2 -tuples_on U),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on U),BOOLEAN:] is non empty set
[:(U *),(U *):] is non empty non trivial Relation-like non finite V166() set
U -concatenation is non empty Relation-like [:(U *),(U *):] -defined U * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233(U * ) Element of bool [:[:(U *),(U *):],(U *):]
[:[:(U *),(U *):],(U *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(U *),(U *):],(U *):] is non empty non trivial non finite V166() set
1 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
id (1 -tuples_on U) is non empty Relation-like non empty-yielding 1 -tuples_on U -defined 1 -tuples_on U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(1 -tuples_on U),(1 -tuples_on U):]
[:(1 -tuples_on U),(1 -tuples_on U):] is non empty Relation-like set
bool [:(1 -tuples_on U),(1 -tuples_on U):] is non empty set
(U -concatenation) .: (id (1 -tuples_on U)) is functional finite-membered FinSequence-membered Element of bool (U *)
bool (U *) is non empty non trivial non finite V166() set
chi (((U -concatenation) .: (id (1 -tuples_on U))),(2 -tuples_on U)) is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
(TheEqSymbOf S) .--> (U -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf S -defined {(TheEqSymbOf S)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf S)} is non empty trivial finite 1 -element set
{(TheEqSymbOf S)} --> (U -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf S)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued {(U -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:]
{(U -deltaInterpreter)} is non empty trivial functional finite 1 -element V165() V166() set
[:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:] is non empty finite finite-membered set
((II,jJ) ReassignIn jJ) +* ((TheEqSymbOf S) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(S -firstChar) . n is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
(((II,jJ) ReassignIn jJ) ===) . ((S -firstChar) . n) is non empty Relation-like (abs (ar ((S -firstChar) . n))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . n,U
ar ((S -firstChar) . n) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
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 V166() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V166() set
the adicity of S . ((S -firstChar) . n) is set
abs (ar ((S -firstChar) . n)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((S -firstChar) . n))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms n is Relation-like NAT -defined (rng n) * -valued (TermSymbolsOf S) * -valued AllTermsOf S -valued Function-like finite abs (ar ((S -firstChar) . n)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
rng n is non empty finite set
(rng n) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng n
TermSymbolsOf S is non empty 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
(TermSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf S
AllTermsOf S is non empty functional finite-membered FinSequence-membered AllSymbolsOf S -prefix S -prefix Element of bool ((AllSymbolsOf S) *)
((AllSymbolsOf S) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf S) *
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) *)
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V166() set
((II,jJ) ReassignIn jJ) -TermEval is non empty Relation-like AllTermsOf S -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),U:]
[:(AllTermsOf S),U:] is non empty Relation-like set
bool [:(AllTermsOf S),U:] is non empty set
(((II,jJ) ReassignIn jJ) -TermEval) (*) (SubTerms n) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((((II,jJ) ReassignIn jJ) ===) . ((S -firstChar) . n)) . ((((II,jJ) ReassignIn jJ) -TermEval) (*) (SubTerms n)) is set
(S,II,l,n) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
n +~ (II,l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((l,jJ) ReassignIn jJ) -TruthEval (S,II,l,n) is boolean Element of BOOLEAN
((l,jJ) ReassignIn jJ) -AtomicEval (S,II,l,n) is boolean Element of BOOLEAN
((l,jJ) ReassignIn jJ) === is Relation-like Function-like Function-yielding V164() S,U -interpreter-like (l,jJ) ReassignIn jJ -extension set
((l,jJ) ReassignIn jJ) +* ((TheEqSymbOf S) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(S -firstChar) . (S,II,l,n) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
(((l,jJ) ReassignIn jJ) ===) . ((S -firstChar) . (S,II,l,n)) is non empty Relation-like (abs (ar ((S -firstChar) . (S,II,l,n)))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . (S,II,l,n),U
ar ((S -firstChar) . (S,II,l,n)) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of S . ((S -firstChar) . (S,II,l,n)) is set
abs (ar ((S -firstChar) . (S,II,l,n))) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((S -firstChar) . (S,II,l,n)))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms (S,II,l,n) is Relation-like NAT -defined (rng (S,II,l,n)) * -valued (TermSymbolsOf S) * -valued AllTermsOf S -valued Function-like finite abs (ar ((S -firstChar) . (S,II,l,n))) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
rng (S,II,l,n) is non empty finite set
(rng (S,II,l,n)) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng (S,II,l,n)
((l,jJ) ReassignIn jJ) -TermEval is non empty Relation-like AllTermsOf S -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),U:]
(((l,jJ) ReassignIn jJ) -TermEval) (*) (SubTerms (S,II,l,n)) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((((l,jJ) ReassignIn jJ) ===) . ((S -firstChar) . (S,II,l,n))) . ((((l,jJ) ReassignIn jJ) -TermEval) (*) (SubTerms (S,II,l,n))) is set
jJ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
jJ + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
g is Element of U
(II,g) ReassignIn jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
{} .--> g is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> g is non empty Relation-like {{}} -defined U -valued {g} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{g}:]
{g} is non empty trivial finite 1 -element set
[:{{}},{g}:] is non empty Relation-like finite set
bool [:{{}},{g}:] is non empty finite finite-membered set
II .--> ({} .--> g) is trivial Relation-like AllSymbolsOf S -defined {II} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{II} is non empty trivial finite 1 -element set
{II} --> ({} .--> g) is non empty Relation-like {II} -defined {({} .--> g)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{II},{({} .--> g)}:]
{({} .--> g)} is non empty trivial functional finite finite-membered 1 -element set
[:{II},{({} .--> g)}:] is non empty Relation-like finite set
bool [:{II},{({} .--> g)}:] is non empty finite finite-membered set
jJ +* (II .--> ({} .--> g)) is Relation-like Function-like Function-yielding V164() set
(l,g) ReassignIn jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
l .--> ({} .--> g) is trivial Relation-like AllSymbolsOf S -defined {l} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} is non empty trivial finite 1 -element set
{l} --> ({} .--> g) is non empty Relation-like {l} -defined {({} .--> g)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({} .--> g)}:]
[:{l},{({} .--> g)}:] is non empty Relation-like finite set
bool [:{l},{({} .--> g)}:] is non empty finite finite-membered set
jJ +* (l .--> ({} .--> g)) is Relation-like Function-like Function-yielding V164() set
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf S) *) \ {{}}
((II,g) ReassignIn jJ) -TruthEval h is boolean Element of BOOLEAN
(S,II,l,h) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf S) *) \ {{}}
h +~ (II,l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((l,g) ReassignIn jJ) -TruthEval (S,II,l,h) is boolean Element of BOOLEAN
Jj is non empty Element of bool (AllSymbolsOf S)
En is non empty Relation-like NAT -defined Jj -valued Function-like finite FinSequence-like FinSubsequence-like finite-support set
En . 1 is set
{(En . 1)} is non empty trivial finite 1 -element set
{(En . 1)} \ ((AllSymbolsOf S) \ {l}) is trivial finite Element of bool {(En . 1)}
bool {(En . 1)} is non empty finite finite-membered set
{(En . 1)} typed\ ((AllSymbolsOf S) \ {l}) is trivial finite Element of bool {(En . 1)}
Enn is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ + 1 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
Enn . 1 is set
(S -firstChar) . Enn is Element of AllSymbolsOf S
(S,II,l,Enn) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ + 1 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
Enn +~ (II,l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
head Enn is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
SubWffsOf Enn is set
K74((SubWffsOf Enn)) is set
hh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
(S,II,l,hh) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
hh +~ (II,l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
s is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff jJ + 1 -wff wff exal Element of ((AllSymbolsOf S) *) \ {{}}
(S -firstChar) . s is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
tail s 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllSymbolsOf S) *
SubWffsOf s is set
K75((SubWffsOf s)) is set
<*((S -firstChar) . s)*> is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support 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 V166() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V166() 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,((S -firstChar) . s)] is non empty set
{[1,((S -firstChar) . s)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
<*((S -firstChar) . s)*> ^ hh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff jJ + 1 -wff 1 + (Depth hh) -wff non Depth hh -wff wff exal Element of ((AllSymbolsOf S) *) \ {{}}
Depth hh is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (Depth hh) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(<*((S -firstChar) . s)*> ^ hh) ^ (tail s) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(<*((S -firstChar) . s)*> ^ hh) null (tail s) is Relation-like NAT -defined (tail s) \/ (dom (<*((S -firstChar) . s)*> ^ hh)) -defined (tail s) \/ (rng (<*((S -firstChar) . s)*> ^ hh)) -valued Function-like finite len (<*((S -firstChar) . s)*> ^ hh) -element FinSequence-like FinSubsequence-like finite-support set
dom (<*((S -firstChar) . s)*> ^ hh) is non empty finite set
(tail s) \/ (dom (<*((S -firstChar) . s)*> ^ hh)) is non empty finite set
rng (<*((S -firstChar) . s)*> ^ hh) is non empty finite set
(tail s) \/ (rng (<*((S -firstChar) . s)*> ^ hh)) is non empty finite set
len (<*((S -firstChar) . s)*> ^ hh) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(<*((S -firstChar) . s)*> ^ hh) \typed/ (tail s) is Relation-like NAT -defined finite Element of bool ((<*((S -firstChar) . s)*> ^ hh) \/ (tail s))
(<*((S -firstChar) . s)*> ^ hh) \/ (tail s) is non empty Relation-like NAT -defined finite set
bool ((<*((S -firstChar) . s)*> ^ hh) \/ (tail s)) is non empty finite finite-membered set
(tail s) ^ (<*((S -firstChar) . s)*> ^ hh) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(II SubstWith l) . s is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf S) *
(II SubstWith l) . <*((S -firstChar) . s)*> is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf S) *
(II SubstWith l) . hh is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf S) *
((II SubstWith l) . <*((S -firstChar) . s)*>) ^ ((II SubstWith l) . hh) is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support set
hhh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
((II SubstWith l) . <*((S -firstChar) . s)*>) ^ hhh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
nE is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ + 1 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
(<*((S -firstChar) . s)*> ^ hh) ^ {} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(<*((S -firstChar) . s)*> ^ hh) null {} is Relation-like NAT -defined {} \/ (dom (<*((S -firstChar) . s)*> ^ hh)) -defined {} \/ (rng (<*((S -firstChar) . s)*> ^ hh)) -valued Function-like finite len (<*((S -firstChar) . s)*> ^ hh) -element FinSequence-like FinSubsequence-like finite-support set
{} \/ (dom (<*((S -firstChar) . s)*> ^ hh)) is non empty finite set
{} \/ (rng (<*((S -firstChar) . s)*> ^ hh)) is non empty finite set
(<*((S -firstChar) . s)*> ^ hh) \typed/ {} is Relation-like NAT -defined finite Element of bool ((<*((S -firstChar) . s)*> ^ hh) \/ {})
(<*((S -firstChar) . s)*> ^ hh) \/ {} is non empty Relation-like NAT -defined finite set
bool ((<*((S -firstChar) . s)*> ^ hh) \/ {}) is non empty finite finite-membered set
{} ^ (<*((S -firstChar) . s)*> ^ hh) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((II,g) ReassignIn jJ) -TruthEval s is boolean Element of BOOLEAN
((l,g) ReassignIn jJ) -TruthEval nE is boolean Element of BOOLEAN
<*l*> is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
[1,l] is non empty set
{[1,l]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
<*l*> ^ hhh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff jJ + 1 -wff 1 + (Depth hhh) -wff non Depth hhh -wff wff exal Element of ((AllSymbolsOf S) *) \ {{}}
Depth hhh is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (Depth hhh) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
c₃₀ is Element of U
(((S -firstChar) . s),c₃₀) ReassignIn ((II,g) ReassignIn jJ) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
{} .--> c₃₀ is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> c₃₀ is non empty Relation-like {{}} -defined U -valued {c₃₀} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{c₃₀}:]
{c₃₀} is non empty trivial finite 1 -element set
[:{{}},{c₃₀}:] is non empty Relation-like finite set
bool [:{{}},{c₃₀}:] is non empty finite finite-membered set
((S -firstChar) . s) .--> ({} .--> c₃₀) is trivial Relation-like AllSymbolsOf S -defined {((S -firstChar) . s)} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{((S -firstChar) . s)} is non empty trivial finite 1 -element set
{((S -firstChar) . s)} --> ({} .--> c₃₀) is non empty Relation-like {((S -firstChar) . s)} -defined {({} .--> c₃₀)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{((S -firstChar) . s)},{({} .--> c₃₀)}:]
{({} .--> c₃₀)} is non empty trivial functional finite finite-membered 1 -element set
[:{((S -firstChar) . s)},{({} .--> c₃₀)}:] is non empty Relation-like finite set
bool [:{((S -firstChar) . s)},{({} .--> c₃₀)}:] is non empty finite finite-membered set
((II,g) ReassignIn jJ) +* (((S -firstChar) . s) .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
((((S -firstChar) . s),c₃₀) ReassignIn ((II,g) ReassignIn jJ)) -TruthEval hh is boolean Element of BOOLEAN
(II,c₃₀) ReassignIn jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
II .--> ({} .--> c₃₀) is trivial Relation-like AllSymbolsOf S -defined {II} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{II} --> ({} .--> c₃₀) is non empty Relation-like {II} -defined {({} .--> c₃₀)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{II},{({} .--> c₃₀)}:]
[:{II},{({} .--> c₃₀)}:] is non empty Relation-like finite set
bool [:{II},{({} .--> c₃₀)}:] is non empty finite finite-membered set
jJ +* (II .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
((II,c₃₀) ReassignIn jJ) -TruthEval hh is boolean Element of BOOLEAN
(l,c₃₀) ReassignIn jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
l .--> ({} .--> c₃₀) is trivial Relation-like AllSymbolsOf S -defined {l} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} --> ({} .--> c₃₀) is non empty Relation-like {l} -defined {({} .--> c₃₀)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({} .--> c₃₀)}:]
[:{l},{({} .--> c₃₀)}:] is non empty Relation-like finite set
bool [:{l},{({} .--> c₃₀)}:] is non empty finite finite-membered set
jJ +* (l .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
((l,c₃₀) ReassignIn jJ) -TruthEval hhh is boolean Element of BOOLEAN
(l,c₃₀) ReassignIn ((l,g) ReassignIn jJ) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
((l,g) ReassignIn jJ) +* (l .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
((l,c₃₀) ReassignIn ((l,g) ReassignIn jJ)) -TruthEval hhh is boolean Element of BOOLEAN
c₃₀ is Element of U
(l,c₃₀) ReassignIn ((l,g) ReassignIn jJ) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
{} .--> c₃₀ is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> c₃₀ is non empty Relation-like {{}} -defined U -valued {c₃₀} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{c₃₀}:]
{c₃₀} is non empty trivial finite 1 -element set
[:{{}},{c₃₀}:] is non empty Relation-like finite set
bool [:{{}},{c₃₀}:] is non empty finite finite-membered set
l .--> ({} .--> c₃₀) is trivial Relation-like AllSymbolsOf S -defined {l} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} --> ({} .--> c₃₀) is non empty Relation-like {l} -defined {({} .--> c₃₀)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({} .--> c₃₀)}:]
{({} .--> c₃₀)} is non empty trivial functional finite finite-membered 1 -element set
[:{l},{({} .--> c₃₀)}:] is non empty Relation-like finite set
bool [:{l},{({} .--> c₃₀)}:] is non empty finite finite-membered set
((l,g) ReassignIn jJ) +* (l .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
((l,c₃₀) ReassignIn ((l,g) ReassignIn jJ)) -TruthEval hhh is boolean Element of BOOLEAN
(l,c₃₀) ReassignIn jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
jJ +* (l .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
((l,c₃₀) ReassignIn jJ) -TruthEval hhh is boolean Element of BOOLEAN
(II,c₃₀) ReassignIn jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
II .--> ({} .--> c₃₀) is trivial Relation-like AllSymbolsOf S -defined {II} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{II} --> ({} .--> c₃₀) is non empty Relation-like {II} -defined {({} .--> c₃₀)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{II},{({} .--> c₃₀)}:]
[:{II},{({} .--> c₃₀)}:] is non empty Relation-like finite set
bool [:{II},{({} .--> c₃₀)}:] is non empty finite finite-membered set
jJ +* (II .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
((II,c₃₀) ReassignIn jJ) -TruthEval hh is boolean Element of BOOLEAN
(((S -firstChar) . s),c₃₀) ReassignIn ((II,g) ReassignIn jJ) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
((S -firstChar) . s) .--> ({} .--> c₃₀) is trivial Relation-like AllSymbolsOf S -defined {((S -firstChar) . s)} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{((S -firstChar) . s)} --> ({} .--> c₃₀) is non empty Relation-like {((S -firstChar) . s)} -defined {({} .--> c₃₀)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{((S -firstChar) . s)},{({} .--> c₃₀)}:]
[:{((S -firstChar) . s)},{({} .--> c₃₀)}:] is non empty Relation-like finite set
bool [:{((S -firstChar) . s)},{({} .--> c₃₀)}:] is non empty finite finite-membered set
((II,g) ReassignIn jJ) +* (((S -firstChar) . s) .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
((((S -firstChar) . s),c₃₀) ReassignIn ((II,g) ReassignIn jJ)) -TruthEval hh is boolean Element of BOOLEAN
<*((S -firstChar) . s)*> ^ hhh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff jJ + 1 -wff 1 + (Depth hhh) -wff non Depth hhh -wff wff exal Element of ((AllSymbolsOf S) *) \ {{}}
Depth hhh is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (Depth hhh) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
c₃₀ is Element of U
(((S -firstChar) . s),c₃₀) ReassignIn ((II,g) ReassignIn jJ) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
{} .--> c₃₀ is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> c₃₀ is non empty Relation-like {{}} -defined U -valued {c₃₀} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{c₃₀}:]
{c₃₀} is non empty trivial finite 1 -element set
[:{{}},{c₃₀}:] is non empty Relation-like finite set
bool [:{{}},{c₃₀}:] is non empty finite finite-membered set
((S -firstChar) . s) .--> ({} .--> c₃₀) is trivial Relation-like AllSymbolsOf S -defined {((S -firstChar) . s)} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{((S -firstChar) . s)} is non empty trivial finite 1 -element set
{((S -firstChar) . s)} --> ({} .--> c₃₀) is non empty Relation-like {((S -firstChar) . s)} -defined {({} .--> c₃₀)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{((S -firstChar) . s)},{({} .--> c₃₀)}:]
{({} .--> c₃₀)} is non empty trivial functional finite finite-membered 1 -element set
[:{((S -firstChar) . s)},{({} .--> c₃₀)}:] is non empty Relation-like finite set
bool [:{((S -firstChar) . s)},{({} .--> c₃₀)}:] is non empty finite finite-membered set
((II,g) ReassignIn jJ) +* (((S -firstChar) . s) .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
((((S -firstChar) . s),c₃₀) ReassignIn ((II,g) ReassignIn jJ)) -TruthEval hh is boolean Element of BOOLEAN
(((S -firstChar) . s),c₃₀) ReassignIn jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
jJ +* (((S -firstChar) . s) .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
(II,g) ReassignIn ((((S -firstChar) . s),c₃₀) ReassignIn jJ) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
((((S -firstChar) . s),c₃₀) ReassignIn jJ) +* (II .--> ({} .--> g)) is Relation-like Function-like Function-yielding V164() set
((II,g) ReassignIn ((((S -firstChar) . s),c₃₀) ReassignIn jJ)) -TruthEval hh is boolean Element of BOOLEAN
(l,g) ReassignIn ((((S -firstChar) . s),c₃₀) ReassignIn jJ) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
((((S -firstChar) . s),c₃₀) ReassignIn jJ) +* (l .--> ({} .--> g)) is Relation-like Function-like Function-yielding V164() set
((l,g) ReassignIn ((((S -firstChar) . s),c₃₀) ReassignIn jJ)) -TruthEval hhh is boolean Element of BOOLEAN
(((S -firstChar) . s),c₃₀) ReassignIn ((l,g) ReassignIn jJ) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
((l,g) ReassignIn jJ) +* (((S -firstChar) . s) .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
((((S -firstChar) . s),c₃₀) ReassignIn ((l,g) ReassignIn jJ)) -TruthEval hhh is boolean Element of BOOLEAN
c₃₀ is Element of U
(((S -firstChar) . s),c₃₀) ReassignIn ((l,g) ReassignIn jJ) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
{} .--> c₃₀ is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> c₃₀ is non empty Relation-like {{}} -defined U -valued {c₃₀} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{c₃₀}:]
{c₃₀} is non empty trivial finite 1 -element set
[:{{}},{c₃₀}:] is non empty Relation-like finite set
bool [:{{}},{c₃₀}:] is non empty finite finite-membered set
((S -firstChar) . s) .--> ({} .--> c₃₀) is trivial Relation-like AllSymbolsOf S -defined {((S -firstChar) . s)} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{((S -firstChar) . s)} --> ({} .--> c₃₀) is non empty Relation-like {((S -firstChar) . s)} -defined {({} .--> c₃₀)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{((S -firstChar) . s)},{({} .--> c₃₀)}:]
{({} .--> c₃₀)} is non empty trivial functional finite finite-membered 1 -element set
[:{((S -firstChar) . s)},{({} .--> c₃₀)}:] is non empty Relation-like finite set
bool [:{((S -firstChar) . s)},{({} .--> c₃₀)}:] is non empty finite finite-membered set
((l,g) ReassignIn jJ) +* (((S -firstChar) . s) .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
((((S -firstChar) . s),c₃₀) ReassignIn ((l,g) ReassignIn jJ)) -TruthEval hhh is boolean Element of BOOLEAN
(((S -firstChar) . s),c₃₀) ReassignIn jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
jJ +* (((S -firstChar) . s) .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
(l,g) ReassignIn ((((S -firstChar) . s),c₃₀) ReassignIn jJ) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
((((S -firstChar) . s),c₃₀) ReassignIn jJ) +* (l .--> ({} .--> g)) is Relation-like Function-like Function-yielding V164() set
((l,g) ReassignIn ((((S -firstChar) . s),c₃₀) ReassignIn jJ)) -TruthEval hhh is boolean Element of BOOLEAN
(II,g) ReassignIn ((((S -firstChar) . s),c₃₀) ReassignIn jJ) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
((((S -firstChar) . s),c₃₀) ReassignIn jJ) +* (II .--> ({} .--> g)) is Relation-like Function-like Function-yielding V164() set
((II,g) ReassignIn ((((S -firstChar) . s),c₃₀) ReassignIn jJ)) -TruthEval hh is boolean Element of BOOLEAN
(((S -firstChar) . s),c₃₀) ReassignIn ((II,g) ReassignIn jJ) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
((II,g) ReassignIn jJ) +* (((S -firstChar) . s) .--> ({} .--> c₃₀)) is Relation-like Function-like Function-yielding V164() set
((((S -firstChar) . s),c₃₀) ReassignIn ((II,g) ReassignIn jJ)) -TruthEval hh is boolean Element of BOOLEAN
s is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff jJ + 1 -wff wff non exal Element of ((AllSymbolsOf S) *) \ {{}}
tail s is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
SubWffsOf s is set
K75((SubWffsOf s)) is set
ss is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
(S,II,l,ss) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
ss +~ (II,l) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(S -firstChar) . s is non relational Element of AllSymbolsOf S
((S -firstChar) . s) \+\ (TheNorSymbOf 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
((S -firstChar) . s) \ (TheNorSymbOf S) is set
((S -firstChar) . s) typed\ (TheNorSymbOf S) is Element of bool ((S -firstChar) . s)
bool ((S -firstChar) . s) is non empty set
((S -firstChar) . s) \ (TheNorSymbOf S) is Element of bool ((S -firstChar) . s)
(TheNorSymbOf S) \ ((S -firstChar) . s) is set
(TheNorSymbOf S) typed\ ((S -firstChar) . s) is Element of bool (TheNorSymbOf S)
bool (TheNorSymbOf S) is non empty set
(TheNorSymbOf S) \ ((S -firstChar) . s) is Element of bool (TheNorSymbOf S)
(((S -firstChar) . s) \ (TheNorSymbOf S)) \/ ((TheNorSymbOf S) \ ((S -firstChar) . s)) is set
<*(TheNorSymbOf S)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf S) *) \ {{}}
[1,(TheNorSymbOf S)] is non empty set
{[1,(TheNorSymbOf S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
<*(TheNorSymbOf S)*> ^ hh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non exal Element of ((AllSymbolsOf S) *) \ {{}}
(<*(TheNorSymbOf S)*> ^ hh) ^ ss is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non max ((Depth hh),(Depth ss)) -wff jJ + 1 -wff wff non exal Element of ((AllSymbolsOf S) *) \ {{}}
Depth hh is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
Depth ss is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((Depth hh),(Depth ss)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
((II,g) ReassignIn jJ) -TruthEval s is boolean Element of BOOLEAN
((II,g) ReassignIn jJ) -TruthEval hh is boolean Element of BOOLEAN
((II,g) ReassignIn jJ) -TruthEval ss is boolean Element of BOOLEAN
hhh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
((l,g) ReassignIn jJ) -TruthEval hhh is boolean Element of BOOLEAN
phi22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
((l,g) ReassignIn jJ) -TruthEval phi22 is boolean Element of BOOLEAN
(II SubstWith l) . s is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf S) *
nE is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support jJ + 1 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
(II SubstWith l) . hh is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf S) *
(II SubstWith l) . ss is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf S) *
(II SubstWith l) . (<*(TheNorSymbOf S)*> ^ hh) is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf S) *
((II SubstWith l) . (<*(TheNorSymbOf S)*> ^ hh)) ^ ((II SubstWith l) . ss) is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support set
(II SubstWith l) . <*(TheNorSymbOf S)*> is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf S) *
((II SubstWith l) . <*(TheNorSymbOf S)*>) ^ ((II SubstWith l) . hh) is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((II SubstWith l) . <*(TheNorSymbOf S)*>) ^ ((II SubstWith l) . hh)) ^ ((II SubstWith l) . ss) is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*(TheNorSymbOf S)*> ^ hhh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non exal Element of ((AllSymbolsOf S) *) \ {{}}
(<*(TheNorSymbOf S)*> ^ hhh) ^ phi22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non max ((Depth hhh),(Depth phi22)) -wff jJ + 1 -wff wff non exal Element of ((AllSymbolsOf S) *) \ {{}}
Depth hhh is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
Depth phi22 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((Depth hhh),(Depth phi22)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
((l,g) ReassignIn jJ) -TruthEval nE is boolean Element of BOOLEAN
Depth E is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
(II,u) ReassignIn jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
{} .--> u is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> u is non empty Relation-like {{}} -defined U -valued {u} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{u}:]
{u} is non empty trivial finite 1 -element set
[:{{}},{u}:] is non empty Relation-like finite set
bool [:{{}},{u}:] is non empty finite finite-membered set
II .--> ({} .--> u) is trivial Relation-like AllSymbolsOf S -defined {II} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{II} is non empty trivial finite 1 -element set
{II} --> ({} .--> u) is non empty Relation-like {II} -defined {({} .--> u)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{II},{({} .--> u)}:]
{({} .--> u)} is non empty trivial functional finite finite-membered 1 -element set
[:{II},{({} .--> u)}:] is non empty Relation-like finite set
bool [:{II},{({} .--> u)}:] is non empty finite finite-membered set
jJ +* (II .--> ({} .--> u)) is Relation-like Function-like Function-yielding V164() set
((II,u) ReassignIn jJ) -TruthEval E is boolean Element of BOOLEAN
(l,u) ReassignIn jJ is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
l .--> ({} .--> u) is trivial Relation-like AllSymbolsOf S -defined {l} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} is non empty trivial finite 1 -element set
{l} --> ({} .--> u) is non empty Relation-like {l} -defined {({} .--> u)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({} .--> u)}:]
[:{l},{({} .--> u)}:] is non empty Relation-like finite set
bool [:{l},{({} .--> u)}:] is non empty finite finite-membered set
jJ +* (l .--> ({} .--> u)) is Relation-like Function-like Function-yielding V164() set
((l,u) ReassignIn jJ) -TruthEval (S,II,l,E) is boolean Element of BOOLEAN
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
E is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth E is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
l + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
TheNorSymbOf U is non literal non low-compounding non relational non own Element of AllSymbolsOf U
<*(TheNorSymbOf U)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,(TheNorSymbOf U)] is non empty set
{[1,(TheNorSymbOf U)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
II is Relation-like Function-like Function-yielding V164() FinSequence-yielding set
head E is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
SubWffsOf E is set
K74((SubWffsOf E)) is set
II . (head E) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*(TheNorSymbOf U)*> ^ (II . (head E)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
tail E is Relation-like NAT -defined AllSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf U) *
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
K75((SubWffsOf E)) is set
II . (tail E) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(<*(TheNorSymbOf U)*> ^ (II . (head E))) ^ (II . (tail E)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
[:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(AllSymbolsOf U) -pr1 is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total V233( AllSymbolsOf U) Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
[:(AllSymbolsOf U),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf U),(AllSymbolsOf U)) is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
MultPlace ((AllSymbolsOf U) -pr1) is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(U -firstChar) . E is Element of AllSymbolsOf U
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
LettersOf U is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
{0} is non empty trivial functional finite finite-membered 1 -element V166() Element of bool NAT
0 * is non empty functional finite-membered FinSequence-membered FinSequenceSet of 0
{0} is non empty trivial functional finite finite-membered 1 -element V166() set
the adicity of U " {0} is Element of bool ( the U1 of U \ { the U3 of U})
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
rng S is non empty finite set
rng (head E) is non empty finite set
(rng S) \/ (rng (head E)) is non empty finite set
{u} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
((rng S) \/ (rng (head E))) \/ {u} is non empty finite set
(LettersOf U) \ (((rng S) \/ (rng (head E))) \/ {u}) is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
(LettersOf U) typed\ (((rng S) \/ (rng (head E))) \/ {u}) is Element of bool (LettersOf U)
bool (LettersOf U) is non empty non trivial non finite V166() set
(LettersOf U) \ (((rng S) \/ (rng (head E))) \/ {u}) is non empty non trivial non finite V166() Element of bool (LettersOf U)
the Element of (LettersOf U) \ (((rng S) \/ (rng (head E))) \/ {u}) is Element of (LettersOf U) \ (((rng S) \/ (rng (head E))) \/ {u})
<* the Element of (LettersOf U) \ (((rng S) \/ (rng (head E))) \/ {u})*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1, the Element of (LettersOf U) \ (((rng S) \/ (rng (head E))) \/ {u})] is non empty set
{[1, the Element of (LettersOf U) \ (((rng S) \/ (rng (head E))) \/ {u})]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(U,((U -firstChar) . E), the Element of (LettersOf U) \ (((rng S) \/ (rng (head E))) \/ {u}),(head E)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
(head E) +~ (((U -firstChar) . E), the Element of (LettersOf U) \ (((rng S) \/ (rng (head E))) \/ {u})) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
II . (U,((U -firstChar) . E), the Element of (LettersOf U) \ (((rng S) \/ (rng (head E))) \/ {u}),(head E)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<* the Element of (LettersOf U) \ (((rng S) \/ (rng (head E))) \/ {u})*> ^ (II . (U,((U -firstChar) . E), the Element of (LettersOf U) \ (((rng S) \/ (rng (head E))) \/ {u}),(head E))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
II . E is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U is V51() V53() eligible Language-like
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf U),(AllFormulasOf U)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U, AllFormulasOf U
u is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
U is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u is V51() V53() eligible Language-like
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
TermSymbolsOf u is non empty set
the U3 of u is Element of the U1 of u
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
AllSymbolsOf u is non empty non trivial non finite V166() set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
AllFormulasOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of bool (((AllSymbolsOf u) *) \ {{}})
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf u),(AllFormulasOf u)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf u, AllFormulasOf u
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
l is non empty Relation-like NAT -defined TermSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf u) *) \ {{}}
II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
head II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
SubWffsOf II is set
K74((SubWffsOf II)) is set
Depth II is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
[:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(AllSymbolsOf u) -pr1 is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total V233( AllSymbolsOf u) Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
[:(AllSymbolsOf u),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf u),(AllSymbolsOf u)) is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
MultPlace ((AllSymbolsOf u) -pr1) is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
UU is Relation-like AllFormulasOf u -defined AllFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
(u,S,l,U,UU,II) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
[:(AllFormulasOf u),(AllFormulasOf u):] is non empty Relation-like set
bool [:(AllFormulasOf u),(AllFormulasOf u):] is non empty set
TheNorSymbOf u is non literal non low-compounding non relational non own Element of AllSymbolsOf u
LettersOf u is non empty non trivial non finite V166() Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
the adicity of u " {0} is Element of bool ( the U1 of u \ { the U3 of u})
rng l is non empty finite set
rng (head II) is non empty finite set
(rng l) \/ (rng (head II)) is non empty finite set
{S} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
((rng l) \/ (rng (head II))) \/ {S} is non empty finite set
(LettersOf u) \ (((rng l) \/ (rng (head II))) \/ {S}) is non empty non trivial non finite V166() Element of bool (AllSymbolsOf u)
(LettersOf u) typed\ (((rng l) \/ (rng (head II))) \/ {S}) is Element of bool (LettersOf u)
bool (LettersOf u) is non empty non trivial non finite V166() set
(LettersOf u) \ (((rng l) \/ (rng (head II))) \/ {S}) is non empty non trivial non finite V166() Element of bool (LettersOf u)
the Element of (LettersOf u) \ (((rng l) \/ (rng (head II))) \/ {S}) is Element of (LettersOf u) \ (((rng l) \/ (rng (head II))) \/ {S})
III is non empty Relation-like non empty-yielding AllFormulasOf u -defined AllFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf u),(AllFormulasOf u):]
jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
III . jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
G is non empty Element of bool (LettersOf u)
U + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
Enn is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff wff non exal Element of ((AllSymbolsOf u) *) \ {{}}
tail Enn is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
SubWffsOf Enn is set
K75((SubWffsOf Enn)) is set
En is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
nE is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
III . nE is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
<*(TheNorSymbOf u)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
[1,(TheNorSymbOf u)] is non empty set
{[1,(TheNorSymbOf u)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
<*(TheNorSymbOf u)*> ^ h is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non exal Element of ((AllSymbolsOf u) *) \ {{}}
hh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
(<*(TheNorSymbOf u)*> ^ h) ^ hh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non max ((Depth h),(Depth hh)) -wff wff non exal Element of ((AllSymbolsOf u) *) \ {{}}
Depth h is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
Depth hh is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((Depth h),(Depth hh)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
U + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(u -firstChar) . II is Element of AllSymbolsOf u
Enn is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff wff exal Element of ((AllSymbolsOf u) *) \ {{}}
(u -firstChar) . Enn is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
En is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
n is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
(u,En,n,(head II)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
(head II) +~ (En,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
nE is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
hh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
III . hh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
<*n*> is non empty trivial Relation-like NAT -defined TermSymbolsOf u -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf u) *) \ {{}}
[1,n] is non empty set
{[1,n]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
hhh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
<*n*> ^ hhh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff 1 + (Depth hhh) -wff non Depth hhh -wff wff exal Element of ((AllSymbolsOf u) *) \ {{}}
Depth hhh is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (Depth hhh) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
U + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
III . g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
(u -firstChar) . II is Element of AllSymbolsOf u
g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
III . g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
U + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(u -firstChar) . II is Element of AllSymbolsOf u
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf U),(AllFormulasOf U)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U, AllFormulasOf U
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
II is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
E is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,l,II,E) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf U),(AllFormulasOf U)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U, AllFormulasOf U
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
II is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
E is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,l,II,E) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
i is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf U),(AllFormulasOf U)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U, AllFormulasOf U
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
II is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
E is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,l,II,E) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(U,u,S,l,II,E) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf U),(AllFormulasOf U)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U, AllFormulasOf U
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
II is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
x is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
[:(AllFormulasOf U),(AllFormulasOf U):] is non empty Relation-like set
bool [:(AllFormulasOf U),(AllFormulasOf U):] is non empty set
O is non empty Relation-like non empty-yielding AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf U),(AllFormulasOf U):]
UU is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
III is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf U
O . X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf U
(U,u,S,x,II,X) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf U
UU . III is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(U,u,S,x,II,III) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf U
III is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
UU . III is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(U,u,S,l,II,III) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
x is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
O is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
[:(AllFormulasOf U),(AllFormulasOf U):] is non empty Relation-like set
bool [:(AllFormulasOf U),(AllFormulasOf U):] is non empty set
X is set
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
x . I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(U,u,S,l,II,I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
O . I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
UU is non empty Relation-like non empty-yielding AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf U),(AllFormulasOf U):]
UU . X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
III is non empty Relation-like non empty-yielding AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf U),(AllFormulasOf U):]
III . X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf U),(AllFormulasOf U)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U, AllFormulasOf U
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
[:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):] is non empty non trivial non finite V166() set
l is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
i is non empty Relation-like NAT -defined Funcs ((AllFormulasOf U),(AllFormulasOf U)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):]
i . 0 is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
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
i . (x + 1) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
i . x is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
(U,u,S,x,(i . x)) is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
i is non empty Relation-like NAT -defined Funcs ((AllFormulasOf U),(AllFormulasOf U)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):]
i . 0 is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
x is non empty Relation-like NAT -defined Funcs ((AllFormulasOf U),(AllFormulasOf U)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):]
x . 0 is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AtomicFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : b₁ is 0wff } is set
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
[:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty Relation-like set
bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty set
AtomicFormulaSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
TheNorSymbOf U is set
{(TheNorSymbOf U)} is non empty trivial finite 1 -element set
(AllSymbolsOf U) \ {(TheNorSymbOf U)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
(AllSymbolsOf U) typed\ {(TheNorSymbOf U)} is Element of bool (AllSymbolsOf U)
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
E is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf U
i is Relation-like Function-like set
dom i is set
x is set
O is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff Element of AtomicFormulasOf U
i . O is set
(U,u,E,O) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
U -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
[:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(AllSymbolsOf U) -pr1 is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total V233( AllSymbolsOf U) Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
[:(AllSymbolsOf U),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf U),(AllSymbolsOf U)) is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
MultPlace ((AllSymbolsOf U) -pr1) is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(U -firstChar) . O is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
<*((U -firstChar) . O)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,((U -firstChar) . O)] is non empty set
{[1,((U -firstChar) . O)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
SubTerms O is Relation-like NAT -defined (rng O) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . O)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
ar ((U -firstChar) . O) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U . ((U -firstChar) . O) is set
abs (ar ((U -firstChar) . O)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng O is non empty finite set
(rng O) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng O
(TermSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf U
AllTermsOf U is non empty functional finite-membered FinSequence-membered AllSymbolsOf U -prefix U -prefix Element of bool ((AllSymbolsOf U) *)
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
(U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
the U2 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) is non empty functional M31((AllTermsOf U) * ,(AllTermsOf U) \/ BOOLEAN)
Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U,K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))
(AllTermsOf U) -InterpretersOf U is non empty functional Element of bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf U -defined K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) : b₁ is U, AllTermsOf U -interpreter-like } is set
(u,E) ReassignIn (U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
{} .--> E is trivial Relation-like {{}} -defined AllTermsOf U -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> E is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf U -valued {E} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{E}:]
{E} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{E}:] is non empty Relation-like finite set
bool [:{{}},{E}:] is non empty finite finite-membered set
u .--> ({} .--> E) is trivial Relation-like AllSymbolsOf U -defined {u} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{u} is non empty trivial finite 1 -element set
{u} --> ({} .--> E) is non empty Relation-like {u} -defined {({} .--> E)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{u},{({} .--> E)}:]
{({} .--> E)} is non empty trivial functional finite finite-membered 1 -element set
[:{u},{({} .--> E)}:] is non empty Relation-like finite set
bool [:{u},{({} .--> E)}:] is non empty finite finite-membered set
(U,{}) +* (u .--> ({} .--> E)) is Relation-like Function-like Function-yielding V164() set
((u,E) ReassignIn (U,{})) -TermEval is non empty Relation-like non empty-yielding AllTermsOf U -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf U),(AllTermsOf U):]
[:(AllTermsOf U),(AllTermsOf U):] is non empty Relation-like set
bool [:(AllTermsOf U),(AllTermsOf U):] is non empty set
(((u,E) ReassignIn (U,{})) -TermEval) (*) (SubTerms O) is Relation-like NAT -defined AllTermsOf U -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(U -multiCat) . ((((u,E) ReassignIn (U,{})) -TermEval) (*) (SubTerms O)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((U -firstChar) . O)*> ^ ((U -multiCat) . ((((u,E) ReassignIn (U,{})) -TermEval) (*) (SubTerms O))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
i . x is set
UU is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
x is non empty Relation-like non empty-yielding AtomicFormulasOf U -defined AtomicFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):]
O is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
UU is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf U
III is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff Element of AtomicFormulasOf U
i . III is set
(U,u,E,III) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
(U -firstChar) . III is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
<*((U -firstChar) . III)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,((U -firstChar) . III)] is non empty set
{[1,((U -firstChar) . III)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
SubTerms III is Relation-like NAT -defined (rng III) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . III)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
ar ((U -firstChar) . III) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U . ((U -firstChar) . III) is set
abs (ar ((U -firstChar) . III)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng III is non empty finite set
(rng III) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng III
(((u,E) ReassignIn (U,{})) -TermEval) (*) (SubTerms III) is Relation-like NAT -defined AllTermsOf U -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(U -multiCat) . ((((u,E) ReassignIn (U,{})) -TermEval) (*) (SubTerms III)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((U -firstChar) . III)*> ^ ((U -multiCat) . ((((u,E) ReassignIn (U,{})) -TermEval) (*) (SubTerms III))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
x . O is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(U,u,UU,O) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
(U -firstChar) . O is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
<*((U -firstChar) . O)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,((U -firstChar) . O)] is non empty set
{[1,((U -firstChar) . O)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
SubTerms O is Relation-like NAT -defined (rng O) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . O)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
ar ((U -firstChar) . O) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U . ((U -firstChar) . O) is set
abs (ar ((U -firstChar) . O)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng O is non empty finite set
(rng O) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng O
(u,UU) ReassignIn (U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
{} .--> UU is trivial Relation-like {{}} -defined AllTermsOf U -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> UU is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf U -valued {UU} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{UU}:]
{UU} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{UU}:] is non empty Relation-like finite set
bool [:{{}},{UU}:] is non empty finite finite-membered set
u .--> ({} .--> UU) is trivial Relation-like AllSymbolsOf U -defined {u} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{u} --> ({} .--> UU) is non empty Relation-like {u} -defined {({} .--> UU)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{u},{({} .--> UU)}:]
{({} .--> UU)} is non empty trivial functional finite finite-membered 1 -element set
[:{u},{({} .--> UU)}:] is non empty Relation-like finite set
bool [:{u},{({} .--> UU)}:] is non empty finite finite-membered set
(U,{}) +* (u .--> ({} .--> UU)) is Relation-like Function-like Function-yielding V164() set
((u,UU) ReassignIn (U,{})) -TermEval is non empty Relation-like non empty-yielding AllTermsOf U -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf U),(AllTermsOf U):]
(((u,UU) ReassignIn (U,{})) -TermEval) (*) (SubTerms O) is Relation-like NAT -defined AllTermsOf U -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(U -multiCat) . ((((u,UU) ReassignIn (U,{})) -TermEval) (*) (SubTerms O)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((U -firstChar) . O)*> ^ ((U -multiCat) . ((((u,UU) ReassignIn (U,{})) -TermEval) (*) (SubTerms O))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
i is non empty Relation-like non empty-yielding AtomicFormulasOf U -defined AtomicFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):]
x is non empty Relation-like non empty-yielding AtomicFormulasOf U -defined AtomicFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):]
O is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff Element of AtomicFormulasOf U
UU is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
III is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
i . III is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
E is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf U
(U,u,E,III) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
U -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
[:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(AllSymbolsOf U) -pr1 is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total V233( AllSymbolsOf U) Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
[:(AllSymbolsOf U),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf U),(AllSymbolsOf U)) is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
MultPlace ((AllSymbolsOf U) -pr1) is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(U -firstChar) . III is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
<*((U -firstChar) . III)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,((U -firstChar) . III)] is non empty set
{[1,((U -firstChar) . III)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
SubTerms III is Relation-like NAT -defined (rng III) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . III)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
ar ((U -firstChar) . III) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U . ((U -firstChar) . III) is set
abs (ar ((U -firstChar) . III)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng III is non empty finite set
(rng III) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng III
(TermSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf U
AllTermsOf U is non empty functional finite-membered FinSequence-membered AllSymbolsOf U -prefix U -prefix Element of bool ((AllSymbolsOf U) *)
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
(U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
the U2 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) is non empty functional M31((AllTermsOf U) * ,(AllTermsOf U) \/ BOOLEAN)
Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U,K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))
(AllTermsOf U) -InterpretersOf U is non empty functional Element of bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf U -defined K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) : b₁ is U, AllTermsOf U -interpreter-like } is set
(u,E) ReassignIn (U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
{} .--> E is trivial Relation-like {{}} -defined AllTermsOf U -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> E is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf U -valued {E} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{E}:]
{E} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{E}:] is non empty Relation-like finite set
bool [:{{}},{E}:] is non empty finite finite-membered set
u .--> ({} .--> E) is trivial Relation-like AllSymbolsOf U -defined {u} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{u} is non empty trivial finite 1 -element set
{u} --> ({} .--> E) is non empty Relation-like {u} -defined {({} .--> E)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{u},{({} .--> E)}:]
{({} .--> E)} is non empty trivial functional finite finite-membered 1 -element set
[:{u},{({} .--> E)}:] is non empty Relation-like finite set
bool [:{u},{({} .--> E)}:] is non empty finite finite-membered set
(U,{}) +* (u .--> ({} .--> E)) is Relation-like Function-like Function-yielding V164() set
((u,E) ReassignIn (U,{})) -TermEval is non empty Relation-like non empty-yielding AllTermsOf U -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf U),(AllTermsOf U):]
[:(AllTermsOf U),(AllTermsOf U):] is non empty Relation-like set
bool [:(AllTermsOf U),(AllTermsOf U):] is non empty set
(((u,E) ReassignIn (U,{})) -TermEval) (*) (SubTerms III) is Relation-like NAT -defined AllTermsOf U -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(U -multiCat) . ((((u,E) ReassignIn (U,{})) -TermEval) (*) (SubTerms III)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((U -firstChar) . III)*> ^ ((U -multiCat) . ((((u,E) ReassignIn (U,{})) -TermEval) (*) (SubTerms III))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
x . III is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
i . O is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff Element of AtomicFormulasOf U
x . O is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff Element of AtomicFormulasOf U
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
id (AllFormulasOf U) is non empty Relation-like non empty-yielding AllFormulasOf U -defined AllFormulasOf U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf U),(AllFormulasOf U):]
[:(AllFormulasOf U),(AllFormulasOf U):] is non empty Relation-like set
bool [:(AllFormulasOf U),(AllFormulasOf U):] is non empty set
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S) is non empty Relation-like non empty-yielding AtomicFormulasOf U -defined AtomicFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):]
AtomicFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : b₁ is 0wff } is set
[:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty Relation-like set
bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty set
(id (AllFormulasOf U)) +* (U,u,S) is non empty Relation-like Function-like Function-yielding V164() set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf U),(AllFormulasOf U)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U, AllFormulasOf U
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S) is Relation-like Function-like set
id (AllFormulasOf U) is non empty Relation-like non empty-yielding AllFormulasOf U -defined AllFormulasOf U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf U),(AllFormulasOf U):]
[:(AllFormulasOf U),(AllFormulasOf U):] is non empty Relation-like set
bool [:(AllFormulasOf U),(AllFormulasOf U):] is non empty set
(U,u,S) is non empty Relation-like non empty-yielding AtomicFormulasOf U -defined AtomicFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):]
AtomicFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : b₁ is 0wff } is set
[:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty Relation-like set
bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty set
(id (AllFormulasOf U)) +* (U,u,S) is non empty Relation-like Function-like Function-yielding V164() set
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf U is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf U
(AtomicFormulasOf U) \ (AllFormulasOf U) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V165() V166() V192() FinSequence-yielding finite-support Element of bool (((AllSymbolsOf U) *) \ {{}})
(AtomicFormulasOf U) typed\ (AllFormulasOf U) is functional finite-membered FinSequence-membered V165() Element of bool (AtomicFormulasOf U)
bool (AtomicFormulasOf U) is non empty set
(AtomicFormulasOf U) \ (AllFormulasOf U) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V165() V166() V192() FinSequence-yielding finite-support Element of bool (AtomicFormulasOf U)
bool (AllFormulasOf U) is non empty set
dom (id (AllFormulasOf U)) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllFormulasOf U)
dom (U,u,S) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AtomicFormulasOf U)
X is functional finite-membered FinSequence-membered V165() Element of bool (AllFormulasOf U)
dom ((id (AllFormulasOf U)) +* (U,u,S)) is non empty set
(AllFormulasOf U) null X is set
(AllFormulasOf U) \typed/ X is functional finite-membered V165() Element of bool ((AllFormulasOf U) \/ X)
(AllFormulasOf U) \/ X is non empty functional finite-membered V165() V166() set
bool ((AllFormulasOf U) \/ X) is non empty set
rng ((id (AllFormulasOf U)) +* (U,u,S)) is non empty set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S) is Relation-like Function-like set
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
id (AllFormulasOf U) is non empty Relation-like non empty-yielding AllFormulasOf U -defined AllFormulasOf U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf U),(AllFormulasOf U):]
[:(AllFormulasOf U),(AllFormulasOf U):] is non empty Relation-like set
bool [:(AllFormulasOf U),(AllFormulasOf U):] is non empty set
(U,u,S) is non empty Relation-like non empty-yielding AtomicFormulasOf U -defined AtomicFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):]
AtomicFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : b₁ is 0wff } is set
[:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty Relation-like set
bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty set
(id (AllFormulasOf U)) +* (U,u,S) is non empty Relation-like Function-like Function-yielding V164() set
Funcs ((AllFormulasOf U),((AllSymbolsOf U) *)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U,(AllSymbolsOf U) *
Funcs ((AllFormulasOf U),(AllFormulasOf U)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U, AllFormulasOf U
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S) is Relation-like Function-like set
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
id (AllFormulasOf U) is non empty Relation-like non empty-yielding AllFormulasOf U -defined AllFormulasOf U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf U),(AllFormulasOf U):]
[:(AllFormulasOf U),(AllFormulasOf U):] is non empty Relation-like set
bool [:(AllFormulasOf U),(AllFormulasOf U):] is non empty set
(U,u,S) is non empty Relation-like non empty-yielding AtomicFormulasOf U -defined AtomicFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):]
AtomicFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : b₁ is 0wff } is set
[:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty Relation-like set
bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty set
(id (AllFormulasOf U)) +* (U,u,S) is non empty Relation-like Function-like Function-yielding V164() set
Funcs ((AllFormulasOf U),(AllFormulasOf U)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U, AllFormulasOf U
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf U),(AllFormulasOf U)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U, AllFormulasOf U
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S) is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
id (AllFormulasOf U) is non empty Relation-like non empty-yielding AllFormulasOf U -defined AllFormulasOf U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf U),(AllFormulasOf U):]
[:(AllFormulasOf U),(AllFormulasOf U):] is non empty Relation-like set
bool [:(AllFormulasOf U),(AllFormulasOf U):] is non empty set
(U,u,S) is non empty Relation-like non empty-yielding AtomicFormulasOf U -defined AtomicFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):]
AtomicFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : b₁ is 0wff } is set
[:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty Relation-like set
bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty set
(id (AllFormulasOf U)) +* (U,u,S) is non empty Relation-like Function-like Function-yielding V164() set
(U,u,S,(U,u,S)) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf U),(AllFormulasOf U)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):]
[:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):] is non empty non trivial non finite V166() set
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
Depth l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(U,u,S,(U,u,S)) . (Depth l) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
((U,u,S,(U,u,S)) . (Depth l)) . l is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
x is non empty Relation-like NAT -defined Funcs ((AllFormulasOf U),(AllFormulasOf U)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):]
i is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
x . i is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
O is non empty Relation-like non empty-yielding AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf U),(AllFormulasOf U):]
UU is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf U
O . UU is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf U
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
TermSymbolsOf U is non empty set
the U3 of U is Element of the U1 of U
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined TermSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf U) *) \ {{}}
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,l) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf U),(AllFormulasOf U)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U, AllFormulasOf U
(U,u,S) is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
id (AllFormulasOf U) is non empty Relation-like non empty-yielding AllFormulasOf U -defined AllFormulasOf U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf U),(AllFormulasOf U):]
[:(AllFormulasOf U),(AllFormulasOf U):] is non empty Relation-like set
bool [:(AllFormulasOf U),(AllFormulasOf U):] is non empty set
(U,u,S) is non empty Relation-like non empty-yielding AtomicFormulasOf U -defined AtomicFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):]
AtomicFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : b₁ is 0wff } is set
[:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty Relation-like set
bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty set
(id (AllFormulasOf U)) +* (U,u,S) is non empty Relation-like Function-like Function-yielding V164() set
(U,u,S,(U,u,S)) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf U),(AllFormulasOf U)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):]
[:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):] is non empty non trivial non finite V166() set
Depth l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(U,u,S,(U,u,S)) . (Depth l) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
((U,u,S,(U,u,S)) . (Depth l)) . l is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
U is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
U + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
u is V51() V53() eligible Language-like
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
TermSymbolsOf u is non empty set
the U3 of u is Element of the U1 of u
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
AllSymbolsOf u is non empty non trivial non finite V166() set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
AllFormulasOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of bool (((AllSymbolsOf u) *) \ {{}})
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf u),(AllFormulasOf u)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf u, AllFormulasOf u
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
l is non empty Relation-like NAT -defined TermSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf u) *) \ {{}}
II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
x is Relation-like AllFormulasOf u -defined AllFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
(u,S,l,x) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf u),(AllFormulasOf u)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):]
[:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):] is non empty non trivial non finite V166() set
(u,S,l,x) . (U + 1) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,x) . (U + 1)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,S,l,x) . U is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
(u,S,l,U,((u,S,l,x) . U),II) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
O is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(u,S,l,x) . O is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
(u,S,l,U,((u,S,l,x) . O)) is Relation-like AllFormulasOf u -defined AllFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
O + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(u,S,l,x) . (O + 1) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,x) . (O + 1)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,S,l,U,((u,S,l,x) . O)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,S,l,U,((u,S,l,x) . O),II) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
U is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u is V51() V53() eligible Language-like
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
TermSymbolsOf u is non empty set
the U3 of u is Element of the U1 of u
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
AllSymbolsOf u is non empty non trivial non finite V166() set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
AllFormulasOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of bool (((AllSymbolsOf u) *) \ {{}})
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf u),(AllFormulasOf u)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf u, AllFormulasOf u
u -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
[:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(AllSymbolsOf u) -pr1 is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total V233( AllSymbolsOf u) Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
[:(AllSymbolsOf u),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf u),(AllSymbolsOf u)) is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
MultPlace ((AllSymbolsOf u) -pr1) is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
l is non empty Relation-like NAT -defined TermSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,l) is Relation-like AllFormulasOf u -defined AllFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
id (AllFormulasOf u) is non empty Relation-like non empty-yielding AllFormulasOf u -defined AllFormulasOf u -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf u),(AllFormulasOf u):]
[:(AllFormulasOf u),(AllFormulasOf u):] is non empty Relation-like set
bool [:(AllFormulasOf u),(AllFormulasOf u):] is non empty set
(u,S,l) is non empty Relation-like non empty-yielding AtomicFormulasOf u -defined AtomicFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf u),(AtomicFormulasOf u):]
AtomicFormulasOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of bool (((AllSymbolsOf u) *) \ {{}})
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}} : b₁ is 0wff } is set
[:(AtomicFormulasOf u),(AtomicFormulasOf u):] is non empty Relation-like set
bool [:(AtomicFormulasOf u),(AtomicFormulasOf u):] is non empty set
(id (AllFormulasOf u)) +* (u,S,l) is non empty Relation-like Function-like Function-yielding V164() set
(u,S,l,(u,S,l)) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf u),(AllFormulasOf u)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):]
[:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):] is non empty non trivial non finite V166() set
II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth II is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth II) + U is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u -firstChar) . II is Element of AllSymbolsOf u
(u,S,l,(u,S,l)) . (Depth II) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,(u,S,l)) . (Depth II)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
O is Relation-like AllFormulasOf u -defined AllFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
(u,S,l,O) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf u),(AllFormulasOf u)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):]
(u,S,l,O) . ((Depth II) + U) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,O) . ((Depth II) + U)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,S,l,O) . (Depth II) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,O) . (Depth II)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
TheNorSymbOf u is non literal non low-compounding non relational non own Element of AllSymbolsOf u
LettersOf u is non empty non trivial non finite V166() Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
the adicity of u " {0} is Element of bool ( the U1 of u \ { the U3 of u})
head II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
SubWffsOf II is set
K74((SubWffsOf II)) is set
Depth (head II) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth II) + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u,S,l,O) . ((Depth II) + 0) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,O) . ((Depth II) + 0)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,S,l,(u,S,l)) . 0 is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,(u,S,l)) . 0) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(Depth II) + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(u,S,l,O) . ((Depth II) + 0) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,O) . ((Depth II) + 0)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
G is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff wff Element of ((AllSymbolsOf u) *) \ {{}}
((u -firstChar) . II) \+\ (TheNorSymbOf u) is set
((u -firstChar) . II) \ (TheNorSymbOf u) is set
((u -firstChar) . II) typed\ (TheNorSymbOf u) is Element of bool ((u -firstChar) . II)
bool ((u -firstChar) . II) is non empty set
((u -firstChar) . II) \ (TheNorSymbOf u) is Element of bool ((u -firstChar) . II)
(TheNorSymbOf u) \ ((u -firstChar) . II) is set
(TheNorSymbOf u) typed\ ((u -firstChar) . II) is Element of bool (TheNorSymbOf u)
bool (TheNorSymbOf u) is non empty set
(TheNorSymbOf u) \ ((u -firstChar) . II) is Element of bool (TheNorSymbOf u)
(((u -firstChar) . II) \ (TheNorSymbOf u)) \/ ((TheNorSymbOf u) \ ((u -firstChar) . II)) is set
n is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
(id (AllFormulasOf u)) . n is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
((id (AllFormulasOf u)) . n) \+\ n 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
((id (AllFormulasOf u)) . n) \ n is Relation-like NAT -defined finite set
((id (AllFormulasOf u)) . n) typed\ n is Relation-like NAT -defined Function-like finite finite-support Element of bool ((id (AllFormulasOf u)) . n)
bool ((id (AllFormulasOf u)) . n) is non empty finite finite-membered set
((id (AllFormulasOf u)) . n) \ n is Relation-like NAT -defined Function-like finite finite-support Element of bool ((id (AllFormulasOf u)) . n)
n \ ((id (AllFormulasOf u)) . n) is Relation-like NAT -defined finite set
n typed\ ((id (AllFormulasOf u)) . n) is Relation-like NAT -defined Function-like finite finite-support Element of bool n
bool n is non empty finite finite-membered set
n \ ((id (AllFormulasOf u)) . n) is Relation-like NAT -defined Function-like finite finite-support Element of bool n
(((id (AllFormulasOf u)) . n) \ n) \/ (n \ ((id (AllFormulasOf u)) . n)) is Relation-like NAT -defined finite set
Enn is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff wff exal Element of ((AllSymbolsOf u) *) \ {{}}
dom (u,S,l) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AtomicFormulasOf u)
bool (AtomicFormulasOf u) is non empty set
(u,S,l) . Enn is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(id (AllFormulasOf u)) . Enn is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
tail Enn is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued AllSymbolsOf u -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllSymbolsOf u) *
SubWffsOf Enn is set
K75((SubWffsOf Enn)) is set
G is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth II) + G is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u,S,l,O) . ((Depth II) + G) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,O) . ((Depth II) + G)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,S,l,(u,S,l)) . G is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,(u,S,l)) . G) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
G + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(Depth II) + (G + 1) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(u,S,l,O) . ((Depth II) + (G + 1)) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,O) . ((Depth II) + (G + 1))) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,S,l,(u,S,l)) . (G + 1) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,(u,S,l)) . (G + 1)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(Depth II) + (G + 1) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
((Depth II) + G) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(u,S,l,O) . ((Depth II) + (G + 1)) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,O) . ((Depth II) + (G + 1))) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,S,l,O) . (((Depth II) + G) + 1) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,O) . (((Depth II) + G) + 1)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,S,l,((Depth II) + G),((u,S,l,O) . ((Depth II) + G)),II) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
((u -firstChar) . II) \+\ (TheNorSymbOf u) is set
((u -firstChar) . II) \ (TheNorSymbOf u) is set
((u -firstChar) . II) typed\ (TheNorSymbOf u) is Element of bool ((u -firstChar) . II)
bool ((u -firstChar) . II) is non empty set
((u -firstChar) . II) \ (TheNorSymbOf u) is Element of bool ((u -firstChar) . II)
(TheNorSymbOf u) \ ((u -firstChar) . II) is set
(TheNorSymbOf u) typed\ ((u -firstChar) . II) is Element of bool (TheNorSymbOf u)
bool (TheNorSymbOf u) is non empty set
(TheNorSymbOf u) \ ((u -firstChar) . II) is Element of bool (TheNorSymbOf u)
(((u -firstChar) . II) \ (TheNorSymbOf u)) \/ ((TheNorSymbOf u) \ ((u -firstChar) . II)) is set
n is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff wff exal Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,l,G,((u,S,l,(u,S,l)) . G),n) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
U is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u is V51() V53() eligible Language-like
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
TermSymbolsOf u is non empty set
the U3 of u is Element of the U1 of u
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
AllSymbolsOf u is non empty non trivial non finite V166() set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
AllFormulasOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of bool (((AllSymbolsOf u) *) \ {{}})
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf u),(AllFormulasOf u)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf u, AllFormulasOf u
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
l is non empty Relation-like NAT -defined TermSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,l) is Relation-like AllFormulasOf u -defined AllFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
id (AllFormulasOf u) is non empty Relation-like non empty-yielding AllFormulasOf u -defined AllFormulasOf u -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf u),(AllFormulasOf u):]
[:(AllFormulasOf u),(AllFormulasOf u):] is non empty Relation-like set
bool [:(AllFormulasOf u),(AllFormulasOf u):] is non empty set
(u,S,l) is non empty Relation-like non empty-yielding AtomicFormulasOf u -defined AtomicFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf u),(AtomicFormulasOf u):]
AtomicFormulasOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of bool (((AllSymbolsOf u) *) \ {{}})
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}} : b₁ is 0wff } is set
[:(AtomicFormulasOf u),(AtomicFormulasOf u):] is non empty Relation-like set
bool [:(AtomicFormulasOf u),(AtomicFormulasOf u):] is non empty set
(id (AllFormulasOf u)) +* (u,S,l) is non empty Relation-like Function-like Function-yielding V164() set
(u,S,l,(u,S,l)) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf u),(AllFormulasOf u)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):]
[:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):] is non empty non trivial non finite V166() set
(u,S,l,(u,S,l)) . U is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,l,II) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth II is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u,S,l,(u,S,l)) . (Depth II) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,(u,S,l)) . (Depth II)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((u,S,l,(u,S,l)) . U) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U - (Depth II) is finite complex ext-real V40() V41() set
x is Relation-like AllFormulasOf u -defined AllFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
(u,S,l,x) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf u),(AllFormulasOf u)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):]
O is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth II) + O is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u,S,l,x) . ((Depth II) + O) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,x) . ((Depth II) + O)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U is V51() V53() eligible Language-like
AllSymbolsOf U is non empty non trivial non finite V166() set
the U1 of U is set
AllSymbolsOf U is non empty non trivial non finite V166() set
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
AllTermsOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of K335((((AllSymbolsOf U) *) \ {{}}))
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf U) *) \ {{}}))
bool (bool (((AllSymbolsOf U) *) \ {{}})) is non empty non trivial non finite V166() set
U -termsOfMaxDepth is Relation-like Function-like set
rng (U -termsOfMaxDepth) is set
union (rng (U -termsOfMaxDepth)) is set
AtomicFormulaSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
TheNorSymbOf U is set
the U3 of U is Element of the U1 of U
{(TheNorSymbOf U)} is non empty trivial finite 1 -element set
(AllSymbolsOf U) \ {(TheNorSymbOf U)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf U)
bool (AllSymbolsOf U) is non empty non trivial non finite V166() set
(AllSymbolsOf U) typed\ {(TheNorSymbOf U)} is Element of bool (AllSymbolsOf U)
u is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf U
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf U
l is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
(U,u,S,l) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf U) *) \ {{}}
AllFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
(AllSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf U
((AllSymbolsOf U) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf U) *)
bool ((AllSymbolsOf U) *) is non empty non trivial non finite V166() set
((AllSymbolsOf U) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf U) *)
bool (((AllSymbolsOf U) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf U),(AllFormulasOf U)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf U, AllFormulasOf U
(U,u,S) is Relation-like AllFormulasOf U -defined AllFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
id (AllFormulasOf U) is non empty Relation-like non empty-yielding AllFormulasOf U -defined AllFormulasOf U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf U),(AllFormulasOf U):]
[:(AllFormulasOf U),(AllFormulasOf U):] is non empty Relation-like set
bool [:(AllFormulasOf U),(AllFormulasOf U):] is non empty set
(U,u,S) is non empty Relation-like non empty-yielding AtomicFormulasOf U -defined AtomicFormulasOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):]
AtomicFormulasOf U is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf U -prefix U -prefix Element of bool (((AllSymbolsOf U) *) \ {{}})
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}} : b₁ is 0wff } is set
[:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty Relation-like set
bool [:(AtomicFormulasOf U),(AtomicFormulasOf U):] is non empty set
(id (AllFormulasOf U)) +* (U,u,S) is non empty Relation-like Function-like Function-yielding V164() set
(U,u,S,(U,u,S)) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf U),(AllFormulasOf U)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):]
[:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllFormulasOf U),(AllFormulasOf U))):] is non empty non trivial non finite V166() set
Depth l 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(U,u,S,(U,u,S)) . (Depth l) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf U),(AllFormulasOf U))
((U,u,S,(U,u,S)) . (Depth l)) . l is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(U,u,S,l) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf U -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf U) *) \ {{}}
U -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
[:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -firstChar is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(AllSymbolsOf U) -pr1 is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total V233( AllSymbolsOf U) Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
[:(AllSymbolsOf U),(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf U),(AllSymbolsOf U)) is non empty Relation-like [:(AllSymbolsOf U),(AllSymbolsOf U):] -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf U),(AllSymbolsOf U):],(AllSymbolsOf U):]
MultPlace ((AllSymbolsOf U) -pr1) is non empty Relation-like ((AllSymbolsOf U) *) \ {{}} -defined AllSymbolsOf U -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf U) *) \ {{}}),(AllSymbolsOf U):]
(U -firstChar) . l is low-compounding relational ofAtomicFormula Element of AllSymbolsOf U
<*((U -firstChar) . l)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf U) *) \ {{}}
[1,((U -firstChar) . l)] is non empty set
{[1,((U -firstChar) . l)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
U -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
((AllSymbolsOf U) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf U) *
[:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf U) -multiCat is non empty Relation-like ((AllSymbolsOf U) *) * -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf U) *) *),((AllSymbolsOf U) *):]
(AllSymbolsOf U) -concatenation is non empty Relation-like [:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf U) * ) Element of bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):]
[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf U) *),((AllSymbolsOf U) *):],((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf U) -concatenation) is non empty Relation-like (((AllSymbolsOf U) *) *) \ {{}} -defined (AllSymbolsOf U) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):]
(((AllSymbolsOf U) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf U) *) *)
bool (((AllSymbolsOf U) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf U) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf U) *) *)
[:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf U) *) *) \ {{}}),((AllSymbolsOf U) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf U) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
SubTerms l is Relation-like NAT -defined (rng l) * -valued (TermSymbolsOf U) * -valued AllTermsOf U -valued Function-like finite abs (ar ((U -firstChar) . l)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf U) *
ar ((U -firstChar) . l) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of U is non empty Relation-like the U1 of U \ { the U3 of U} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of U \ { the U3 of U}),INT:]
{ the U3 of U} is non empty trivial finite 1 -element set
the U1 of U \ { the U3 of U} is non empty Element of bool the U1 of U
bool the U1 of U is non empty set
the U1 of U typed\ { the U3 of U} is Element of bool the U1 of U
[:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of U \ { the U3 of U}),INT:] is non empty non trivial non finite V166() set
the adicity of U . ((U -firstChar) . l) is set
abs (ar ((U -firstChar) . l)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng l is non empty finite set
(rng l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng l
TermSymbolsOf U is non empty set
the adicity of U " NAT is Element of bool ( the U1 of U \ { the U3 of U})
bool ( the U1 of U \ { the U3 of U}) is non empty set
(TermSymbolsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf U
AllTermsOf U is non empty functional finite-membered FinSequence-membered AllSymbolsOf U -prefix U -prefix Element of bool ((AllSymbolsOf U) *)
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf U) *) *)
(U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
OwnSymbolsOf U is non empty Element of bool (AllSymbolsOf U)
the U2 of U is Element of the U1 of U
{ the U2 of U, the U3 of U} is non empty finite set
the U1 of U \ { the U2 of U, the U3 of U} is Element of bool the U1 of U
the U1 of U typed\ { the U2 of U, the U3 of U} is Element of bool the U1 of U
(AllTermsOf U) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf U
(AllTermsOf U) \/ BOOLEAN is non empty set
K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) is non empty functional M31((AllTermsOf U) * ,(AllTermsOf U) \/ BOOLEAN)
Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf U,K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))
(AllTermsOf U) -InterpretersOf U is non empty functional Element of bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf U -defined K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf U),K546(((AllTermsOf U) *),((AllTermsOf U) \/ BOOLEAN))) : b₁ is U, AllTermsOf U -interpreter-like } is set
(u,S) ReassignIn (U,{}) is Relation-like OwnSymbolsOf U -defined Function-like total Function-yielding V164() U, AllTermsOf U -interpreter-like Element of (AllTermsOf U) -InterpretersOf U
{} .--> S is trivial Relation-like {{}} -defined AllTermsOf U -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> S is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf U -valued {S} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{S}:]
{S} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{S}:] is non empty Relation-like finite set
bool [:{{}},{S}:] is non empty finite finite-membered set
u .--> ({} .--> S) is trivial Relation-like AllSymbolsOf U -defined {u} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{u} is non empty trivial finite 1 -element set
{u} --> ({} .--> S) is non empty Relation-like {u} -defined {({} .--> S)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{u},{({} .--> S)}:]
{({} .--> S)} is non empty trivial functional finite finite-membered 1 -element set
[:{u},{({} .--> S)}:] is non empty Relation-like finite set
bool [:{u},{({} .--> S)}:] is non empty finite finite-membered set
(U,{}) +* (u .--> ({} .--> S)) is Relation-like Function-like Function-yielding V164() set
((u,S) ReassignIn (U,{})) -TermEval is non empty Relation-like non empty-yielding AllTermsOf U -defined AllTermsOf U -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf U),(AllTermsOf U):]
[:(AllTermsOf U),(AllTermsOf U):] is non empty Relation-like set
bool [:(AllTermsOf U),(AllTermsOf U):] is non empty set
(((u,S) ReassignIn (U,{})) -TermEval) (*) (SubTerms l) is Relation-like NAT -defined AllTermsOf U -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(U -multiCat) . ((((u,S) ReassignIn (U,{})) -TermEval) (*) (SubTerms l)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((U -firstChar) . l)*> ^ ((U -multiCat) . ((((u,S) ReassignIn (U,{})) -TermEval) (*) (SubTerms l))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom (U,u,S) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AtomicFormulasOf U)
bool (AtomicFormulasOf U) is non empty set
III is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of dom (U,u,S)
(U,u,S) . III is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(U,u,S) . III is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff Element of AtomicFormulasOf U
U is non empty set
U * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of U
U \/ BOOLEAN is non empty set
K546((U *),(U \/ BOOLEAN)) is non empty functional M31(U * ,U \/ BOOLEAN)
u is V51() V53() eligible Language-like
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
AllSymbolsOf u is non empty non trivial non finite V166() set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
OwnSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
the U2 of u is Element of the U1 of u
the U3 of u is Element of the U1 of u
{ the U2 of u, the U3 of u} is non empty finite set
the U1 of u \ { the U2 of u, the U3 of u} is Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U2 of u, the U3 of u} is Element of bool the U1 of u
Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf u,K546((U *),(U \/ BOOLEAN))
U -InterpretersOf u is non empty functional Element of bool (Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf u -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN))) : b₁ is u,U -interpreter-like } is set
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
l is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth l is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u
(u,S,II,l) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
AllFormulasOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of bool (((AllSymbolsOf u) *) \ {{}})
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf u),(AllFormulasOf u)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf u, AllFormulasOf u
(u,S,II) is Relation-like AllFormulasOf u -defined AllFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
id (AllFormulasOf u) is non empty Relation-like non empty-yielding AllFormulasOf u -defined AllFormulasOf u -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf u),(AllFormulasOf u):]
[:(AllFormulasOf u),(AllFormulasOf u):] is non empty Relation-like set
bool [:(AllFormulasOf u),(AllFormulasOf u):] is non empty set
(u,S,II) is non empty Relation-like non empty-yielding AtomicFormulasOf u -defined AtomicFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf u),(AtomicFormulasOf u):]
AtomicFormulasOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of bool (((AllSymbolsOf u) *) \ {{}})
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}} : b₁ is 0wff } is set
[:(AtomicFormulasOf u),(AtomicFormulasOf u):] is non empty Relation-like set
bool [:(AtomicFormulasOf u),(AtomicFormulasOf u):] is non empty set
(id (AllFormulasOf u)) +* (u,S,II) is non empty Relation-like Function-like Function-yielding V164() set
(u,S,II,(u,S,II)) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf u),(AllFormulasOf u)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):]
[:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):] is non empty non trivial non finite V166() set
(u,S,II,(u,S,II)) . (Depth l) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,II,(u,S,II)) . (Depth l)) . l is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
Depth (u,S,II,l) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
u -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
[:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(AllSymbolsOf u) -pr1 is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total V233( AllSymbolsOf u) Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
[:(AllSymbolsOf u),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf u),(AllSymbolsOf u)) is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
MultPlace ((AllSymbolsOf u) -pr1) is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
LettersOf u is non empty non trivial non finite V166() Element of bool (AllSymbolsOf u)
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
the adicity of u " {0} is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
TheNorSymbOf u is non literal non low-compounding non relational non own Element of AllSymbolsOf u
(u,{},II) is non empty Relation-like NAT -defined {} \/ (dom II) -defined {} \/ (rng II) -valued TermSymbolsOf u -valued Function-like finite len II -element FinSequence-like FinSubsequence-like finite-support termal (Depth II) + {} -termal Element of ((AllSymbolsOf u) *) \ {{}}
dom II is non empty finite set
{} \/ (dom II) is non empty finite set
rng II is non empty finite set
{} \/ (rng II) is non empty finite set
TermSymbolsOf u is non empty set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
len II is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
Depth II is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth II) + {} is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
II \typed/ {} is Relation-like NAT -defined finite Element of bool (II \/ {})
II \/ {} is non empty Relation-like NAT -defined finite set
bool (II \/ {}) is non empty finite finite-membered set
II null {} is Relation-like NAT -defined {} \/ (dom II) -defined {} \/ (rng II) -valued Function-like finite len II -element FinSequence-like FinSubsequence-like finite-support set
II ^ {} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
{} ^ II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(rng II) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng II
jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth jJ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u,S,II,jJ) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,II,(u,S,II)) . (Depth jJ) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,II,(u,S,II)) . (Depth jJ)) . jJ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
Depth (u,S,II,jJ) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
AtomicFormulaSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
TheNorSymbOf u is set
{(TheNorSymbOf u)} is non empty trivial finite 1 -element set
(AllSymbolsOf u) \ {(TheNorSymbOf u)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
(AllSymbolsOf u) typed\ {(TheNorSymbOf u)} is Element of bool (AllSymbolsOf u)
G is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,II,G) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth G 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(u,S,II,(u,S,II)) . (Depth G) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,II,(u,S,II)) . (Depth G)) . G is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,S,II,G) is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
(u -firstChar) . G is low-compounding relational ofAtomicFormula Element of AllSymbolsOf u
<*((u -firstChar) . G)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
[1,((u -firstChar) . G)] is non empty set
{[1,((u -firstChar) . G)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
u -multiCat is non empty Relation-like ((AllSymbolsOf u) *) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):]
((AllSymbolsOf u) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf u) *
[:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -multiCat is non empty Relation-like ((AllSymbolsOf u) *) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):]
(AllSymbolsOf u) -concatenation is non empty Relation-like [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf u) * ) Element of bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):]
[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf u) -concatenation) is non empty Relation-like (((AllSymbolsOf u) *) *) \ {{}} -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):]
(((AllSymbolsOf u) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf u) *) *)
bool (((AllSymbolsOf u) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf u) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf u) *) *)
[:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf u) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
SubTerms G is Relation-like NAT -defined (rng G) * -valued (TermSymbolsOf u) * -valued AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . G)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
ar ((u -firstChar) . G) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of u . ((u -firstChar) . G) is set
abs (ar ((u -firstChar) . G)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
rng G is non empty finite set
(rng G) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng G
(TermSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf u
AllTermsOf u is non empty functional finite-membered FinSequence-membered AllSymbolsOf u -prefix u -prefix Element of bool ((AllSymbolsOf u) *)
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf u) *) *)
(u,{}) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u, AllTermsOf u -interpreter-like Element of (AllTermsOf u) -InterpretersOf u
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf u
(AllTermsOf u) \/ BOOLEAN is non empty set
K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN)) is non empty functional M31((AllTermsOf u) * ,(AllTermsOf u) \/ BOOLEAN)
Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf u,K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))
(AllTermsOf u) -InterpretersOf u is non empty functional Element of bool (Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf u -defined K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf u),K546(((AllTermsOf u) *),((AllTermsOf u) \/ BOOLEAN))) : b₁ is u, AllTermsOf u -interpreter-like } is set
(S,II) ReassignIn (u,{}) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u, AllTermsOf u -interpreter-like Element of (AllTermsOf u) -InterpretersOf u
{} .--> II is trivial Relation-like {{}} -defined AllTermsOf u -valued Function-like one-to-one constant finite Function-yielding V164() FinSequence-yielding finite-support set
{{}} --> II is non empty Relation-like non-empty non empty-yielding {{}} -defined AllTermsOf u -valued {II} -valued Function-like constant finite total quasi_total Function-yielding V164() FinSequence-yielding finite-support Element of bool [:{{}},{II}:]
{II} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{{}},{II}:] is non empty Relation-like finite set
bool [:{{}},{II}:] is non empty finite finite-membered set
S .--> ({} .--> II) is trivial Relation-like AllSymbolsOf u -defined {S} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{S} is non empty trivial finite 1 -element set
{S} --> ({} .--> II) is non empty Relation-like {S} -defined {({} .--> II)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{S},{({} .--> II)}:]
{({} .--> II)} is non empty trivial functional finite finite-membered 1 -element set
[:{S},{({} .--> II)}:] is non empty Relation-like finite set
bool [:{S},{({} .--> II)}:] is non empty finite finite-membered set
(u,{}) +* (S .--> ({} .--> II)) is Relation-like Function-like Function-yielding V164() set
((S,II) ReassignIn (u,{})) -TermEval is non empty Relation-like non empty-yielding AllTermsOf u -defined AllTermsOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AllTermsOf u),(AllTermsOf u):]
[:(AllTermsOf u),(AllTermsOf u):] is non empty Relation-like set
bool [:(AllTermsOf u),(AllTermsOf u):] is non empty set
(((S,II) ReassignIn (u,{})) -TermEval) (*) (SubTerms G) is Relation-like NAT -defined AllTermsOf u -valued Function-like finite Function-yielding V164() FinSequence-yielding finite-support set
(u -multiCat) . ((((S,II) ReassignIn (u,{})) -TermEval) (*) (SubTerms G)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*((u -firstChar) . G)*> ^ ((u -multiCat) . ((((S,II) ReassignIn (u,{})) -TermEval) (*) (SubTerms G))) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
Depth (u,S,II,G) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
n is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
n -TruthEval (u,S,II,jJ) is boolean Element of BOOLEAN
n -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(n -TermEval) . II is Element of U
(S,((n -TermEval) . II)) ReassignIn n is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> ((n -TermEval) . II) is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> ((n -TermEval) . II) is non empty Relation-like {{}} -defined U -valued {((n -TermEval) . II)} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{((n -TermEval) . II)}:]
{((n -TermEval) . II)} is non empty trivial finite 1 -element set
[:{{}},{((n -TermEval) . II)}:] is non empty Relation-like finite set
bool [:{{}},{((n -TermEval) . II)}:] is non empty finite finite-membered set
S .--> ({} .--> ((n -TermEval) . II)) is trivial Relation-like AllSymbolsOf u -defined {S} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{S} --> ({} .--> ((n -TermEval) . II)) is non empty Relation-like {S} -defined {({} .--> ((n -TermEval) . II))} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{S},{({} .--> ((n -TermEval) . II))}:]
{({} .--> ((n -TermEval) . II))} is non empty trivial functional finite finite-membered 1 -element set
[:{S},{({} .--> ((n -TermEval) . II))}:] is non empty Relation-like finite set
bool [:{S},{({} .--> ((n -TermEval) . II))}:] is non empty finite finite-membered set
n +* (S .--> ({} .--> ((n -TermEval) . II))) is Relation-like Function-like Function-yielding V164() set
((S,((n -TermEval) . II)) ReassignIn n) -TruthEval jJ is boolean Element of BOOLEAN
n -TruthEval (u,S,II,G) is boolean Element of BOOLEAN
n -AtomicEval (u,S,II,G) is boolean Element of BOOLEAN
n === is Relation-like Function-like Function-yielding V164() u,U -interpreter-like n -extension set
TheEqSymbOf u is Element of AtomicFormulaSymbolsOf u
U -deltaInterpreter is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
2 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
[:(2 -tuples_on U),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on U),BOOLEAN:] is non empty set
[:(U *),(U *):] is non empty non trivial Relation-like non finite V166() set
U -concatenation is non empty Relation-like [:(U *),(U *):] -defined U * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233(U * ) Element of bool [:[:(U *),(U *):],(U *):]
[:[:(U *),(U *):],(U *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(U *),(U *):],(U *):] is non empty non trivial non finite V166() set
1 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
id (1 -tuples_on U) is non empty Relation-like non empty-yielding 1 -tuples_on U -defined 1 -tuples_on U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(1 -tuples_on U),(1 -tuples_on U):]
[:(1 -tuples_on U),(1 -tuples_on U):] is non empty Relation-like set
bool [:(1 -tuples_on U),(1 -tuples_on U):] is non empty set
(U -concatenation) .: (id (1 -tuples_on U)) is functional finite-membered FinSequence-membered Element of bool (U *)
bool (U *) is non empty non trivial non finite V166() set
chi (((U -concatenation) .: (id (1 -tuples_on U))),(2 -tuples_on U)) is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
(TheEqSymbOf u) .--> (U -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf u -defined {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf u)} is non empty trivial finite 1 -element set
{(TheEqSymbOf u)} --> (U -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued {(U -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:]
{(U -deltaInterpreter)} is non empty trivial functional finite 1 -element V165() V166() set
[:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty finite finite-membered set
n +* ((TheEqSymbOf u) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(u -firstChar) . (u,S,II,G) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf u
(n ===) . ((u -firstChar) . (u,S,II,G)) is non empty Relation-like (abs (ar ((u -firstChar) . (u,S,II,G)))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . (u,S,II,G),U
ar ((u -firstChar) . (u,S,II,G)) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of u . ((u -firstChar) . (u,S,II,G)) is set
abs (ar ((u -firstChar) . (u,S,II,G))) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((u -firstChar) . (u,S,II,G)))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms (u,S,II,G) is Relation-like NAT -defined (rng (u,S,II,G)) * -valued (TermSymbolsOf u) * -valued AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . (u,S,II,G))) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
rng (u,S,II,G) is non empty finite set
(rng (u,S,II,G)) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng (u,S,II,G)
(n -TermEval) (*) (SubTerms (u,S,II,G)) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((n ===) . ((u -firstChar) . (u,S,II,G))) . ((n -TermEval) (*) (SubTerms (u,S,II,G))) is set
((S,((n -TermEval) . II)) ReassignIn n) -TruthEval G is boolean Element of BOOLEAN
((S,((n -TermEval) . II)) ReassignIn n) -AtomicEval G is boolean Element of BOOLEAN
((S,((n -TermEval) . II)) ReassignIn n) === is Relation-like Function-like Function-yielding V164() u,U -interpreter-like (S,((n -TermEval) . II)) ReassignIn n -extension set
((S,((n -TermEval) . II)) ReassignIn n) +* ((TheEqSymbOf u) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(((S,((n -TermEval) . II)) ReassignIn n) ===) . ((u -firstChar) . G) is non empty Relation-like (abs (ar ((u -firstChar) . G))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . G,U
(abs (ar ((u -firstChar) . G))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
((S,((n -TermEval) . II)) ReassignIn n) -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
(((S,((n -TermEval) . II)) ReassignIn n) -TermEval) (*) (SubTerms G) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((((S,((n -TermEval) . II)) ReassignIn n) ===) . ((u -firstChar) . G)) . ((((S,((n -TermEval) . II)) ReassignIn n) -TermEval) (*) (SubTerms G)) is set
jJ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
jJ + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth g is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u,S,II,g) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,II,(u,S,II)) . (Depth g) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,II,(u,S,II)) . (Depth g)) . g is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
Depth (u,S,II,g) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
bool (LettersOf u) is non empty non trivial non finite V166() set
head g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
SubWffsOf g is set
K74((SubWffsOf g)) is set
rng (head g) is non empty finite set
(rng II) \/ (rng (head g)) is non empty finite set
{S} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
((rng II) \/ (rng (head g))) \/ {S} is non empty finite set
(LettersOf u) \ (((rng II) \/ (rng (head g))) \/ {S}) is non empty non trivial non finite V166() Element of bool (AllSymbolsOf u)
(LettersOf u) typed\ (((rng II) \/ (rng (head g))) \/ {S}) is Element of bool (LettersOf u)
(LettersOf u) \ (((rng II) \/ (rng (head g))) \/ {S}) is non empty non trivial non finite V166() Element of bool (LettersOf u)
h is non empty non trivial non finite V166() Element of bool (LettersOf u)
the Element of h is Element of h
Enn is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
En is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff wff exal Element of ((AllSymbolsOf u) *) \ {{}}
Depth En is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
nE is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
nE + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
hhh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff nE + 1 -wff wff exal Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,II,hhh) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth hhh is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(u,S,II,(u,S,II)) . (Depth hhh) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,II,(u,S,II)) . (Depth hhh)) . hhh is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u -firstChar) . hhh is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
head hhh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support nE -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
SubWffsOf hhh is set
K74((SubWffsOf hhh)) is set
c₃₀ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
Depth c₃₀ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
tail hhh is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued AllSymbolsOf u -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllSymbolsOf u) *
K75((SubWffsOf hhh)) is set
phi22 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
(u,phi22,Enn,g) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
g +~ (phi22,Enn) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,phi22,Enn,(head hhh)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support nE -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
(head hhh) +~ (phi22,Enn) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support nE -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth b2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth b2) \+\ (Depth c₃₀) is finite set
(Depth b2) \ (Depth c₃₀) is finite set
(Depth b2) typed\ (Depth c₃₀) is finite Element of bool (Depth b2)
bool (Depth b2) is non empty finite finite-membered set
(Depth b2) \ (Depth c₃₀) is finite Element of bool (Depth b2)
(Depth c₃₀) \ (Depth b2) is finite set
(Depth c₃₀) typed\ (Depth b2) is finite Element of bool (Depth c₃₀)
bool (Depth c₃₀) is non empty finite finite-membered set
(Depth c₃₀) \ (Depth b2) is finite Element of bool (Depth c₃₀)
((Depth b2) \ (Depth c₃₀)) \/ ((Depth c₃₀) \ (Depth b2)) is finite set
(u,S,II,b2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,II,(u,S,II)) . (Depth b2) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,II,(u,S,II)) . (Depth b2)) . b2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*phi22*> is non empty trivial Relation-like NAT -defined TermSymbolsOf u -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf u) *) \ {{}}
[1,phi22] is non empty set
{[1,phi22]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
<*phi22*> ^ c₃₀ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff 1 + (Depth c₃₀) -wff non Depth c₃₀ -wff wff exal Element of ((AllSymbolsOf u) *) \ {{}}
1 + (Depth c₃₀) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
b1 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(<*phi22*> ^ c₃₀) ^ b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(<*phi22*> ^ c₃₀) null b1 is Relation-like NAT -defined b1 \/ (dom (<*phi22*> ^ c₃₀)) -defined b1 \/ (rng (<*phi22*> ^ c₃₀)) -valued Function-like finite len (<*phi22*> ^ c₃₀) -element FinSequence-like FinSubsequence-like finite-support set
dom (<*phi22*> ^ c₃₀) is non empty finite set
b1 \/ (dom (<*phi22*> ^ c₃₀)) is non empty finite set
rng (<*phi22*> ^ c₃₀) is non empty finite set
b1 \/ (rng (<*phi22*> ^ c₃₀)) is non empty finite set
len (<*phi22*> ^ c₃₀) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(<*phi22*> ^ c₃₀) \typed/ b1 is Relation-like NAT -defined finite Element of bool ((<*phi22*> ^ c₃₀) \/ b1)
(<*phi22*> ^ c₃₀) \/ b1 is non empty Relation-like NAT -defined finite set
bool ((<*phi22*> ^ c₃₀) \/ b1) is non empty finite finite-membered set
b1 ^ (<*phi22*> ^ c₃₀) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
c2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth c2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
Depth (head hhh) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
nE - (Depth c₃₀) is finite complex ext-real V40() V41() set
(u,S,II,c₃₀) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,II,(u,S,II)) . (Depth c₃₀) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,II,(u,S,II)) . (Depth c₃₀)) . c₃₀ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
A2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth A2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
hh is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(u,S,II,(u,S,II)) . hh is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
(u,S,II,nE,((u,S,II,(u,S,II)) . hh),hhh) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
<*Enn*> is non empty trivial Relation-like NAT -defined TermSymbolsOf u -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf u) *) \ {{}}
[1,Enn] is non empty set
{[1,Enn]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(u,phi22,Enn,c₃₀) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
c₃₀ +~ (phi22,Enn) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((u,S,II,(u,S,II)) . hh) . (u,phi22,Enn,c₃₀) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*Enn*> ^ (((u,S,II,(u,S,II)) . hh) . (u,phi22,Enn,c₃₀)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*Enn*> ^ (u,S,II,b2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff 1 + (Depth (u,S,II,b2)) -wff non Depth (u,S,II,b2) -wff wff exal Element of ((AllSymbolsOf u) *) \ {{}}
Depth (u,S,II,b2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (Depth (u,S,II,b2)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
Depth (u,S,II,hhh) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth c₃₀) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
t2 is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
t2 -TruthEval (u,S,II,g) is boolean Element of BOOLEAN
t2 -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(t2 -TermEval) . II is Element of U
(S,((t2 -TermEval) . II)) ReassignIn t2 is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> ((t2 -TermEval) . II) is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> ((t2 -TermEval) . II) is non empty Relation-like {{}} -defined U -valued {((t2 -TermEval) . II)} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{((t2 -TermEval) . II)}:]
{((t2 -TermEval) . II)} is non empty trivial finite 1 -element set
[:{{}},{((t2 -TermEval) . II)}:] is non empty Relation-like finite set
bool [:{{}},{((t2 -TermEval) . II)}:] is non empty finite finite-membered set
S .--> ({} .--> ((t2 -TermEval) . II)) is trivial Relation-like AllSymbolsOf u -defined {S} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{S} is non empty trivial finite 1 -element set
{S} --> ({} .--> ((t2 -TermEval) . II)) is non empty Relation-like {S} -defined {({} .--> ((t2 -TermEval) . II))} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{S},{({} .--> ((t2 -TermEval) . II))}:]
{({} .--> ((t2 -TermEval) . II))} is non empty trivial functional finite finite-membered 1 -element set
[:{S},{({} .--> ((t2 -TermEval) . II))}:] is non empty Relation-like finite set
bool [:{S},{({} .--> ((t2 -TermEval) . II))}:] is non empty finite finite-membered set
t2 +* (S .--> ({} .--> ((t2 -TermEval) . II))) is Relation-like Function-like Function-yielding V164() set
((S,((t2 -TermEval) . II)) ReassignIn t2) -TruthEval g is boolean Element of BOOLEAN
t2 -TruthEval (u,S,II,hhh) is boolean Element of BOOLEAN
((S,((t2 -TermEval) . II)) ReassignIn t2) -TruthEval hhh is boolean Element of BOOLEAN
EE1 is Element of U
(Enn,EE1) ReassignIn t2 is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> EE1 is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> EE1 is non empty Relation-like {{}} -defined U -valued {EE1} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{EE1}:]
{EE1} is non empty trivial finite 1 -element set
[:{{}},{EE1}:] is non empty Relation-like finite set
bool [:{{}},{EE1}:] is non empty finite finite-membered set
Enn .--> ({} .--> EE1) is trivial Relation-like AllSymbolsOf u -defined {Enn} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{Enn} is non empty trivial finite 1 -element set
{Enn} --> ({} .--> EE1) is non empty Relation-like {Enn} -defined {({} .--> EE1)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{Enn},{({} .--> EE1)}:]
{({} .--> EE1)} is non empty trivial functional finite finite-membered 1 -element set
[:{Enn},{({} .--> EE1)}:] is non empty Relation-like finite set
bool [:{Enn},{({} .--> EE1)}:] is non empty finite finite-membered set
t2 +* (Enn .--> ({} .--> EE1)) is Relation-like Function-like Function-yielding V164() set
((Enn,EE1) ReassignIn t2) -TruthEval c2 is boolean Element of BOOLEAN
((Enn,EE1) ReassignIn t2) -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
(((Enn,EE1) ReassignIn t2) -TermEval) . II is Element of U
(S,((((Enn,EE1) ReassignIn t2) -TermEval) . II)) ReassignIn ((Enn,EE1) ReassignIn t2) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II) is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> ((((Enn,EE1) ReassignIn t2) -TermEval) . II) is non empty Relation-like {{}} -defined U -valued {((((Enn,EE1) ReassignIn t2) -TermEval) . II)} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{((((Enn,EE1) ReassignIn t2) -TermEval) . II)}:]
{((((Enn,EE1) ReassignIn t2) -TermEval) . II)} is non empty trivial finite 1 -element set
[:{{}},{((((Enn,EE1) ReassignIn t2) -TermEval) . II)}:] is non empty Relation-like finite set
bool [:{{}},{((((Enn,EE1) ReassignIn t2) -TermEval) . II)}:] is non empty finite finite-membered set
S .--> ({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II)) is trivial Relation-like AllSymbolsOf u -defined {S} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{S} --> ({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II)) is non empty Relation-like {S} -defined {({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II))} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{S},{({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II))}:]
{({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II))} is non empty trivial functional finite finite-membered 1 -element set
[:{S},{({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II))}:] is non empty Relation-like finite set
bool [:{S},{({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II))}:] is non empty finite finite-membered set
((Enn,EE1) ReassignIn t2) +* (S .--> ({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II))) is Relation-like Function-like Function-yielding V164() set
((S,((((Enn,EE1) ReassignIn t2) -TermEval) . II)) ReassignIn ((Enn,EE1) ReassignIn t2)) -TruthEval b2 is boolean Element of BOOLEAN
(S,((t2 -TermEval) . II)) ReassignIn ((Enn,EE1) ReassignIn t2) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
((Enn,EE1) ReassignIn t2) +* (S .--> ({} .--> ((t2 -TermEval) . II))) is Relation-like Function-like Function-yielding V164() set
((S,((t2 -TermEval) . II)) ReassignIn ((Enn,EE1) ReassignIn t2)) -TruthEval b2 is boolean Element of BOOLEAN
(Enn,EE1) ReassignIn ((S,((t2 -TermEval) . II)) ReassignIn t2) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
((S,((t2 -TermEval) . II)) ReassignIn t2) +* (Enn .--> ({} .--> EE1)) is Relation-like Function-like Function-yielding V164() set
((Enn,EE1) ReassignIn ((S,((t2 -TermEval) . II)) ReassignIn t2)) -TruthEval b2 is boolean Element of BOOLEAN
(phi22,EE1) ReassignIn ((S,((t2 -TermEval) . II)) ReassignIn t2) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
phi22 .--> ({} .--> EE1) is trivial Relation-like AllSymbolsOf u -defined {phi22} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{phi22} is non empty trivial finite 1 -element set
{phi22} --> ({} .--> EE1) is non empty Relation-like {phi22} -defined {({} .--> EE1)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{phi22},{({} .--> EE1)}:]
[:{phi22},{({} .--> EE1)}:] is non empty Relation-like finite set
bool [:{phi22},{({} .--> EE1)}:] is non empty finite finite-membered set
((S,((t2 -TermEval) . II)) ReassignIn t2) +* (phi22 .--> ({} .--> EE1)) is Relation-like Function-like Function-yielding V164() set
((phi22,EE1) ReassignIn ((S,((t2 -TermEval) . II)) ReassignIn t2)) -TruthEval (head hhh) is boolean Element of BOOLEAN
EE1 is Element of U
(phi22,EE1) ReassignIn ((S,((t2 -TermEval) . II)) ReassignIn t2) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> EE1 is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> EE1 is non empty Relation-like {{}} -defined U -valued {EE1} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{EE1}:]
{EE1} is non empty trivial finite 1 -element set
[:{{}},{EE1}:] is non empty Relation-like finite set
bool [:{{}},{EE1}:] is non empty finite finite-membered set
phi22 .--> ({} .--> EE1) is trivial Relation-like AllSymbolsOf u -defined {phi22} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{phi22} --> ({} .--> EE1) is non empty Relation-like {phi22} -defined {({} .--> EE1)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{phi22},{({} .--> EE1)}:]
{({} .--> EE1)} is non empty trivial functional finite finite-membered 1 -element set
[:{phi22},{({} .--> EE1)}:] is non empty Relation-like finite set
bool [:{phi22},{({} .--> EE1)}:] is non empty finite finite-membered set
((S,((t2 -TermEval) . II)) ReassignIn t2) +* (phi22 .--> ({} .--> EE1)) is Relation-like Function-like Function-yielding V164() set
((phi22,EE1) ReassignIn ((S,((t2 -TermEval) . II)) ReassignIn t2)) -TruthEval (head hhh) is boolean Element of BOOLEAN
(Enn,EE1) ReassignIn ((S,((t2 -TermEval) . II)) ReassignIn t2) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
Enn .--> ({} .--> EE1) is trivial Relation-like AllSymbolsOf u -defined {Enn} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{Enn} --> ({} .--> EE1) is non empty Relation-like {Enn} -defined {({} .--> EE1)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{Enn},{({} .--> EE1)}:]
[:{Enn},{({} .--> EE1)}:] is non empty Relation-like finite set
bool [:{Enn},{({} .--> EE1)}:] is non empty finite finite-membered set
((S,((t2 -TermEval) . II)) ReassignIn t2) +* (Enn .--> ({} .--> EE1)) is Relation-like Function-like Function-yielding V164() set
((Enn,EE1) ReassignIn ((S,((t2 -TermEval) . II)) ReassignIn t2)) -TruthEval b2 is boolean Element of BOOLEAN
(Enn,EE1) ReassignIn t2 is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
t2 +* (Enn .--> ({} .--> EE1)) is Relation-like Function-like Function-yielding V164() set
(S,((t2 -TermEval) . II)) ReassignIn ((Enn,EE1) ReassignIn t2) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
((Enn,EE1) ReassignIn t2) +* (S .--> ({} .--> ((t2 -TermEval) . II))) is Relation-like Function-like Function-yielding V164() set
((S,((t2 -TermEval) . II)) ReassignIn ((Enn,EE1) ReassignIn t2)) -TruthEval b2 is boolean Element of BOOLEAN
((Enn,EE1) ReassignIn t2) -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
(((Enn,EE1) ReassignIn t2) -TermEval) . II is Element of U
(S,((((Enn,EE1) ReassignIn t2) -TermEval) . II)) ReassignIn ((Enn,EE1) ReassignIn t2) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II) is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> ((((Enn,EE1) ReassignIn t2) -TermEval) . II) is non empty Relation-like {{}} -defined U -valued {((((Enn,EE1) ReassignIn t2) -TermEval) . II)} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{((((Enn,EE1) ReassignIn t2) -TermEval) . II)}:]
{((((Enn,EE1) ReassignIn t2) -TermEval) . II)} is non empty trivial finite 1 -element set
[:{{}},{((((Enn,EE1) ReassignIn t2) -TermEval) . II)}:] is non empty Relation-like finite set
bool [:{{}},{((((Enn,EE1) ReassignIn t2) -TermEval) . II)}:] is non empty finite finite-membered set
S .--> ({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II)) is trivial Relation-like AllSymbolsOf u -defined {S} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{S} --> ({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II)) is non empty Relation-like {S} -defined {({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II))} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{S},{({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II))}:]
{({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II))} is non empty trivial functional finite finite-membered 1 -element set
[:{S},{({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II))}:] is non empty Relation-like finite set
bool [:{S},{({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II))}:] is non empty finite finite-membered set
((Enn,EE1) ReassignIn t2) +* (S .--> ({} .--> ((((Enn,EE1) ReassignIn t2) -TermEval) . II))) is Relation-like Function-like Function-yielding V164() set
((S,((((Enn,EE1) ReassignIn t2) -TermEval) . II)) ReassignIn ((Enn,EE1) ReassignIn t2)) -TruthEval b2 is boolean Element of BOOLEAN
((Enn,EE1) ReassignIn t2) -TruthEval c2 is boolean Element of BOOLEAN
t2 is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
t2 -TruthEval (u,S,II,g) is boolean Element of BOOLEAN
t2 -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(t2 -TermEval) . II is Element of U
(S,((t2 -TermEval) . II)) ReassignIn t2 is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> ((t2 -TermEval) . II) is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> ((t2 -TermEval) . II) is non empty Relation-like {{}} -defined U -valued {((t2 -TermEval) . II)} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{((t2 -TermEval) . II)}:]
{((t2 -TermEval) . II)} is non empty trivial finite 1 -element set
[:{{}},{((t2 -TermEval) . II)}:] is non empty Relation-like finite set
bool [:{{}},{((t2 -TermEval) . II)}:] is non empty finite finite-membered set
S .--> ({} .--> ((t2 -TermEval) . II)) is trivial Relation-like AllSymbolsOf u -defined {S} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{S} is non empty trivial finite 1 -element set
{S} --> ({} .--> ((t2 -TermEval) . II)) is non empty Relation-like {S} -defined {({} .--> ((t2 -TermEval) . II))} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{S},{({} .--> ((t2 -TermEval) . II))}:]
{({} .--> ((t2 -TermEval) . II))} is non empty trivial functional finite finite-membered 1 -element set
[:{S},{({} .--> ((t2 -TermEval) . II))}:] is non empty Relation-like finite set
bool [:{S},{({} .--> ((t2 -TermEval) . II))}:] is non empty finite finite-membered set
t2 +* (S .--> ({} .--> ((t2 -TermEval) . II))) is Relation-like Function-like Function-yielding V164() set
((S,((t2 -TermEval) . II)) ReassignIn t2) -TruthEval g is boolean Element of BOOLEAN
((S,((t2 -TermEval) . II)) ReassignIn t2) -TruthEval hhh is boolean Element of BOOLEAN
t2 -TruthEval hhh is boolean Element of BOOLEAN
EE1 is Element of U
(phi22,EE1) ReassignIn ((S,((t2 -TermEval) . II)) ReassignIn t2) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> EE1 is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> EE1 is non empty Relation-like {{}} -defined U -valued {EE1} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{EE1}:]
{EE1} is non empty trivial finite 1 -element set
[:{{}},{EE1}:] is non empty Relation-like finite set
bool [:{{}},{EE1}:] is non empty finite finite-membered set
phi22 .--> ({} .--> EE1) is trivial Relation-like AllSymbolsOf u -defined {phi22} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{phi22} is non empty trivial finite 1 -element set
{phi22} --> ({} .--> EE1) is non empty Relation-like {phi22} -defined {({} .--> EE1)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{phi22},{({} .--> EE1)}:]
{({} .--> EE1)} is non empty trivial functional finite finite-membered 1 -element set
[:{phi22},{({} .--> EE1)}:] is non empty Relation-like finite set
bool [:{phi22},{({} .--> EE1)}:] is non empty finite finite-membered set
((S,((t2 -TermEval) . II)) ReassignIn t2) +* (phi22 .--> ({} .--> EE1)) is Relation-like Function-like Function-yielding V164() set
((phi22,EE1) ReassignIn ((S,((t2 -TermEval) . II)) ReassignIn t2)) -TruthEval c₃₀ is boolean Element of BOOLEAN
(phi22,EE1) ReassignIn t2 is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
t2 +* (phi22 .--> ({} .--> EE1)) is Relation-like Function-like Function-yielding V164() set
((phi22,EE1) ReassignIn t2) -TruthEval c₃₀ is boolean Element of BOOLEAN
EE1 is Element of U
(phi22,EE1) ReassignIn t2 is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> EE1 is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> EE1 is non empty Relation-like {{}} -defined U -valued {EE1} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{EE1}:]
{EE1} is non empty trivial finite 1 -element set
[:{{}},{EE1}:] is non empty Relation-like finite set
bool [:{{}},{EE1}:] is non empty finite finite-membered set
phi22 .--> ({} .--> EE1) is trivial Relation-like AllSymbolsOf u -defined {phi22} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{phi22} --> ({} .--> EE1) is non empty Relation-like {phi22} -defined {({} .--> EE1)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{phi22},{({} .--> EE1)}:]
{({} .--> EE1)} is non empty trivial functional finite finite-membered 1 -element set
[:{phi22},{({} .--> EE1)}:] is non empty Relation-like finite set
bool [:{phi22},{({} .--> EE1)}:] is non empty finite finite-membered set
t2 +* (phi22 .--> ({} .--> EE1)) is Relation-like Function-like Function-yielding V164() set
((phi22,EE1) ReassignIn t2) -TruthEval c₃₀ is boolean Element of BOOLEAN
(phi22,EE1) ReassignIn ((S,((t2 -TermEval) . II)) ReassignIn t2) is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
((S,((t2 -TermEval) . II)) ReassignIn t2) +* (phi22 .--> ({} .--> EE1)) is Relation-like Function-like Function-yielding V164() set
((phi22,EE1) ReassignIn ((S,((t2 -TermEval) . II)) ReassignIn t2)) -TruthEval c₃₀ is boolean Element of BOOLEAN
t2 -TruthEval g is boolean Element of BOOLEAN
En is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff wff non exal Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,II,En) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth En is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() set
(u,S,II,(u,S,II)) . (Depth En) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,II,(u,S,II)) . (Depth En)) . En is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
hhh is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
hhh + 1 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 complex ext-real non positive negative V40() V41() set
(hhh + 1) + (- 1) is finite complex ext-real V40() V41() set
(jJ + 1) - 1 is finite complex ext-real V40() V41() set
ss is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff hhh + 1 -wff wff non exal Element of ((AllSymbolsOf u) *) \ {{}}
head ss is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support hhh -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
SubWffsOf ss is set
K74((SubWffsOf ss)) is set
tail ss is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support hhh -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
K75((SubWffsOf ss)) is set
phi22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
Depth phi22 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
c₃₀ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of AllFormulasOf u
Depth c₃₀ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u -firstChar) . ss is non relational Element of AllSymbolsOf u
((u -firstChar) . ss) \+\ (TheNorSymbOf u) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
((u -firstChar) . ss) \ (TheNorSymbOf u) is set
((u -firstChar) . ss) typed\ (TheNorSymbOf u) is Element of bool ((u -firstChar) . ss)
bool ((u -firstChar) . ss) is non empty set
((u -firstChar) . ss) \ (TheNorSymbOf u) is Element of bool ((u -firstChar) . ss)
(TheNorSymbOf u) \ ((u -firstChar) . ss) is set
(TheNorSymbOf u) typed\ ((u -firstChar) . ss) is Element of bool (TheNorSymbOf u)
bool (TheNorSymbOf u) is non empty set
(TheNorSymbOf u) \ ((u -firstChar) . ss) is Element of bool (TheNorSymbOf u)
(((u -firstChar) . ss) \ (TheNorSymbOf u)) \/ ((TheNorSymbOf u) \ ((u -firstChar) . ss)) is set
<*((u -firstChar) . ss)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
[1,((u -firstChar) . ss)] is non empty set
{[1,((u -firstChar) . ss)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
<*((u -firstChar) . ss)*> ^ phi22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff Element of ((AllSymbolsOf u) *) \ {{}}
(<*((u -firstChar) . ss)*> ^ phi22) ^ c₃₀ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff Element of ((AllSymbolsOf u) *) \ {{}}
<*(TheNorSymbOf u)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
[1,(TheNorSymbOf u)] is non empty set
{[1,(TheNorSymbOf u)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
<*(TheNorSymbOf u)*> ^ phi22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non exal Element of ((AllSymbolsOf u) *) \ {{}}
(<*(TheNorSymbOf u)*> ^ phi22) ^ c₃₀ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non max ((Depth phi22),(Depth c₃₀)) -wff wff non exal Element of ((AllSymbolsOf u) *) \ {{}}
max ((Depth phi22),(Depth c₃₀)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
hhh - (Depth phi22) is finite complex ext-real V40() V41() set
hhh - (Depth c₃₀) is finite complex ext-real V40() V41() set
(u,S,II,phi22) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,II,(u,S,II)) . (Depth phi22) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,II,(u,S,II)) . (Depth phi22)) . phi22 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,S,II,c₃₀) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,II,(u,S,II)) . (Depth c₃₀) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,II,(u,S,II)) . (Depth c₃₀)) . c₃₀ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
c2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth c2 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 finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
Depth A1 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() Element of NAT
(u,S,II,(u,S,II)) . s is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
(u,S,II,hhh,((u,S,II,(u,S,II)) . s),ss) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
c1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth phi22) + c1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u,S,II,(u,S,II)) . ((Depth phi22) + c1) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,II,(u,S,II)) . ((Depth phi22) + c1)) . phi22 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*(TheNorSymbOf u)*> ^ (((u,S,II,(u,S,II)) . ((Depth phi22) + c1)) . phi22) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
b2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth c₃₀) + b2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u,S,II,(u,S,II)) . ((Depth c₃₀) + b2) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,II,(u,S,II)) . ((Depth c₃₀) + b2)) . c₃₀ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(<*(TheNorSymbOf u)*> ^ (((u,S,II,(u,S,II)) . ((Depth phi22) + c1)) . phi22)) ^ (((u,S,II,(u,S,II)) . ((Depth c₃₀) + b2)) . c₃₀) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*(TheNorSymbOf u)*> ^ c2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non exal Element of ((AllSymbolsOf u) *) \ {{}}
(<*(TheNorSymbOf u)*> ^ c2) ^ (((u,S,II,(u,S,II)) . ((Depth c₃₀) + b2)) . c₃₀) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(<*(TheNorSymbOf u)*> ^ c2) ^ A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non max ((Depth c2),(Depth A1)) -wff wff non exal Element of ((AllSymbolsOf u) *) \ {{}}
max ((Depth c2),(Depth A1)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
Depth (u,S,II,En) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (max ((Depth c2),(Depth A1))) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
max ((Depth phi22),(Depth A1)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (max ((Depth phi22),(Depth A1))) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
1 + (max ((Depth phi22),(Depth c₃₀))) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
t2 is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
t2 -TruthEval (u,S,II,g) is boolean Element of BOOLEAN
t2 -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(t2 -TermEval) . II is Element of U
(S,((t2 -TermEval) . II)) ReassignIn t2 is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> ((t2 -TermEval) . II) is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> ((t2 -TermEval) . II) is non empty Relation-like {{}} -defined U -valued {((t2 -TermEval) . II)} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{((t2 -TermEval) . II)}:]
{((t2 -TermEval) . II)} is non empty trivial finite 1 -element set
[:{{}},{((t2 -TermEval) . II)}:] is non empty Relation-like finite set
bool [:{{}},{((t2 -TermEval) . II)}:] is non empty finite finite-membered set
S .--> ({} .--> ((t2 -TermEval) . II)) is trivial Relation-like AllSymbolsOf u -defined {S} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{S} is non empty trivial finite 1 -element set
{S} --> ({} .--> ((t2 -TermEval) . II)) is non empty Relation-like {S} -defined {({} .--> ((t2 -TermEval) . II))} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{S},{({} .--> ((t2 -TermEval) . II))}:]
{({} .--> ((t2 -TermEval) . II))} is non empty trivial functional finite finite-membered 1 -element set
[:{S},{({} .--> ((t2 -TermEval) . II))}:] is non empty Relation-like finite set
bool [:{S},{({} .--> ((t2 -TermEval) . II))}:] is non empty finite finite-membered set
t2 +* (S .--> ({} .--> ((t2 -TermEval) . II))) is Relation-like Function-like Function-yielding V164() set
((S,((t2 -TermEval) . II)) ReassignIn t2) -TruthEval g is boolean Element of BOOLEAN
t2 -TruthEval (u,S,II,En) is boolean Element of BOOLEAN
((S,((t2 -TermEval) . II)) ReassignIn t2) -TruthEval ss is boolean Element of BOOLEAN
t2 -TruthEval c2 is boolean Element of BOOLEAN
((S,((t2 -TermEval) . II)) ReassignIn t2) -TruthEval phi22 is boolean Element of BOOLEAN
t2 -TruthEval A1 is boolean Element of BOOLEAN
((S,((t2 -TermEval) . II)) ReassignIn t2) -TruthEval c₃₀ is boolean Element of BOOLEAN
En is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
En -TruthEval (u,S,II,g) is boolean Element of BOOLEAN
En -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(En -TermEval) . II is Element of U
(S,((En -TermEval) . II)) ReassignIn En is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> ((En -TermEval) . II) is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> ((En -TermEval) . II) is non empty Relation-like {{}} -defined U -valued {((En -TermEval) . II)} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{((En -TermEval) . II)}:]
{((En -TermEval) . II)} is non empty trivial finite 1 -element set
[:{{}},{((En -TermEval) . II)}:] is non empty Relation-like finite set
bool [:{{}},{((En -TermEval) . II)}:] is non empty finite finite-membered set
S .--> ({} .--> ((En -TermEval) . II)) is trivial Relation-like AllSymbolsOf u -defined {S} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{S} is non empty trivial finite 1 -element set
{S} --> ({} .--> ((En -TermEval) . II)) is non empty Relation-like {S} -defined {({} .--> ((En -TermEval) . II))} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{S},{({} .--> ((En -TermEval) . II))}:]
{({} .--> ((En -TermEval) . II))} is non empty trivial functional finite finite-membered 1 -element set
[:{S},{({} .--> ((En -TermEval) . II))}:] is non empty Relation-like finite set
bool [:{S},{({} .--> ((En -TermEval) . II))}:] is non empty finite finite-membered set
En +* (S .--> ({} .--> ((En -TermEval) . II))) is Relation-like Function-like Function-yielding V164() set
((S,((En -TermEval) . II)) ReassignIn En) -TruthEval g is boolean Element of BOOLEAN
g is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
g -TruthEval (u,S,II,l) is boolean Element of BOOLEAN
g -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(g -TermEval) . II is Element of U
(S,((g -TermEval) . II)) ReassignIn g is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> ((g -TermEval) . II) is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> ((g -TermEval) . II) is non empty Relation-like {{}} -defined U -valued {((g -TermEval) . II)} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{((g -TermEval) . II)}:]
{((g -TermEval) . II)} is non empty trivial finite 1 -element set
[:{{}},{((g -TermEval) . II)}:] is non empty Relation-like finite set
bool [:{{}},{((g -TermEval) . II)}:] is non empty finite finite-membered set
S .--> ({} .--> ((g -TermEval) . II)) is trivial Relation-like AllSymbolsOf u -defined {S} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{S} is non empty trivial finite 1 -element set
{S} --> ({} .--> ((g -TermEval) . II)) is non empty Relation-like {S} -defined {({} .--> ((g -TermEval) . II))} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{S},{({} .--> ((g -TermEval) . II))}:]
{({} .--> ((g -TermEval) . II))} is non empty trivial functional finite finite-membered 1 -element set
[:{S},{({} .--> ((g -TermEval) . II))}:] is non empty Relation-like finite set
bool [:{S},{({} .--> ((g -TermEval) . II))}:] is non empty finite finite-membered set
g +* (S .--> ({} .--> ((g -TermEval) . II))) is Relation-like Function-like Function-yielding V164() set
((S,((g -TermEval) . II)) ReassignIn g) -TruthEval l is boolean Element of BOOLEAN
u is V51() V53() eligible Language-like
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
TermSymbolsOf u is non empty set
the U3 of u is Element of the U1 of u
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
AllSymbolsOf u is non empty non trivial non finite V166() set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
U is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
l is non empty Relation-like NAT -defined TermSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf u) *) \ {{}}
II is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support U -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,l,II) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
AllFormulasOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of bool (((AllSymbolsOf u) *) \ {{}})
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}} : ex b₂ being epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set st b₁ is b₂ -wff } is set
Funcs ((AllFormulasOf u),(AllFormulasOf u)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf u, AllFormulasOf u
(u,S,l) is Relation-like AllFormulasOf u -defined AllFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
id (AllFormulasOf u) is non empty Relation-like non empty-yielding AllFormulasOf u -defined AllFormulasOf u -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(AllFormulasOf u),(AllFormulasOf u):]
[:(AllFormulasOf u),(AllFormulasOf u):] is non empty Relation-like set
bool [:(AllFormulasOf u),(AllFormulasOf u):] is non empty set
(u,S,l) is non empty Relation-like non empty-yielding AtomicFormulasOf u -defined AtomicFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf u),(AtomicFormulasOf u):]
AtomicFormulasOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of bool (((AllSymbolsOf u) *) \ {{}})
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}} : b₁ is 0wff } is set
[:(AtomicFormulasOf u),(AtomicFormulasOf u):] is non empty Relation-like set
bool [:(AtomicFormulasOf u),(AtomicFormulasOf u):] is non empty set
(id (AllFormulasOf u)) +* (u,S,l) is non empty Relation-like Function-like Function-yielding V164() set
(u,S,l,(u,S,l)) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf u),(AllFormulasOf u)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):]
[:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):] is non empty non trivial non finite V166() set
Depth II is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(u,S,l,(u,S,l)) . (Depth II) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,l,(u,S,l)) . (Depth II)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
x is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of AllTermsOf u
(u,S,x,II) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
(u,S,x) is Relation-like AllFormulasOf u -defined AllFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
(u,S,x) is non empty Relation-like non empty-yielding AtomicFormulasOf u -defined AtomicFormulasOf u -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(AtomicFormulasOf u),(AtomicFormulasOf u):]
(id (AllFormulasOf u)) +* (u,S,x) is non empty Relation-like Function-like Function-yielding V164() set
(u,S,x,(u,S,x)) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf u),(AllFormulasOf u)) -valued Function-like total quasi_total Function-yielding V164() Element of bool [:NAT,(Funcs ((AllFormulasOf u),(AllFormulasOf u))):]
(u,S,x,(u,S,x)) . (Depth II) is Relation-like Function-like Function-yielding V164() FinSequence-yielding Element of Funcs ((AllFormulasOf u),(AllFormulasOf u))
((u,S,x,(u,S,x)) . (Depth II)) . II is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
U - (Depth II) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
Depth (u,S,x,II) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
UU is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
0 * UU 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(Depth II) + (0 * UU) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
III is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Depth II -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
(Depth II) + UU is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
U is set
U * is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
u is non empty set
u * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of u
u \/ BOOLEAN is non empty set
K546((u *),(u \/ BOOLEAN)) is non empty functional M31(u * ,u \/ 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 V166() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V166() 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
Funcs ((OwnSymbolsOf S),K546((u *),(u \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S,K546((u *),(u \/ BOOLEAN))
u -InterpretersOf S is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),K546((u *),(u \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf S),K546((u *),(u \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined K546((u *),(u \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),K546((u *),(u \/ BOOLEAN))) : b₁ is S,u -interpreter-like } is 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 V166() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V166() set
the adicity of S | U is Relation-like U -defined the U1 of S \ { the U3 of S} -defined INT -valued Function-like Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
AllTermsOf S is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() set
S -termsOfMaxDepth is Relation-like Function-like set
rng (S -termsOfMaxDepth) is set
union (rng (S -termsOfMaxDepth)) is set
l is V51() V53() eligible Language-like
OwnSymbolsOf l is non empty Element of bool (AllSymbolsOf l)
AllSymbolsOf l is non empty non trivial non finite V166() set
the U1 of l is set
bool (AllSymbolsOf l) is non empty non trivial non finite V166() set
the U2 of l is Element of the U1 of l
the U3 of l is Element of the U1 of l
{ the U2 of l, the U3 of l} is non empty finite set
the U1 of l \ { the U2 of l, the U3 of l} is Element of bool the U1 of l
bool the U1 of l is non empty set
the U1 of l typed\ { the U2 of l, the U3 of l} is Element of bool the U1 of l
Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf l,K546((u *),(u \/ BOOLEAN))
u -InterpretersOf l is non empty functional Element of bool (Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf l -defined K546((u *),(u \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN))) : b₁ is l,u -interpreter-like } is set
{ the U3 of l} is non empty trivial finite 1 -element set
the U1 of l \ { the U3 of l} is non empty Element of bool the U1 of l
the U1 of l typed\ { the U3 of l} is Element of bool the U1 of l
the adicity of l is non empty Relation-like the U1 of l \ { the U3 of l} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of l \ { the U3 of l}),INT:]
[:( the U1 of l \ { the U3 of l}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of l \ { the U3 of l}),INT:] is non empty non trivial non finite V166() set
the adicity of l | U is Relation-like U -defined the U1 of l \ { the U3 of l} -defined INT -valued Function-like Element of bool [:( the U1 of l \ { the U3 of l}),INT:]
AllTermsOf l is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
(AllSymbolsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf l
((AllSymbolsOf l) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf l) *)
bool ((AllSymbolsOf l) *) is non empty non trivial non finite V166() set
((AllSymbolsOf l) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
bool (((AllSymbolsOf l) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf l) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf l) *) \ {{}}))
bool (bool (((AllSymbolsOf l) *) \ {{}})) is non empty non trivial non finite V166() set
l -termsOfMaxDepth is Relation-like Function-like set
rng (l -termsOfMaxDepth) is set
union (rng (l -termsOfMaxDepth)) is set
S -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf S) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf S) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf S) *) \ {{}})):] is non empty non trivial non finite V166() set
AllSymbolsOf S is non empty non trivial non finite V166() set
LettersOf S is non empty non trivial non finite V166() Element of bool (AllSymbolsOf S)
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 V166() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V166() 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 V233( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V166() set
K415((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() FinSequence-yielding Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
((AllSymbolsOf S) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf S) *
[:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf S) -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
(AllSymbolsOf S) -concatenation is non empty Relation-like [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf S) * ) Element of bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):]
[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf S) -concatenation) is non empty Relation-like (((AllSymbolsOf S) *) *) \ {{}} -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):]
(((AllSymbolsOf S) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf S) *) *)
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf S) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf S) *) *)
[:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf S) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
AtomicTermsOf S is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
LettersOf S is non empty non trivial non finite V166() set
1 -tuples_on (LettersOf S) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of LettersOf S
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
l -termsOfMaxDepth is non empty Relation-like NAT -defined K335((((AllSymbolsOf l) *) \ {{}})) -valued Function-like total quasi_total Element of bool [:NAT,K335((((AllSymbolsOf l) *) \ {{}})):]
[:NAT,K335((((AllSymbolsOf l) *) \ {{}})):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335((((AllSymbolsOf l) *) \ {{}})):] is non empty non trivial non finite V166() set
AllSymbolsOf l is non empty non trivial non finite V166() set
LettersOf l is non empty non trivial non finite V166() Element of bool (AllSymbolsOf l)
the adicity of l " {0} is Element of bool ( the U1 of l \ { the U3 of l})
bool ( the U1 of l \ { the U3 of l}) is non empty set
l -firstChar is non empty Relation-like ((AllSymbolsOf l) *) \ {{}} -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):]
[:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):] is non empty non trivial non finite V166() set
(AllSymbolsOf l) -firstChar is non empty Relation-like ((AllSymbolsOf l) *) \ {{}} -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):]
(AllSymbolsOf l) -pr1 is non empty Relation-like [:(AllSymbolsOf l),(AllSymbolsOf l):] -defined AllSymbolsOf l -valued Function-like total quasi_total V233( AllSymbolsOf l) Element of bool [:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):]
[:(AllSymbolsOf l),(AllSymbolsOf l):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf l),(AllSymbolsOf l)) is non empty Relation-like [:(AllSymbolsOf l),(AllSymbolsOf l):] -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf l),(AllSymbolsOf l):],(AllSymbolsOf l):]
MultPlace ((AllSymbolsOf l) -pr1) is non empty Relation-like ((AllSymbolsOf l) *) \ {{}} -defined AllSymbolsOf l -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf l) *) \ {{}}),(AllSymbolsOf l):]
l -multiCat is non empty Relation-like ((AllSymbolsOf l) *) * -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf l) *) *),((AllSymbolsOf l) *):]
((AllSymbolsOf l) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf l) *
[:(((AllSymbolsOf l) *) *),((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf l) *) *),((AllSymbolsOf l) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf l) -multiCat is non empty Relation-like ((AllSymbolsOf l) *) * -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf l) *) *),((AllSymbolsOf l) *):]
(AllSymbolsOf l) -concatenation is non empty Relation-like [:((AllSymbolsOf l) *),((AllSymbolsOf l) *):] -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf l) * ) Element of bool [:[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):],((AllSymbolsOf l) *):]
[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):],((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf l) *),((AllSymbolsOf l) *):],((AllSymbolsOf l) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf l) -concatenation) is non empty Relation-like (((AllSymbolsOf l) *) *) \ {{}} -defined (AllSymbolsOf l) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf l) *) *) \ {{}}),((AllSymbolsOf l) *):]
(((AllSymbolsOf l) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf l) *) *)
bool (((AllSymbolsOf l) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf l) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf l) *) *)
[:((((AllSymbolsOf l) *) *) \ {{}}),((AllSymbolsOf l) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf l) *) *) \ {{}}),((AllSymbolsOf l) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf l) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
AtomicTermsOf l is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
LettersOf l is non empty non trivial non finite V166() set
1 -tuples_on (LettersOf l) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of LettersOf l
(AllSymbolsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf l
((AllSymbolsOf l) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf l) *)
bool ((AllSymbolsOf l) *) is non empty non trivial non finite V166() set
((AllSymbolsOf l) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
s is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,u -interpreter-like Element of u -InterpretersOf S
s | U is Relation-like U -defined OwnSymbolsOf S -defined Function-like Function-yielding V164() set
s -TermEval is non empty Relation-like AllTermsOf S -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),u:]
[:(AllTermsOf S),u:] is non empty Relation-like set
bool [:(AllTermsOf S),u:] is non empty set
(s -TermEval) | (U *) is Relation-like U * -defined AllTermsOf S -defined u -valued Function-like Element of bool [:(AllTermsOf S),u:]
ss is Relation-like OwnSymbolsOf l -defined Function-like total Function-yielding V164() l,u -interpreter-like Element of u -InterpretersOf l
ss | U is Relation-like U -defined OwnSymbolsOf l -defined Function-like Function-yielding V164() set
ss -TermEval is non empty Relation-like AllTermsOf l -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),u:]
[:(AllTermsOf l),u:] is non empty Relation-like set
bool [:(AllTermsOf l),u:] is non empty set
(ss -TermEval) | (U *) is Relation-like U * -defined AllTermsOf l -defined u -valued Function-like Element of bool [:(AllTermsOf l),u:]
dom s is Element of bool (OwnSymbolsOf S)
bool (OwnSymbolsOf S) is non empty set
dom ss is Element of bool (OwnSymbolsOf l)
bool (OwnSymbolsOf l) is non empty set
dom (s -TermEval) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf S)
bool (AllTermsOf S) is non empty set
dom (ss -TermEval) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf l)
bool (AllTermsOf l) is non empty set
U /\ (dom s) is Element of bool (OwnSymbolsOf S)
U typed/\ (dom s) is Element of bool U
bool U is non empty set
U /\ (dom s) is set
U /\typed (dom s) is Element of bool (dom s)
bool (dom s) is non empty set
dom (ss | U) is Element of bool U
U /\ (dom ss) is Element of bool (OwnSymbolsOf l)
U typed/\ (dom ss) is Element of bool U
U /\ (dom ss) is set
U /\typed (dom ss) is Element of bool (dom ss)
bool (dom ss) is non empty set
{ <*b₁*> where b₁ is Element of a₁ : verum } is set
(S -termsOfMaxDepth) . 0 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
(U *) /\ ((S -termsOfMaxDepth) . 0) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf S) *) \ {{}})
(U *) typed/\ ((S -termsOfMaxDepth) . 0) is functional finite-membered FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
(U *) /\ ((S -termsOfMaxDepth) . 0) is functional set
(U *) /\typed ((S -termsOfMaxDepth) . 0) is functional finite-membered FinSequence-membered V165() Element of bool ((S -termsOfMaxDepth) . 0)
bool ((S -termsOfMaxDepth) . 0) is non empty set
(s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0)) is Relation-like AllTermsOf S -defined (U *) /\ ((S -termsOfMaxDepth) . 0) -defined AllTermsOf S -defined u -valued Function-like Element of bool [:(AllTermsOf S),u:]
(l -termsOfMaxDepth) . 0 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
(U *) /\ ((l -termsOfMaxDepth) . 0) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf l) *) \ {{}})
(U *) typed/\ ((l -termsOfMaxDepth) . 0) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ ((l -termsOfMaxDepth) . 0) is functional set
(U *) /\typed ((l -termsOfMaxDepth) . 0) is functional finite-membered FinSequence-membered V165() Element of bool ((l -termsOfMaxDepth) . 0)
bool ((l -termsOfMaxDepth) . 0) is non empty set
(ss -TermEval) | ((U *) /\ ((l -termsOfMaxDepth) . 0)) is Relation-like AllTermsOf l -defined (U *) /\ ((l -termsOfMaxDepth) . 0) -defined AllTermsOf l -defined u -valued Function-like Element of bool [:(AllTermsOf l),u:]
c1 is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
(s -TermEval) | c1 is Relation-like AllTermsOf S -defined c1 -defined AllTermsOf S -defined u -valued Function-like total Element of bool [:(AllTermsOf S),u:]
b2 is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf l)
(ss -TermEval) | b2 is Relation-like AllTermsOf l -defined b2 -defined AllTermsOf l -defined u -valued Function-like total Element of bool [:(AllTermsOf l),u:]
dom ((s -TermEval) | c1) is functional finite-membered FinSequence-membered V165() Element of bool c1
bool c1 is non empty set
dom ((ss -TermEval) | b2) is functional finite-membered FinSequence-membered V165() Element of bool b2
bool b2 is non empty set
A2 is set
(U *) /\ (AtomicTermsOf S) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
(U *) typed/\ (AtomicTermsOf S) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ (AtomicTermsOf S) is functional set
(U *) /\typed (AtomicTermsOf S) is functional finite-membered FinSequence-membered Element of bool (AtomicTermsOf S)
bool (AtomicTermsOf S) is non empty set
U /\ (LettersOf S) is Element of bool (AllSymbolsOf S)
U typed/\ (LettersOf S) is Element of bool U
U /\ (LettersOf S) is set
U /\typed (LettersOf S) is Element of bool (LettersOf S)
bool (LettersOf S) is non empty non trivial non finite V166() set
1 -tuples_on (U /\ (LettersOf S)) is functional finite-membered FinSequence-membered FinSequenceSet of U /\ (LettersOf S)
X1 is non empty set
{ <*b₁*> where b₁ is Element of X1 : verum } is set
E11 is Element of X1
<*E11*> is non empty trivial Relation-like NAT -defined X1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support FinSequence of X1
[1,E11] is non empty set
{[1,E11]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
EE1 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
U /\ (OwnSymbolsOf l) is Element of bool (AllSymbolsOf l)
U typed/\ (OwnSymbolsOf l) is Element of bool U
U /\ (OwnSymbolsOf l) is set
U /\typed (OwnSymbolsOf l) is Element of bool (OwnSymbolsOf l)
t2 is non empty set
E22 is own ofAtomicFormula Element of AllSymbolsOf l
ss | t2 is Relation-like t2 -defined OwnSymbolsOf l -defined Function-like Function-yielding V164() set
EE2 is Element of t2
(ss | t2) . EE2 is Relation-like Function-like set
ss . EE2 is Relation-like Function-like set
((ss | t2) . EE2) \+\ (ss . EE2) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
((ss | t2) . EE2) \ (ss . EE2) is Relation-like set
((ss | t2) . EE2) typed\ (ss . EE2) is Relation-like Function-like Element of bool ((ss | t2) . EE2)
bool ((ss | t2) . EE2) is non empty set
((ss | t2) . EE2) \ (ss . EE2) is Relation-like Function-like Element of bool ((ss | t2) . EE2)
(ss . EE2) \ ((ss | t2) . EE2) is Relation-like set
(ss . EE2) typed\ ((ss | t2) . EE2) is Relation-like Function-like Element of bool (ss . EE2)
bool (ss . EE2) is non empty set
(ss . EE2) \ ((ss | t2) . EE2) is Relation-like Function-like Element of bool (ss . EE2)
(((ss | t2) . EE2) \ (ss . EE2)) \/ ((ss . EE2) \ ((ss | t2) . EE2)) is Relation-like set
s | t2 is Relation-like t2 -defined OwnSymbolsOf S -defined Function-like Function-yielding V164() set
Y1 is Element of t2
(s | t2) . Y1 is Relation-like Function-like set
s . Y1 is Relation-like Function-like set
((s | t2) . Y1) \+\ (s . Y1) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
((s | t2) . Y1) \ (s . Y1) is Relation-like set
((s | t2) . Y1) typed\ (s . Y1) is Relation-like Function-like Element of bool ((s | t2) . Y1)
bool ((s | t2) . Y1) is non empty set
((s | t2) . Y1) \ (s . Y1) is Relation-like Function-like Element of bool ((s | t2) . Y1)
(s . Y1) \ ((s | t2) . Y1) is Relation-like set
(s . Y1) typed\ ((s | t2) . Y1) is Relation-like Function-like Element of bool (s . Y1)
bool (s . Y1) is non empty set
(s . Y1) \ ((s | t2) . Y1) is Relation-like Function-like Element of bool (s . Y1)
(((s | t2) . Y1) \ (s . Y1)) \/ ((s . Y1) \ ((s | t2) . Y1)) is Relation-like set
(ss | U) . E22 is Relation-like Function-like set
ss . E22 is non empty Relation-like (abs (ar E22)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of E22,u
ar E22 is finite complex ext-real V40() V41() Element of INT
the adicity of l . E22 is set
abs (ar E22) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar E22)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
(s | U) . EE1 is Relation-like Function-like set
s . EE1 is non empty Relation-like (abs (ar EE1)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of EE1,u
ar EE1 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of S . EE1 is set
abs (ar EE1) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(abs (ar EE1)) -tuples_on u is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of u
0 -tuples_on u is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of u
dom (ss . E22) is non empty functional finite-membered FinSequence-membered Element of bool ((abs (ar E22)) -tuples_on u)
bool ((abs (ar E22)) -tuples_on u) is non empty set
TermSymbolsOf S is non empty set
the adicity of S " NAT is Element of bool ( the U1 of S \ { the U3 of S})
f2 is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf S)
f1 is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
Y2 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
t2 /\ (LettersOf l) is Element of bool (AllSymbolsOf l)
t2 typed/\ (LettersOf l) is Element of bool t2
bool t2 is non empty set
t2 /\ (LettersOf l) is set
t2 /\typed (LettersOf l) is Element of bool (LettersOf l)
bool (LettersOf l) is non empty non trivial non finite V166() set
r2 is non empty set
phi2 is Element of r2
<*phi2*> is non empty trivial Relation-like NAT -defined r2 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support FinSequence of r2
[1,phi2] is non empty set
{[1,phi2]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
{ <*b₁*> where b₁ is Element of r2 : verum } is set
1 -tuples_on r2 is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of r2
(U *) /\ (AtomicTermsOf l) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
(U *) typed/\ (AtomicTermsOf l) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ (AtomicTermsOf l) is functional set
(U *) /\typed (AtomicTermsOf l) is functional finite-membered FinSequence-membered Element of bool (AtomicTermsOf l)
bool (AtomicTermsOf l) is non empty set
tt22 is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf l)
f1 . 1 is set
o2 is Element of t2
(s | t2) . o2 is Relation-like Function-like set
s . o2 is Relation-like Function-like set
((s | t2) . o2) \+\ (s . o2) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
((s | t2) . o2) \ (s . o2) is Relation-like set
((s | t2) . o2) typed\ (s . o2) is Relation-like Function-like Element of bool ((s | t2) . o2)
bool ((s | t2) . o2) is non empty set
((s | t2) . o2) \ (s . o2) is Relation-like Function-like Element of bool ((s | t2) . o2)
(s . o2) \ ((s | t2) . o2) is Relation-like set
(s . o2) typed\ ((s | t2) . o2) is Relation-like Function-like Element of bool (s . o2)
bool (s . o2) is non empty set
(s . o2) \ ((s | t2) . o2) is Relation-like Function-like Element of bool (s . o2)
(((s | t2) . o2) \ (s . o2)) \/ ((s . o2) \ ((s | t2) . o2)) is Relation-like set
(ss | t2) . o2 is Relation-like Function-like set
ss . o2 is Relation-like Function-like set
((ss | t2) . o2) \+\ (ss . o2) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
((ss | t2) . o2) \ (ss . o2) is Relation-like set
((ss | t2) . o2) typed\ (ss . o2) is Relation-like Function-like Element of bool ((ss | t2) . o2)
bool ((ss | t2) . o2) is non empty set
((ss | t2) . o2) \ (ss . o2) is Relation-like Function-like Element of bool ((ss | t2) . o2)
(ss . o2) \ ((ss | t2) . o2) is Relation-like set
(ss . o2) typed\ ((ss | t2) . o2) is Relation-like Function-like Element of bool (ss . o2)
bool (ss . o2) is non empty set
(ss . o2) \ ((ss | t2) . o2) is Relation-like Function-like Element of bool (ss . o2)
(((ss | t2) . o2) \ (ss . o2)) \/ ((ss . o2) \ ((ss | t2) . o2)) is Relation-like set
(ss -TermEval) | tt22 is Relation-like AllTermsOf l -defined tt22 -defined AllTermsOf l -defined u -valued Function-like total Element of bool [:(AllTermsOf l),u:]
ox is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of tt22
((ss -TermEval) | tt22) . ox is set
(ss -TermEval) . ox is Element of u
(((ss -TermEval) | tt22) . ox) \+\ ((ss -TermEval) . ox) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((ss -TermEval) | tt22) . ox) \ ((ss -TermEval) . ox) is set
(((ss -TermEval) | tt22) . ox) typed\ ((ss -TermEval) . ox) is Element of bool (((ss -TermEval) | tt22) . ox)
bool (((ss -TermEval) | tt22) . ox) is non empty set
(((ss -TermEval) | tt22) . ox) \ ((ss -TermEval) . ox) is Element of bool (((ss -TermEval) | tt22) . ox)
((ss -TermEval) . ox) \ (((ss -TermEval) | tt22) . ox) is set
((ss -TermEval) . ox) typed\ (((ss -TermEval) | tt22) . ox) is Element of bool ((ss -TermEval) . ox)
bool ((ss -TermEval) . ox) is non empty set
((ss -TermEval) . ox) \ (((ss -TermEval) | tt22) . ox) is Element of bool ((ss -TermEval) . ox)
((((ss -TermEval) | tt22) . ox) \ ((ss -TermEval) . ox)) \/ (((ss -TermEval) . ox) \ (((ss -TermEval) | tt22) . ox)) is set
(s | U) . o2 is Relation-like Function-like set
(ss | U) . o2 is Relation-like Function-like set
(s -TermEval) | f2 is Relation-like AllTermsOf S -defined f2 -defined AllTermsOf S -defined u -valued Function-like total Element of bool [:(AllTermsOf S),u:]
r2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of f2
((s -TermEval) | f2) . r2 is set
(s -TermEval) . r2 is Element of u
(((s -TermEval) | f2) . r2) \+\ ((s -TermEval) . r2) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((s -TermEval) | f2) . r2) \ ((s -TermEval) . r2) is set
(((s -TermEval) | f2) . r2) typed\ ((s -TermEval) . r2) is Element of bool (((s -TermEval) | f2) . r2)
bool (((s -TermEval) | f2) . r2) is non empty set
(((s -TermEval) | f2) . r2) \ ((s -TermEval) . r2) is Element of bool (((s -TermEval) | f2) . r2)
((s -TermEval) . r2) \ (((s -TermEval) | f2) . r2) is set
((s -TermEval) . r2) typed\ (((s -TermEval) | f2) . r2) is Element of bool ((s -TermEval) . r2)
bool ((s -TermEval) . r2) is non empty set
((s -TermEval) . r2) \ (((s -TermEval) | f2) . r2) is Element of bool ((s -TermEval) . r2)
((((s -TermEval) | f2) . r2) \ ((s -TermEval) . r2)) \/ (((s -TermEval) . r2) \ (((s -TermEval) | f2) . r2)) is set
((s -TermEval) | c1) . A2 is set
(s -TermEval) . f1 is set
(S -firstChar) . f1 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
s . ((S -firstChar) . f1) is non empty Relation-like (abs (ar ((S -firstChar) . f1))) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . f1,u
ar ((S -firstChar) . f1) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of S . ((S -firstChar) . f1) is set
abs (ar ((S -firstChar) . f1)) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(abs (ar ((S -firstChar) . f1))) -tuples_on u is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of u
SubTerms f1 is empty trivial Relation-like non-empty empty-yielding NAT -defined (rng f1) * -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 finite-membered cardinal {} -element abs (ar f1) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllTermsOf S) *
rng f1 is non empty trivial finite 1 -element set
(rng f1) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng f1
AllTermsOf S is non empty functional finite-membered FinSequence-membered AllSymbolsOf S -prefix S -prefix Element of bool ((AllSymbolsOf S) *)
ar f1 is finite complex ext-real V40() V41() Element of INT
abs (ar f1) 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 finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) *)
(s -TermEval) (*) (SubTerms f1) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued u -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element len (SubTerms f1) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
len (SubTerms f1) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(s . ((S -firstChar) . f1)) . ((s -TermEval) (*) (SubTerms f1)) is set
ss . Y2 is non empty Relation-like (abs (ar Y2)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of Y2,u
ar Y2 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of l . Y2 is set
abs (ar Y2) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(abs (ar Y2)) -tuples_on u is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of u
(ss . Y2) . {} is set
<*Y2*> is non empty trivial Relation-like NAT -defined TermSymbolsOf l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf l) *) \ {{}}
TermSymbolsOf l is non empty set
the adicity of l " NAT is Element of bool ( the U1 of l \ { the U3 of l})
[1,Y2] is non empty set
{[1,Y2]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
<*Y2*> . 1 is set
ss . (<*Y2*> . 1) is Relation-like Function-like set
(ss . (<*Y2*> . 1)) . {} is set
(l -firstChar) . <*Y2*> is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
ss . ((l -firstChar) . <*Y2*>) is non empty Relation-like (abs (ar ((l -firstChar) . <*Y2*>))) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (l -firstChar) . <*Y2*>,u
ar ((l -firstChar) . <*Y2*>) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of l . ((l -firstChar) . <*Y2*>) is set
abs (ar ((l -firstChar) . <*Y2*>)) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(abs (ar ((l -firstChar) . <*Y2*>))) -tuples_on u is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of u
SubTerms <*Y2*> is empty trivial Relation-like non-empty empty-yielding NAT -defined (rng <*Y2*>) * -valued AllTermsOf l -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element abs (ar <*Y2*>) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllTermsOf l) *
rng <*Y2*> is non empty trivial finite 1 -element set
(rng <*Y2*>) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng <*Y2*>
AllTermsOf l is non empty functional finite-membered FinSequence-membered AllSymbolsOf l -prefix l -prefix Element of bool ((AllSymbolsOf l) *)
ar <*Y2*> is finite complex ext-real V40() V41() Element of INT
abs (ar <*Y2*>) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(AllTermsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf l) *) *)
(ss -TermEval) (*) (SubTerms <*Y2*>) is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued u -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element len (SubTerms <*Y2*>) -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
len (SubTerms <*Y2*>) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(ss . ((l -firstChar) . <*Y2*>)) . ((ss -TermEval) (*) (SubTerms <*Y2*>)) is set
((ss -TermEval) | b2) . A2 is set
c1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(S -termsOfMaxDepth) . c1 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
(U *) /\ ((S -termsOfMaxDepth) . c1) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf S) *) \ {{}})
(U *) typed/\ ((S -termsOfMaxDepth) . c1) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ ((S -termsOfMaxDepth) . c1) is functional set
(U *) /\typed ((S -termsOfMaxDepth) . c1) is functional finite-membered FinSequence-membered V165() Element of bool ((S -termsOfMaxDepth) . c1)
bool ((S -termsOfMaxDepth) . c1) is non empty set
(s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . c1)) is Relation-like AllTermsOf S -defined (U *) /\ ((S -termsOfMaxDepth) . c1) -defined AllTermsOf S -defined u -valued Function-like Element of bool [:(AllTermsOf S),u:]
(l -termsOfMaxDepth) . c1 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
(U *) /\ ((l -termsOfMaxDepth) . c1) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf l) *) \ {{}})
(U *) typed/\ ((l -termsOfMaxDepth) . c1) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ ((l -termsOfMaxDepth) . c1) is functional set
(U *) /\typed ((l -termsOfMaxDepth) . c1) is functional finite-membered FinSequence-membered V165() Element of bool ((l -termsOfMaxDepth) . c1)
bool ((l -termsOfMaxDepth) . c1) is non empty set
(ss -TermEval) | ((U *) /\ ((l -termsOfMaxDepth) . c1)) is Relation-like AllTermsOf l -defined (U *) /\ ((l -termsOfMaxDepth) . c1) -defined AllTermsOf l -defined u -valued Function-like Element of bool [:(AllTermsOf l),u:]
c1 + 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) . (c1 + 1) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
(U *) /\ ((S -termsOfMaxDepth) . (c1 + 1)) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf S) *) \ {{}})
(U *) typed/\ ((S -termsOfMaxDepth) . (c1 + 1)) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ ((S -termsOfMaxDepth) . (c1 + 1)) is functional set
(U *) /\typed ((S -termsOfMaxDepth) . (c1 + 1)) is functional finite-membered FinSequence-membered V165() Element of bool ((S -termsOfMaxDepth) . (c1 + 1))
bool ((S -termsOfMaxDepth) . (c1 + 1)) is non empty set
(s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . (c1 + 1))) is Relation-like AllTermsOf S -defined (U *) /\ ((S -termsOfMaxDepth) . (c1 + 1)) -defined AllTermsOf S -defined u -valued Function-like Element of bool [:(AllTermsOf S),u:]
(l -termsOfMaxDepth) . (c1 + 1) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
(U *) /\ ((l -termsOfMaxDepth) . (c1 + 1)) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf l) *) \ {{}})
(U *) typed/\ ((l -termsOfMaxDepth) . (c1 + 1)) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ ((l -termsOfMaxDepth) . (c1 + 1)) is functional set
(U *) /\typed ((l -termsOfMaxDepth) . (c1 + 1)) is functional finite-membered FinSequence-membered V165() Element of bool ((l -termsOfMaxDepth) . (c1 + 1))
bool ((l -termsOfMaxDepth) . (c1 + 1)) is non empty set
(ss -TermEval) | ((U *) /\ ((l -termsOfMaxDepth) . (c1 + 1))) is Relation-like AllTermsOf l -defined (U *) /\ ((l -termsOfMaxDepth) . (c1 + 1)) -defined AllTermsOf l -defined u -valued Function-like Element of bool [:(AllTermsOf l),u:]
c2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(l -termsOfMaxDepth) . c2 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
(S -termsOfMaxDepth) . c2 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
b2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S -termsOfMaxDepth) . b2 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
(l -termsOfMaxDepth) . b2 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
(U *) /\ ((S -termsOfMaxDepth) . c2) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf S) *) \ {{}})
(U *) typed/\ ((S -termsOfMaxDepth) . c2) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ ((S -termsOfMaxDepth) . c2) is functional set
(U *) /\typed ((S -termsOfMaxDepth) . c2) is functional finite-membered FinSequence-membered V165() Element of bool ((S -termsOfMaxDepth) . c2)
bool ((S -termsOfMaxDepth) . c2) is non empty set
(U *) /\ ((S -termsOfMaxDepth) . b2) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf S) *) \ {{}})
(U *) typed/\ ((S -termsOfMaxDepth) . b2) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ ((S -termsOfMaxDepth) . b2) is functional set
(U *) /\typed ((S -termsOfMaxDepth) . b2) is functional finite-membered FinSequence-membered V165() Element of bool ((S -termsOfMaxDepth) . b2)
bool ((S -termsOfMaxDepth) . b2) is non empty set
(U *) /\ ((l -termsOfMaxDepth) . c2) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf l) *) \ {{}})
(U *) typed/\ ((l -termsOfMaxDepth) . c2) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ ((l -termsOfMaxDepth) . c2) is functional set
(U *) /\typed ((l -termsOfMaxDepth) . c2) is functional finite-membered FinSequence-membered V165() Element of bool ((l -termsOfMaxDepth) . c2)
bool ((l -termsOfMaxDepth) . c2) is non empty set
(U *) /\ ((l -termsOfMaxDepth) . b2) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf l) *) \ {{}})
(U *) typed/\ ((l -termsOfMaxDepth) . b2) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ ((l -termsOfMaxDepth) . b2) is functional set
(U *) /\typed ((l -termsOfMaxDepth) . b2) is functional finite-membered FinSequence-membered V165() Element of bool ((l -termsOfMaxDepth) . b2)
bool ((l -termsOfMaxDepth) . b2) is non empty set
A1 is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
(s -TermEval) | A1 is Relation-like AllTermsOf S -defined A1 -defined AllTermsOf S -defined u -valued Function-like total Element of bool [:(AllTermsOf S),u:]
X1 is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf l)
(ss -TermEval) | X1 is Relation-like AllTermsOf l -defined X1 -defined AllTermsOf l -defined u -valued Function-like total Element of bool [:(AllTermsOf l),u:]
dom ((s -TermEval) | A1) is functional finite-membered FinSequence-membered V165() Element of bool A1
bool A1 is non empty set
dom ((ss -TermEval) | X1) is functional finite-membered FinSequence-membered V165() Element of bool X1
bool X1 is non empty set
A2 is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
(s -TermEval) | A2 is Relation-like AllTermsOf S -defined A2 -defined AllTermsOf S -defined u -valued Function-like total Element of bool [:(AllTermsOf S),u:]
dom ((s -TermEval) | A2) is functional finite-membered FinSequence-membered V165() Element of bool A2
bool A2 is non empty set
t2 is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf l)
(ss -TermEval) | t2 is Relation-like AllTermsOf l -defined t2 -defined AllTermsOf l -defined u -valued Function-like total Element of bool [:(AllTermsOf l),u:]
dom ((ss -TermEval) | t2) is functional finite-membered FinSequence-membered V165() Element of bool t2
bool t2 is non empty set
EE1 is functional finite-membered FinSequence-membered V165() Element of bool t2
EE2 is set
Y1 is non empty set
Y2 is Element of Y1
b2 + 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})
f1 is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal b2 + 1 -termal Element of ((AllSymbolsOf S) *) \ {{}}
(S -firstChar) . f1 is non relational termal own ofAtomicFormula Element of AllSymbolsOf S
f2 is non relational termal own ofAtomicFormula Element of AllSymbolsOf S
ar f2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of S . f2 is set
abs (ar f2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
r2 is non empty set
r2 * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of r2
f1 . 1 is set
{(f1 . 1)} is non empty trivial finite 1 -element set
{(f1 . 1)} \ r2 is trivial finite Element of bool {(f1 . 1)}
bool {(f1 . 1)} is non empty finite finite-membered set
{(f1 . 1)} typed\ r2 is trivial finite Element of bool {(f1 . 1)}
r2 /\ (OwnSymbolsOf l) is Element of bool (AllSymbolsOf l)
r2 typed/\ (OwnSymbolsOf l) is Element of bool r2
bool r2 is non empty set
r2 /\ (OwnSymbolsOf l) is set
r2 /\typed (OwnSymbolsOf l) is Element of bool (OwnSymbolsOf l)
phi2 is own ofAtomicFormula Element of AllSymbolsOf l
ox is Element of r2
the adicity of S . ox is set
the adicity of S | r2 is Relation-like the U1 of S \ { the U3 of S} -defined r2 -defined the U1 of S \ { the U3 of S} -defined INT -valued Function-like Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
( the adicity of S | r2) . ox is set
( the adicity of S . ox) \+\ (( the adicity of S | r2) . ox) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
( the adicity of S . ox) \ (( the adicity of S | r2) . ox) is set
( the adicity of S . ox) typed\ (( the adicity of S | r2) . ox) is Element of bool ( the adicity of S . ox)
bool ( the adicity of S . ox) is non empty set
( the adicity of S . ox) \ (( the adicity of S | r2) . ox) is Element of bool ( the adicity of S . ox)
(( the adicity of S | r2) . ox) \ ( the adicity of S . ox) is set
(( the adicity of S | r2) . ox) typed\ ( the adicity of S . ox) is Element of bool (( the adicity of S | r2) . ox)
bool (( the adicity of S | r2) . ox) is non empty set
(( the adicity of S | r2) . ox) \ ( the adicity of S . ox) is Element of bool (( the adicity of S | r2) . ox)
(( the adicity of S . ox) \ (( the adicity of S | r2) . ox)) \/ ((( the adicity of S | r2) . ox) \ ( the adicity of S . ox)) is set
the adicity of l . ox is set
the adicity of l | r2 is Relation-like the U1 of l \ { the U3 of l} -defined r2 -defined the U1 of l \ { the U3 of l} -defined INT -valued Function-like Element of bool [:( the U1 of l \ { the U3 of l}),INT:]
( the adicity of l | r2) . ox is set
( the adicity of l . ox) \+\ (( the adicity of l | r2) . ox) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
( the adicity of l . ox) \ (( the adicity of l | r2) . ox) is set
( the adicity of l . ox) typed\ (( the adicity of l | r2) . ox) is Element of bool ( the adicity of l . ox)
bool ( the adicity of l . ox) is non empty set
( the adicity of l . ox) \ (( the adicity of l | r2) . ox) is Element of bool ( the adicity of l . ox)
(( the adicity of l | r2) . ox) \ ( the adicity of l . ox) is set
(( the adicity of l | r2) . ox) typed\ ( the adicity of l . ox) is Element of bool (( the adicity of l | r2) . ox)
bool (( the adicity of l | r2) . ox) is non empty set
(( the adicity of l | r2) . ox) \ ( the adicity of l . ox) is Element of bool (( the adicity of l | r2) . ox)
(( the adicity of l . ox) \ (( the adicity of l | r2) . ox)) \/ ((( the adicity of l | r2) . ox) \ ( the adicity of l . ox)) is set
( the adicity of S | U) . f2 is set
the adicity of l . phi2 is set
( the adicity of l | U) . phi2 is set
tt22 is ofAtomicFormula Element of AllSymbolsOf l
ar tt22 is finite complex ext-real V40() V41() Element of INT
the adicity of l . tt22 is set
o2 is non relational termal own ofAtomicFormula Element of AllSymbolsOf l
ar o2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of l . o2 is set
abs (ar o2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
s . ox is Relation-like Function-like set
s | r2 is Relation-like r2 -defined OwnSymbolsOf S -defined Function-like Function-yielding V164() set
(s | r2) . ox is Relation-like Function-like set
(s . ox) \+\ ((s | r2) . ox) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(s . ox) \ ((s | r2) . ox) is Relation-like set
(s . ox) typed\ ((s | r2) . ox) is Relation-like Function-like Element of bool (s . ox)
bool (s . ox) is non empty set
(s . ox) \ ((s | r2) . ox) is Relation-like Function-like Element of bool (s . ox)
((s | r2) . ox) \ (s . ox) is Relation-like set
((s | r2) . ox) typed\ (s . ox) is Relation-like Function-like Element of bool ((s | r2) . ox)
bool ((s | r2) . ox) is non empty set
((s | r2) . ox) \ (s . ox) is Relation-like Function-like Element of bool ((s | r2) . ox)
((s . ox) \ ((s | r2) . ox)) \/ (((s | r2) . ox) \ (s . ox)) is Relation-like set
ss . ox is Relation-like Function-like set
ss | r2 is Relation-like r2 -defined OwnSymbolsOf l -defined Function-like Function-yielding V164() set
(ss | r2) . ox is Relation-like Function-like set
(ss . ox) \+\ ((ss | r2) . ox) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(ss . ox) \ ((ss | r2) . ox) is Relation-like set
(ss . ox) typed\ ((ss | r2) . ox) is Relation-like Function-like Element of bool (ss . ox)
bool (ss . ox) is non empty set
(ss . ox) \ ((ss | r2) . ox) is Relation-like Function-like Element of bool (ss . ox)
((ss | r2) . ox) \ (ss . ox) is Relation-like set
((ss | r2) . ox) typed\ (ss . ox) is Relation-like Function-like Element of bool ((ss | r2) . ox)
bool ((ss | r2) . ox) is non empty set
((ss | r2) . ox) \ (ss . ox) is Relation-like Function-like Element of bool ((ss | r2) . ox)
((ss . ox) \ ((ss | r2) . ox)) \/ (((ss | r2) . ox) \ (ss . ox)) is Relation-like set
(s | r2) . f2 is Relation-like Function-like set
SubTerms f1 is Relation-like NAT -defined (S -termsOfMaxDepth) . b2 -valued (rng f1) * -valued AllTermsOf S -valued Function-like finite abs (ar f1) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
K335(((AllSymbolsOf S) *)) is non empty non trivial non finite V166() Element of bool (bool ((AllSymbolsOf S) *))
bool (bool ((AllSymbolsOf S) *)) is non empty non trivial non finite V166() set
S -termsOfMaxDepth is non empty Relation-like NAT -defined K335(((AllSymbolsOf S) *)) -valued Function-like total quasi_total Element of bool [:NAT,K335(((AllSymbolsOf S) *)):]
[:NAT,K335(((AllSymbolsOf S) *)):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335(((AllSymbolsOf S) *)):] is non empty non trivial non finite V166() set
(S -termsOfMaxDepth) . b2 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335(((AllSymbolsOf S) *))
rng f1 is non empty finite set
(rng f1) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng f1
AllTermsOf S is non empty functional finite-membered FinSequence-membered AllSymbolsOf S -prefix S -prefix Element of bool ((AllSymbolsOf S) *)
ar f1 is finite complex ext-real V40() V41() Element of INT
ar ((S -firstChar) . f1) 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) . f1) is set
abs (ar f1) 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 finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) *)
rng (SubTerms f1) is finite set
B is non empty Element of bool r2
B * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (r2 *)
bool (r2 *) is non empty non trivial non finite V166() set
(((AllSymbolsOf l) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf l) *) \ {{}}
((l -termsOfMaxDepth) . b2) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf l) *) \ {{}}) *)
bool ((((AllSymbolsOf l) *) \ {{}}) *) is non empty non trivial non finite V166() set
st2 is Relation-like NAT -defined (l -termsOfMaxDepth) . b2 -valued Function-like finite abs (ar o2) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of ((l -termsOfMaxDepth) . b2) *
T2n is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf l)
T2n * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((AllTermsOf l) *)
(AllTermsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf l
bool ((AllTermsOf l) *) is non empty non trivial non finite V166() set
(AllTermsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf l) *) \ {{}}) *)
TermSymbolsOf l is non empty set
the adicity of l " NAT is Element of bool ( the U1 of l \ { the U3 of l})
(l,o2,st2) is non empty Relation-like NAT -defined TermSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal b2 + 1 -termal Element of ((AllSymbolsOf l) *) \ {{}}
<*o2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf l) *) \ {{}}
[1,o2] is non empty set
{[1,o2]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
((AllSymbolsOf l) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf l) *
(l -multiCat) . st2 is Relation-like NAT -defined AllSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf l) *
<*o2*> ^ ((l -multiCat) . st2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
n1 is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf S) *) \ {{}}
(r2 *) /\ ((S -termsOfMaxDepth) . 0) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf S) *) \ {{}})
(r2 *) typed/\ ((S -termsOfMaxDepth) . 0) is functional finite-membered FinSequence-membered Element of bool (r2 *)
(r2 *) /\ ((S -termsOfMaxDepth) . 0) is functional set
(r2 *) /\typed ((S -termsOfMaxDepth) . 0) is functional finite-membered FinSequence-membered V165() Element of bool ((S -termsOfMaxDepth) . 0)
nn1 is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
(s -TermEval) | nn1 is Relation-like AllTermsOf S -defined nn1 -defined AllTermsOf S -defined u -valued Function-like total Element of bool [:(AllTermsOf S),u:]
st11 is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf l)
(ss -TermEval) | st11 is Relation-like AllTermsOf l -defined st11 -defined AllTermsOf l -defined u -valued Function-like total Element of bool [:(AllTermsOf l),u:]
dom ((s -TermEval) | nn1) is functional finite-membered FinSequence-membered V165() Element of bool nn1
bool nn1 is non empty set
dom ((ss -TermEval) | st11) is functional finite-membered FinSequence-membered V165() Element of bool st11
bool st11 is non empty set
0 * c2 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
0 + (0 * c2) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
t2 is non empty trivial Relation-like NAT -defined TermSymbolsOf l -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf l) *) \ {{}}
0 + c2 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
A11 is non empty set
A22 is non empty set
D22 is non empty set
(s -TermEval) | Y1 is Relation-like AllTermsOf S -defined Y1 -defined AllTermsOf S -defined u -valued Function-like Element of bool [:(AllTermsOf S),u:]
((s -TermEval) | Y1) . Y2 is set
(s -TermEval) . Y2 is set
(((s -TermEval) | Y1) . Y2) \+\ ((s -TermEval) . Y2) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((s -TermEval) | Y1) . Y2) \ ((s -TermEval) . Y2) is set
(((s -TermEval) | Y1) . Y2) typed\ ((s -TermEval) . Y2) is Element of bool (((s -TermEval) | Y1) . Y2)
bool (((s -TermEval) | Y1) . Y2) is non empty set
(((s -TermEval) | Y1) . Y2) \ ((s -TermEval) . Y2) is Element of bool (((s -TermEval) | Y1) . Y2)
((s -TermEval) . Y2) \ (((s -TermEval) | Y1) . Y2) is set
((s -TermEval) . Y2) typed\ (((s -TermEval) | Y1) . Y2) is Element of bool ((s -TermEval) . Y2)
bool ((s -TermEval) . Y2) is non empty set
((s -TermEval) . Y2) \ (((s -TermEval) | Y1) . Y2) is Element of bool ((s -TermEval) . Y2)
((((s -TermEval) | Y1) . Y2) \ ((s -TermEval) . Y2)) \/ (((s -TermEval) . Y2) \ (((s -TermEval) | Y1) . Y2)) is set
t111 is Element of A11
((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111 is set
(s -TermEval) . t111 is set
(((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111) \+\ ((s -TermEval) . t111) is set
(((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111) \ ((s -TermEval) . t111) is set
(((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111) typed\ ((s -TermEval) . t111) is Element of bool (((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111)
bool (((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111) is non empty set
(((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111) \ ((s -TermEval) . t111) is Element of bool (((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111)
((s -TermEval) . t111) \ (((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111) is set
((s -TermEval) . t111) typed\ (((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111) is Element of bool ((s -TermEval) . t111)
bool ((s -TermEval) . t111) is non empty set
((s -TermEval) . t111) \ (((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111) is Element of bool ((s -TermEval) . t111)
((((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111) \ ((s -TermEval) . t111)) \/ (((s -TermEval) . t111) \ (((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . t111)) is set
t02 is Element of A22
((ss -TermEval) | st11) . t02 is set
(ss -TermEval) . t02 is set
(((ss -TermEval) | st11) . t02) \+\ ((ss -TermEval) . t02) is set
(((ss -TermEval) | st11) . t02) \ ((ss -TermEval) . t02) is set
(((ss -TermEval) | st11) . t02) typed\ ((ss -TermEval) . t02) is Element of bool (((ss -TermEval) | st11) . t02)
bool (((ss -TermEval) | st11) . t02) is non empty set
(((ss -TermEval) | st11) . t02) \ ((ss -TermEval) . t02) is Element of bool (((ss -TermEval) | st11) . t02)
((ss -TermEval) . t02) \ (((ss -TermEval) | st11) . t02) is set
((ss -TermEval) . t02) typed\ (((ss -TermEval) | st11) . t02) is Element of bool ((ss -TermEval) . t02)
bool ((ss -TermEval) . t02) is non empty set
((ss -TermEval) . t02) \ (((ss -TermEval) | st11) . t02) is Element of bool ((ss -TermEval) . t02)
((((ss -TermEval) | st11) . t02) \ ((ss -TermEval) . t02)) \/ (((ss -TermEval) . t02) \ (((ss -TermEval) | st11) . t02)) is set
(ss -TermEval) | D22 is Relation-like AllTermsOf l -defined D22 -defined AllTermsOf l -defined u -valued Function-like Element of bool [:(AllTermsOf l),u:]
t20 is Element of D22
((ss -TermEval) | D22) . t20 is set
(ss -TermEval) . t20 is set
(((ss -TermEval) | D22) . t20) \+\ ((ss -TermEval) . t20) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((ss -TermEval) | D22) . t20) \ ((ss -TermEval) . t20) is set
(((ss -TermEval) | D22) . t20) typed\ ((ss -TermEval) . t20) is Element of bool (((ss -TermEval) | D22) . t20)
bool (((ss -TermEval) | D22) . t20) is non empty set
(((ss -TermEval) | D22) . t20) \ ((ss -TermEval) . t20) is Element of bool (((ss -TermEval) | D22) . t20)
((ss -TermEval) . t20) \ (((ss -TermEval) | D22) . t20) is set
((ss -TermEval) . t20) typed\ (((ss -TermEval) | D22) . t20) is Element of bool ((ss -TermEval) . t20)
bool ((ss -TermEval) . t20) is non empty set
((ss -TermEval) . t20) \ (((ss -TermEval) | D22) . t20) is Element of bool ((ss -TermEval) . t20)
((((ss -TermEval) | D22) . t20) \ ((ss -TermEval) . t20)) \/ (((ss -TermEval) . t20) \ (((ss -TermEval) | D22) . t20)) is set
((s -TermEval) | A1) . EE2 is set
(s -TermEval) . EE2 is set
((s -TermEval) | ((U *) /\ ((S -termsOfMaxDepth) . 0))) . EE2 is set
((ss -TermEval) | ((U *) /\ ((l -termsOfMaxDepth) . 0))) . EE2 is set
(ss -TermEval) . EE2 is set
((ss -TermEval) | X1) . EE2 is set
n1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
n1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
nn1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
nn1 + 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 functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf S) *) \ {{}}
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf S) *) \ {{}}) *)
bool ((((AllSymbolsOf S) *) \ {{}}) *) is non empty non trivial non finite V166() set
st11 is non empty Relation-like non empty-yielding NAT -defined AllTermsOf S -valued Function-like finite nn1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
(l -multiCat) . st11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(S -multiCat) . (SubTerms f1) is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf S) *
(l -multiCat) . (SubTerms f1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
t2 is non empty Relation-like NAT -defined TermSymbolsOf l -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal b2 + 1 -termal Element of ((AllSymbolsOf l) *) \ {{}}
D22 is non empty set
(l -firstChar) . t2 is non relational termal own ofAtomicFormula Element of AllSymbolsOf l
t2 . 1 is set
st22 is Relation-like NAT -defined AllTermsOf l -valued Function-like finite abs (ar o2) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf l) *
SubTerms t2 is Relation-like NAT -defined (l -termsOfMaxDepth) . b2 -valued (rng t2) * -valued AllTermsOf l -valued Function-like finite abs (ar t2) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf l) *
K335(((AllSymbolsOf l) *)) is non empty non trivial non finite V166() Element of bool (bool ((AllSymbolsOf l) *))
bool (bool ((AllSymbolsOf l) *)) is non empty non trivial non finite V166() set
l -termsOfMaxDepth is non empty Relation-like NAT -defined K335(((AllSymbolsOf l) *)) -valued Function-like total quasi_total Element of bool [:NAT,K335(((AllSymbolsOf l) *)):]
[:NAT,K335(((AllSymbolsOf l) *)):] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,K335(((AllSymbolsOf l) *)):] is non empty non trivial non finite V166() set
(l -termsOfMaxDepth) . b2 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335(((AllSymbolsOf l) *))
rng t2 is non empty finite set
(rng t2) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng t2
AllTermsOf l is non empty functional finite-membered FinSequence-membered AllSymbolsOf l -prefix l -prefix Element of bool ((AllSymbolsOf l) *)
ar t2 is finite complex ext-real V40() V41() Element of INT
ar ((l -firstChar) . t2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of INT
the adicity of l . ((l -firstChar) . t2) is set
abs (ar t2) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(AllTermsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf l) *) *)
((ss -TermEval) | t2) | A2 is Relation-like AllTermsOf l -defined A2 -defined AllTermsOf l -defined u -valued Function-like Element of bool [:(AllTermsOf l),u:]
EE1 null t2 is set
t2 /\ EE1 is functional finite-membered FinSequence-membered V165() Element of bool t2
t2 typed/\ EE1 is functional finite-membered FinSequence-membered V165() Element of bool t2
t2 /\ EE1 is functional set
t2 /\typed EE1 is functional finite-membered FinSequence-membered V165() Element of bool EE1
bool EE1 is non empty set
EE1 \typed/ t2 is functional finite-membered V165() Element of bool (EE1 \/ t2)
EE1 \/ t2 is functional finite-membered V165() set
bool (EE1 \/ t2) is non empty set
(ss -TermEval) | (EE1 null t2) is Relation-like AllTermsOf l -defined EE1 null t2 -defined AllTermsOf l -defined u -valued Function-like Element of bool [:(AllTermsOf l),u:]
(s -TermEval) | Y1 is Relation-like AllTermsOf S -defined Y1 -defined AllTermsOf S -defined u -valued Function-like Element of bool [:(AllTermsOf S),u:]
((s -TermEval) | Y1) . Y2 is set
(s -TermEval) . Y2 is set
(((s -TermEval) | Y1) . Y2) \+\ ((s -TermEval) . Y2) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((s -TermEval) | Y1) . Y2) \ ((s -TermEval) . Y2) is set
(((s -TermEval) | Y1) . Y2) typed\ ((s -TermEval) . Y2) is Element of bool (((s -TermEval) | Y1) . Y2)
bool (((s -TermEval) | Y1) . Y2) is non empty set
(((s -TermEval) | Y1) . Y2) \ ((s -TermEval) . Y2) is Element of bool (((s -TermEval) | Y1) . Y2)
((s -TermEval) . Y2) \ (((s -TermEval) | Y1) . Y2) is set
((s -TermEval) . Y2) typed\ (((s -TermEval) | Y1) . Y2) is Element of bool ((s -TermEval) . Y2)
bool ((s -TermEval) . Y2) is non empty set
((s -TermEval) . Y2) \ (((s -TermEval) | Y1) . Y2) is Element of bool ((s -TermEval) . Y2)
((((s -TermEval) | Y1) . Y2) \ ((s -TermEval) . Y2)) \/ (((s -TermEval) . Y2) \ (((s -TermEval) | Y1) . Y2)) is set
(ss -TermEval) | D22 is Relation-like AllTermsOf l -defined D22 -defined AllTermsOf l -defined u -valued Function-like Element of bool [:(AllTermsOf l),u:]
tt2 is Element of D22
((ss -TermEval) | D22) . tt2 is set
(ss -TermEval) . tt2 is set
(((ss -TermEval) | D22) . tt2) \+\ ((ss -TermEval) . tt2) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(((ss -TermEval) | D22) . tt2) \ ((ss -TermEval) . tt2) is set
(((ss -TermEval) | D22) . tt2) typed\ ((ss -TermEval) . tt2) is Element of bool (((ss -TermEval) | D22) . tt2)
bool (((ss -TermEval) | D22) . tt2) is non empty set
(((ss -TermEval) | D22) . tt2) \ ((ss -TermEval) . tt2) is Element of bool (((ss -TermEval) | D22) . tt2)
((ss -TermEval) . tt2) \ (((ss -TermEval) | D22) . tt2) is set
((ss -TermEval) . tt2) typed\ (((ss -TermEval) | D22) . tt2) is Element of bool ((ss -TermEval) . tt2)
bool ((ss -TermEval) . tt2) is non empty set
((ss -TermEval) . tt2) \ (((ss -TermEval) | D22) . tt2) is Element of bool ((ss -TermEval) . tt2)
((((ss -TermEval) | D22) . tt2) \ ((ss -TermEval) . tt2)) \/ (((ss -TermEval) . tt2) \ (((ss -TermEval) | D22) . tt2)) is set
((s -TermEval) | A1) . Y2 is set
((ss -TermEval) | X1) . t2 is set
(ss -TermEval) . t2 is set
((s -TermEval) | A1) . EE2 is set
s . f2 is non empty Relation-like (abs (ar f2)) -tuples_on u -defined u \/ BOOLEAN -valued Function-like total quasi_total Interpreter of f2,u
(abs (ar f2)) -tuples_on u is non empty functional finite-membered FinSequence-membered FinSequenceSet of u
(s -TermEval) (*) (SubTerms f1) is Relation-like NAT -defined u -valued Function-like finite finite-support set
(s . f2) . ((s -TermEval) (*) (SubTerms f1)) is set
((s -TermEval) | A2) (*) (SubTerms f1) is Relation-like NAT -defined u -valued Function-like finite finite-support set
(s . f2) . (((s -TermEval) | A2) (*) (SubTerms f1)) is set
(ss -TermEval) (*) (SubTerms f1) is Relation-like NAT -defined u -valued Function-like finite finite-support set
(s . f2) . ((ss -TermEval) (*) (SubTerms f1)) is set
((ss -TermEval) | X1) . EE2 is set
dom ((s -TermEval) | (U *)) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ (AllTermsOf S) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf S) *) \ {{}})
(U *) typed/\ (AllTermsOf S) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ (AllTermsOf S) is functional set
(U *) /\typed (AllTermsOf S) is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
dom ((ss -TermEval) | (U *)) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ (AllTermsOf l) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf l) *) \ {{}})
(U *) typed/\ (AllTermsOf l) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ (AllTermsOf l) is functional set
(U *) /\typed (AllTermsOf l) is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf l)
c2 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})
A1 is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Element of ((AllSymbolsOf S) *) \ {{}}
Depth A1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
t2 is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support termal Depth A1 -termal Element of ((AllSymbolsOf S) *) \ {{}}
(S -termsOfMaxDepth) . (Depth A1) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
(U *) /\ ((S -termsOfMaxDepth) . (Depth A1)) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf S) *) \ {{}})
(U *) typed/\ ((S -termsOfMaxDepth) . (Depth A1)) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ ((S -termsOfMaxDepth) . (Depth A1)) is functional set
(U *) /\typed ((S -termsOfMaxDepth) . (Depth A1)) is functional finite-membered FinSequence-membered V165() Element of bool ((S -termsOfMaxDepth) . (Depth A1))
bool ((S -termsOfMaxDepth) . (Depth A1)) is non empty set
X1 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(S -termsOfMaxDepth) . X1 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
(l -termsOfMaxDepth) . X1 is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
(l -termsOfMaxDepth) . (Depth A1) is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
(U *) /\ ((l -termsOfMaxDepth) . (Depth A1)) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf l) *) \ {{}})
(U *) typed/\ ((l -termsOfMaxDepth) . (Depth A1)) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) /\ ((l -termsOfMaxDepth) . (Depth A1)) is functional set
(U *) /\typed ((l -termsOfMaxDepth) . (Depth A1)) is functional finite-membered FinSequence-membered V165() Element of bool ((l -termsOfMaxDepth) . (Depth A1))
bool ((l -termsOfMaxDepth) . (Depth A1)) is non empty set
tt2 is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf S)
(s -TermEval) | tt2 is Relation-like AllTermsOf S -defined tt2 -defined AllTermsOf S -defined u -valued Function-like total Element of bool [:(AllTermsOf S),u:]
E11 is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf l)
(ss -TermEval) | E11 is Relation-like AllTermsOf l -defined E11 -defined AllTermsOf l -defined u -valued Function-like total Element of bool [:(AllTermsOf l),u:]
dom ((s -TermEval) | tt2) is functional finite-membered FinSequence-membered V165() Element of bool tt2
bool tt2 is non empty set
dom ((ss -TermEval) | E11) is functional finite-membered FinSequence-membered V165() Element of bool E11
bool E11 is non empty set
((s -TermEval) | tt2) . c2 is set
((ss -TermEval) | E11) . c2 is set
((s -TermEval) | (U *)) . c2 is set
EE1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of tt2
(s -TermEval) . EE1 is Element of u
((s -TermEval) | tt2) . EE1 is set
(ss -TermEval) . EE1 is set
((ss -TermEval) | (U *)) . c2 is set
U is set
U * is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
u is non empty set
u * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of u
u \/ BOOLEAN is non empty set
K546((u *),(u \/ BOOLEAN)) is non empty functional M31(u * ,u \/ 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 V166() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V166() 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
Funcs ((OwnSymbolsOf S),K546((u *),(u \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S,K546((u *),(u \/ BOOLEAN))
u -InterpretersOf S is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),K546((u *),(u \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf S),K546((u *),(u \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined K546((u *),(u \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),K546((u *),(u \/ BOOLEAN))) : b₁ is S,u -interpreter-like } is 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 V166() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V166() set
the adicity of S | U is Relation-like U -defined the U1 of S \ { the U3 of S} -defined INT -valued Function-like Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
AllTermsOf S is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() set
S -termsOfMaxDepth is Relation-like Function-like set
rng (S -termsOfMaxDepth) is set
union (rng (S -termsOfMaxDepth)) is set
l is V51() V53() eligible Language-like
OwnSymbolsOf l is non empty Element of bool (AllSymbolsOf l)
AllSymbolsOf l is non empty non trivial non finite V166() set
the U1 of l is set
bool (AllSymbolsOf l) is non empty non trivial non finite V166() set
the U2 of l is Element of the U1 of l
the U3 of l is Element of the U1 of l
{ the U2 of l, the U3 of l} is non empty finite set
the U1 of l \ { the U2 of l, the U3 of l} is Element of bool the U1 of l
bool the U1 of l is non empty set
the U1 of l typed\ { the U2 of l, the U3 of l} is Element of bool the U1 of l
Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf l,K546((u *),(u \/ BOOLEAN))
u -InterpretersOf l is non empty functional Element of bool (Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf l -defined K546((u *),(u \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN))) : b₁ is l,u -interpreter-like } is set
{ the U3 of l} is non empty trivial finite 1 -element set
the U1 of l \ { the U3 of l} is non empty Element of bool the U1 of l
the U1 of l typed\ { the U3 of l} is Element of bool the U1 of l
the adicity of l is non empty Relation-like the U1 of l \ { the U3 of l} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of l \ { the U3 of l}),INT:]
[:( the U1 of l \ { the U3 of l}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of l \ { the U3 of l}),INT:] is non empty non trivial non finite V166() set
the adicity of l | U is Relation-like U -defined the U1 of l \ { the U3 of l} -defined INT -valued Function-like Element of bool [:( the U1 of l \ { the U3 of l}),INT:]
AllTermsOf l is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf l -prefix l -prefix Element of K335((((AllSymbolsOf l) *) \ {{}}))
(AllSymbolsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf l
((AllSymbolsOf l) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf l) *)
bool ((AllSymbolsOf l) *) is non empty non trivial non finite V166() set
((AllSymbolsOf l) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
bool (((AllSymbolsOf l) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf l) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf l) *) \ {{}}))
bool (bool (((AllSymbolsOf l) *) \ {{}})) is non empty non trivial non finite V166() set
l -termsOfMaxDepth is Relation-like Function-like set
rng (l -termsOfMaxDepth) is set
union (rng (l -termsOfMaxDepth)) is set
i is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,u -interpreter-like Element of u -InterpretersOf S
i | U is Relation-like U -defined OwnSymbolsOf S -defined Function-like Function-yielding V164() set
i -TermEval is non empty Relation-like AllTermsOf S -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),u:]
[:(AllTermsOf S),u:] is non empty Relation-like set
bool [:(AllTermsOf S),u:] is non empty set
(i -TermEval) | (U *) is Relation-like U * -defined AllTermsOf S -defined u -valued Function-like Element of bool [:(AllTermsOf S),u:]
x is Relation-like OwnSymbolsOf l -defined Function-like total Function-yielding V164() l,u -interpreter-like Element of u -InterpretersOf l
x | U is Relation-like U -defined OwnSymbolsOf l -defined Function-like Function-yielding V164() set
x -TermEval is non empty Relation-like AllTermsOf l -defined u -valued Function-like total quasi_total Element of bool [:(AllTermsOf l),u:]
[:(AllTermsOf l),u:] is non empty Relation-like set
bool [:(AllTermsOf l),u:] is non empty set
(x -TermEval) | (U *) is Relation-like U * -defined AllTermsOf l -defined u -valued Function-like Element of bool [:(AllTermsOf l),u:]
U is non empty set
U * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of U
U \/ BOOLEAN is non empty set
K546((U *),(U \/ BOOLEAN)) is non empty functional M31(U * ,U \/ BOOLEAN)
u is V51() V53() eligible Language-like
AtomicFormulaSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
AllSymbolsOf u is non empty non trivial non finite V166() set
TheNorSymbOf u is set
the U3 of u is Element of the U1 of u
{(TheNorSymbOf u)} is non empty trivial finite 1 -element set
(AllSymbolsOf u) \ {(TheNorSymbOf u)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
(AllSymbolsOf u) typed\ {(TheNorSymbOf u)} is Element of bool (AllSymbolsOf u)
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
OwnSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
the U2 of u is Element of the U1 of u
{ the U2 of u, the U3 of u} is non empty finite set
the U1 of u \ { the U2 of u, the U3 of u} is Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U2 of u, the U3 of u} is Element of bool the U1 of u
Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf u,K546((U *),(U \/ BOOLEAN))
U -InterpretersOf u is non empty functional Element of bool (Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf u -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN))) : b₁ is u,U -interpreter-like } is set
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
TheEqSymbOf u is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf u
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 V166() set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite V166() 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
Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S,K546((U *),(U \/ BOOLEAN))
U -InterpretersOf S is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN))) : b₁ is S,U -interpreter-like } is 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 V166() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V166() set
TheEqSymbOf S is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf S
AllSymbolsOf S is non empty non trivial non finite V166() set
AtomicFormulaSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
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 V166() Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V166() set
(AllSymbolsOf S) typed\ {(TheNorSymbOf S)} is Element of bool (AllSymbolsOf S)
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered 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 V166() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V166() 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 V233( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V166() set
K415((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):]
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
AllTermsOf S is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() set
S -termsOfMaxDepth is Relation-like Function-like set
rng (S -termsOfMaxDepth) is set
union (rng (S -termsOfMaxDepth)) is set
S -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
((AllSymbolsOf S) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf S) *
[:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf S) -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
(AllSymbolsOf S) -concatenation is non empty Relation-like [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf S) * ) Element of bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):]
[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf S) -concatenation) is non empty Relation-like (((AllSymbolsOf S) *) *) \ {{}} -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):]
(((AllSymbolsOf S) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf S) *) *)
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf S) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf S) *) *)
[:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf S) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
u -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
[:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(AllSymbolsOf u) -pr1 is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total V233( AllSymbolsOf u) Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
[:(AllSymbolsOf u),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf u),(AllSymbolsOf u)) is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
MultPlace ((AllSymbolsOf u) -pr1) is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
TermSymbolsOf u is non empty set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
TermSymbolsOf S is non empty 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
u -multiCat is non empty Relation-like ((AllSymbolsOf u) *) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):]
((AllSymbolsOf u) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf u) *
[:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -multiCat is non empty Relation-like ((AllSymbolsOf u) *) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):]
(AllSymbolsOf u) -concatenation is non empty Relation-like [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf u) * ) Element of bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):]
[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf u) -concatenation) is non empty Relation-like (((AllSymbolsOf u) *) *) \ {{}} -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):]
(((AllSymbolsOf u) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf u) *) *)
bool (((AllSymbolsOf u) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf u) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf u) *) *)
[:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf u) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
U -deltaInterpreter is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
2 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
[:(2 -tuples_on U),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on U),BOOLEAN:] is non empty set
[:(U *),(U *):] is non empty non trivial Relation-like non finite V166() set
U -concatenation is non empty Relation-like [:(U *),(U *):] -defined U * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233(U * ) Element of bool [:[:(U *),(U *):],(U *):]
[:[:(U *),(U *):],(U *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(U *),(U *):],(U *):] is non empty non trivial non finite V166() set
1 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
id (1 -tuples_on U) is non empty Relation-like non empty-yielding 1 -tuples_on U -defined 1 -tuples_on U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(1 -tuples_on U),(1 -tuples_on U):]
[:(1 -tuples_on U),(1 -tuples_on U):] is non empty Relation-like set
bool [:(1 -tuples_on U),(1 -tuples_on U):] is non empty set
(U -concatenation) .: (id (1 -tuples_on U)) is functional finite-membered FinSequence-membered Element of bool (U *)
bool (U *) is non empty non trivial non finite V166() set
chi (((U -concatenation) .: (id (1 -tuples_on U))),(2 -tuples_on U)) is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
RelSymbolsOf u is set
INT \ NAT is Element of bool INT
bool INT is non empty non trivial non finite V166() set
INT typed\ NAT is Element of bool INT
the adicity of u " (INT \ NAT) is Element of bool ( the U1 of u \ { the U3 of u})
bool (OwnSymbolsOf u) is non empty set
bool (OwnSymbolsOf S) is non empty set
hhh is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
rng hhh is non empty finite set
(rng hhh) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
(rng hhh) typed/\ (OwnSymbolsOf u) is finite Element of bool (rng hhh)
bool (rng hhh) is non empty finite finite-membered set
(rng hhh) /\ (OwnSymbolsOf u) is finite set
(rng hhh) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
the adicity of u | ((rng hhh) /\ (OwnSymbolsOf u)) is Relation-like the U1 of u \ { the U3 of u} -defined (rng hhh) /\ (OwnSymbolsOf u) -defined the U1 of u \ { the U3 of u} -defined INT -valued Function-like finite finite-support Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
the adicity of S | ((rng hhh) /\ (OwnSymbolsOf u)) is Relation-like the U1 of S \ { the U3 of S} -defined (rng hhh) /\ (OwnSymbolsOf u) -defined the U1 of S \ { the U3 of S} -defined INT -valued Function-like finite finite-support Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
s is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
s | ((rng hhh) /\ (OwnSymbolsOf u)) is Relation-like (rng hhh) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
s -AtomicEval hhh is boolean Element of BOOLEAN
s === is Relation-like Function-like Function-yielding V164() u,U -interpreter-like s -extension set
TheEqSymbOf u is Element of AtomicFormulaSymbolsOf u
(TheEqSymbOf u) .--> (U -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf u -defined {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf u)} is non empty trivial finite 1 -element set
{(TheEqSymbOf u)} --> (U -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued {(U -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:]
{(U -deltaInterpreter)} is non empty trivial functional finite 1 -element V165() V166() set
[:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty finite finite-membered set
s +* ((TheEqSymbOf u) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(u -firstChar) . hhh is low-compounding relational ofAtomicFormula Element of AllSymbolsOf u
(s ===) . ((u -firstChar) . hhh) is non empty Relation-like (abs (ar ((u -firstChar) . hhh))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . hhh,U
ar ((u -firstChar) . hhh) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of u . ((u -firstChar) . hhh) is set
abs (ar ((u -firstChar) . hhh)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((u -firstChar) . hhh))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms hhh is Relation-like NAT -defined (rng hhh) * -valued (TermSymbolsOf u) * -valued AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . hhh)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
(rng hhh) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng hhh
(TermSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf u
AllTermsOf u is non empty functional finite-membered FinSequence-membered AllSymbolsOf u -prefix u -prefix Element of bool ((AllSymbolsOf u) *)
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf u) *) *)
s -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(s -TermEval) (*) (SubTerms hhh) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((s ===) . ((u -firstChar) . hhh)) . ((s -TermEval) (*) (SubTerms hhh)) is set
s -TruthEval hhh is boolean Element of BOOLEAN
ss is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
ss | ((rng hhh) /\ (OwnSymbolsOf u)) is Relation-like (rng hhh) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf S -defined Function-like finite Function-yielding V164() finite-support set
ss -TermEval is non empty Relation-like AllTermsOf S -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),U:]
[:(AllTermsOf S),U:] is non empty Relation-like set
bool [:(AllTermsOf S),U:] is non empty set
((rng hhh) /\ (OwnSymbolsOf u)) * is non empty functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
(s -TermEval) | (((rng hhh) /\ (OwnSymbolsOf u)) *) is Relation-like AllTermsOf u -defined ((rng hhh) /\ (OwnSymbolsOf u)) * -defined AllTermsOf u -defined U -valued Function-like Element of bool [:(AllTermsOf u),U:]
(ss -TermEval) | (((rng hhh) /\ (OwnSymbolsOf u)) *) is Relation-like AllTermsOf S -defined ((rng hhh) /\ (OwnSymbolsOf u)) * -defined AllTermsOf S -defined U -valued Function-like Element of bool [:(AllTermsOf S),U:]
dom ((s -TermEval) | (((rng hhh) /\ (OwnSymbolsOf u)) *)) is functional finite-membered FinSequence-membered Element of bool (((rng hhh) /\ (OwnSymbolsOf u)) *)
bool (((rng hhh) /\ (OwnSymbolsOf u)) *) is non empty set
dom (ss -TermEval) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf S)
bool (AllTermsOf S) is non empty set
(((rng hhh) /\ (OwnSymbolsOf u)) *) /\ (dom (ss -TermEval)) is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
(((rng hhh) /\ (OwnSymbolsOf u)) *) typed/\ (dom (ss -TermEval)) is functional finite-membered FinSequence-membered Element of bool (((rng hhh) /\ (OwnSymbolsOf u)) *)
(((rng hhh) /\ (OwnSymbolsOf u)) *) /\ (dom (ss -TermEval)) is functional set
(((rng hhh) /\ (OwnSymbolsOf u)) *) /\typed (dom (ss -TermEval)) is functional finite-membered FinSequence-membered V165() Element of bool (dom (ss -TermEval))
bool (dom (ss -TermEval)) is non empty set
(((rng hhh) /\ (OwnSymbolsOf u)) *) /\ (AllTermsOf S) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf S) *) \ {{}})
(((rng hhh) /\ (OwnSymbolsOf u)) *) typed/\ (AllTermsOf S) is functional finite-membered FinSequence-membered Element of bool (((rng hhh) /\ (OwnSymbolsOf u)) *)
(((rng hhh) /\ (OwnSymbolsOf u)) *) /\ (AllTermsOf S) is functional set
(((rng hhh) /\ (OwnSymbolsOf u)) *) /\typed (AllTermsOf S) is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf S)
dom (s -TermEval) is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf u)
bool (AllTermsOf u) is non empty set
(((rng hhh) /\ (OwnSymbolsOf u)) *) /\ (dom (s -TermEval)) is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf u)
(((rng hhh) /\ (OwnSymbolsOf u)) *) typed/\ (dom (s -TermEval)) is functional finite-membered FinSequence-membered Element of bool (((rng hhh) /\ (OwnSymbolsOf u)) *)
(((rng hhh) /\ (OwnSymbolsOf u)) *) /\ (dom (s -TermEval)) is functional set
(((rng hhh) /\ (OwnSymbolsOf u)) *) /\typed (dom (s -TermEval)) is functional finite-membered FinSequence-membered V165() Element of bool (dom (s -TermEval))
bool (dom (s -TermEval)) is non empty set
(((rng hhh) /\ (OwnSymbolsOf u)) *) /\ (AllTermsOf u) is functional finite-membered FinSequence-membered V165() Element of bool (((AllSymbolsOf u) *) \ {{}})
(((rng hhh) /\ (OwnSymbolsOf u)) *) typed/\ (AllTermsOf u) is functional finite-membered FinSequence-membered Element of bool (((rng hhh) /\ (OwnSymbolsOf u)) *)
(((rng hhh) /\ (OwnSymbolsOf u)) *) /\ (AllTermsOf u) is functional set
(((rng hhh) /\ (OwnSymbolsOf u)) *) /\typed (AllTermsOf u) is functional finite-membered FinSequence-membered V165() Element of bool (AllTermsOf u)
b1 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf u
ar b1 is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of u . b1 is set
abs (ar b1) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
{(TheEqSymbOf u)} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf u)
((rng hhh) /\ (OwnSymbolsOf u)) \/ {(TheEqSymbOf u)} is non empty finite Element of bool (AllSymbolsOf u)
{(TheEqSymbOf S)} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf S)
((rng hhh) /\ (OwnSymbolsOf u)) \/ {(TheEqSymbOf S)} is non empty finite set
(u,{},hhh) is non empty Relation-like NAT -defined {} \/ (dom hhh) -defined {} \/ (rng hhh) -valued Function-like finite len hhh -element FinSequence-like FinSubsequence-like finite-support (Depth hhh) + {} -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
dom hhh is non empty finite set
{} \/ (dom hhh) is non empty finite set
{} \/ (rng hhh) is non empty finite set
len hhh is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
Depth hhh 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(Depth hhh) + {} 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
hhh \typed/ {} is Relation-like NAT -defined finite Element of bool (hhh \/ {})
hhh \/ {} is non empty Relation-like NAT -defined finite set
bool (hhh \/ {}) is non empty finite finite-membered set
hhh null {} is Relation-like NAT -defined {} \/ (dom hhh) -defined {} \/ (rng hhh) -valued Function-like finite len hhh -element FinSequence-like FinSubsequence-like finite-support set
hhh ^ {} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
{} ^ hhh is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(u,{},hhh) . 1 is set
{((u,{},hhh) . 1)} is non empty trivial finite 1 -element set
(rng hhh) \/ {} is non empty finite set
{((u,{},hhh) . 1)} \ ((rng hhh) \/ {}) is trivial finite Element of bool {((u,{},hhh) . 1)}
bool {((u,{},hhh) . 1)} is non empty finite finite-membered set
{((u,{},hhh) . 1)} typed\ ((rng hhh) \/ {}) is trivial finite Element of bool {((u,{},hhh) . 1)}
hhh . 1 is set
(RelSymbolsOf u) \ (OwnSymbolsOf u) is Element of bool (RelSymbolsOf u)
bool (RelSymbolsOf u) is non empty set
(RelSymbolsOf u) typed\ (OwnSymbolsOf u) is Element of bool (RelSymbolsOf u)
(abs (ar b1)) + 0 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
nE is non empty Element of bool (OwnSymbolsOf u)
nE * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((OwnSymbolsOf u) *)
(OwnSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of OwnSymbolsOf u
bool ((OwnSymbolsOf u) *) is non empty non trivial non finite V166() set
A1 is non empty Relation-like non empty-yielding NAT -defined AllTermsOf u -valued Function-like finite (abs (ar b1)) + 0 -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of AllTermsOf u
(OwnSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((AllSymbolsOf u) *)
(abs (ar b1)) -tuples_on ((OwnSymbolsOf u) *) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of (OwnSymbolsOf u) *
(abs (ar b1)) -tuples_on ((rng hhh) *) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of (rng hhh) *
((abs (ar b1)) -tuples_on ((rng hhh) *)) /\ ((abs (ar b1)) -tuples_on ((OwnSymbolsOf u) *)) is functional set
((abs (ar b1)) -tuples_on ((rng hhh) *)) typed/\ ((abs (ar b1)) -tuples_on ((OwnSymbolsOf u) *)) is functional finite-membered FinSequence-membered V165() Element of bool ((abs (ar b1)) -tuples_on ((rng hhh) *))
bool ((abs (ar b1)) -tuples_on ((rng hhh) *)) is non empty set
((abs (ar b1)) -tuples_on ((rng hhh) *)) /\typed ((abs (ar b1)) -tuples_on ((OwnSymbolsOf u) *)) is functional finite-membered FinSequence-membered V165() Element of bool ((abs (ar b1)) -tuples_on ((OwnSymbolsOf u) *))
bool ((abs (ar b1)) -tuples_on ((OwnSymbolsOf u) *)) is non empty set
((rng hhh) *) /\ ((OwnSymbolsOf u) *) is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
((rng hhh) *) typed/\ ((OwnSymbolsOf u) *) is functional finite-membered FinSequence-membered Element of bool ((rng hhh) *)
bool ((rng hhh) *) is non empty non trivial non finite V166() set
((rng hhh) *) /\ ((OwnSymbolsOf u) *) is functional set
((rng hhh) *) /\typed ((OwnSymbolsOf u) *) is functional finite-membered FinSequence-membered Element of bool ((OwnSymbolsOf u) *)
bool ((OwnSymbolsOf u) *) is non empty non trivial non finite V166() set
(abs (ar b1)) -tuples_on (((rng hhh) *) /\ ((OwnSymbolsOf u) *)) is functional finite-membered FinSequence-membered FinSequenceSet of ((rng hhh) *) /\ ((OwnSymbolsOf u) *)
(abs (ar b1)) -tuples_on (((rng hhh) /\ (OwnSymbolsOf u)) *) is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of ((rng hhh) /\ (OwnSymbolsOf u)) *
rng A1 is non empty finite set
A2 is non empty functional finite-membered FinSequence-membered V165() V166() Element of bool (AllTermsOf S)
t2 is Relation-like NAT -defined A2 -valued Function-like finite abs (ar b1) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support FinSequence of A2
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllTermsOf S
A2 * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((AllTermsOf S) *)
bool ((AllTermsOf S) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf S) *) \ {{}}) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of ((AllSymbolsOf S) *) \ {{}}
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool ((((AllSymbolsOf S) *) \ {{}}) *)
bool ((((AllSymbolsOf S) *) \ {{}}) *) is non empty non trivial non finite V166() set
bool (AtomicFormulaSymbolsOf u) is non empty set
E11 is Element of AtomicFormulaSymbolsOf u
{E11} is non empty trivial finite 1 -element Element of bool (AtomicFormulaSymbolsOf u)
bool (AtomicFormulaSymbolsOf S) is non empty set
E22 is Element of AtomicFormulaSymbolsOf S
{E22} is non empty trivial finite 1 -element Element of bool (AtomicFormulaSymbolsOf S)
EE1 is non empty Element of bool (AtomicFormulaSymbolsOf u)
((rng hhh) /\ (OwnSymbolsOf u)) \/ EE1 is non empty set
EE2 is non empty Element of bool (AtomicFormulaSymbolsOf S)
((rng hhh) /\ (OwnSymbolsOf u)) \/ EE2 is non empty set
the adicity of u | EE1 is Relation-like the U1 of u \ { the U3 of u} -defined EE1 -defined the U1 of u \ { the U3 of u} -defined INT -valued Function-like Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
the adicity of S | EE2 is Relation-like the U1 of S \ { the U3 of S} -defined EE2 -defined the U1 of S \ { the U3 of S} -defined INT -valued Function-like Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
dom ( the adicity of u | EE1) is Element of bool EE1
bool EE1 is non empty set
dom ( the adicity of S | EE2) is Element of bool EE2
bool EE2 is non empty set
r2 is set
( the adicity of u | EE1) . r2 is set
the adicity of u . r2 is set
the adicity of S . r2 is set
( the adicity of S | EE2) . r2 is set
( the adicity of S | ((rng hhh) /\ (OwnSymbolsOf u))) +* ( the adicity of S | EE2) is Relation-like the U1 of S \ { the U3 of S} -defined INT -valued Function-like Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
the adicity of u | (((rng hhh) /\ (OwnSymbolsOf u)) \/ EE1) is Relation-like the U1 of u \ { the U3 of u} -defined ((rng hhh) /\ (OwnSymbolsOf u)) \/ EE1 -defined the U1 of u \ { the U3 of u} -defined INT -valued Function-like Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
the adicity of S | (((rng hhh) /\ (OwnSymbolsOf u)) \/ EE2) is Relation-like the U1 of S \ { the U3 of S} -defined ((rng hhh) /\ (OwnSymbolsOf u)) \/ EE2 -defined the U1 of S \ { the U3 of S} -defined INT -valued Function-like Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
( the adicity of u | (((rng hhh) /\ (OwnSymbolsOf u)) \/ EE1)) . b1 is set
the adicity of S . b1 is set
dom the adicity of S is non empty Element of bool ( the U1 of S \ { the U3 of S})
r2 is ofAtomicFormula Element of AllSymbolsOf S
ar r2 is finite complex ext-real V40() V41() Element of INT
the adicity of S . r2 is set
r2 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
tt2 is Relation-like NAT -defined AllTermsOf S -valued Function-like finite abs (ar b1) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
(S,r2,tt2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf S) *) \ {{}}
<*r2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf S) *) \ {{}}
[1,r2] is non empty set
{[1,r2]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf S) *
(S -multiCat) . tt2 is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf S) *
<*r2*> ^ ((S -multiCat) . tt2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
phi2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
ss -AtomicEval phi2 is boolean Element of BOOLEAN
ss === is Relation-like Function-like Function-yielding V164() S,U -interpreter-like ss -extension set
TheEqSymbOf S is Element of AtomicFormulaSymbolsOf S
(TheEqSymbOf S) .--> (U -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf S -defined {(TheEqSymbOf S)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf S)} is non empty trivial finite 1 -element set
{(TheEqSymbOf S)} --> (U -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf S)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued {(U -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:]
[:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:] is non empty finite finite-membered set
ss +* ((TheEqSymbOf S) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(S -firstChar) . phi2 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
(ss ===) . ((S -firstChar) . phi2) is non empty Relation-like (abs (ar ((S -firstChar) . phi2))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . phi2,U
ar ((S -firstChar) . phi2) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of S . ((S -firstChar) . phi2) is set
abs (ar ((S -firstChar) . phi2)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((S -firstChar) . phi2))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms phi2 is Relation-like NAT -defined (rng phi2) * -valued (TermSymbolsOf S) * -valued AllTermsOf S -valued Function-like finite abs (ar ((S -firstChar) . phi2)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
rng phi2 is non empty finite set
(rng phi2) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng phi2
(TermSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf S
AllTermsOf S is non empty functional finite-membered FinSequence-membered AllSymbolsOf S -prefix S -prefix Element of bool ((AllSymbolsOf S) *)
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) *)
(ss -TermEval) (*) (SubTerms phi2) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((ss ===) . ((S -firstChar) . phi2)) . ((ss -TermEval) (*) (SubTerms phi2)) is set
ss -TruthEval phi2 is boolean Element of BOOLEAN
<*b1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
[1,b1] is non empty set
{[1,b1]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
(u -multiCat) . A1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
<*b1*> ^ ((u -multiCat) . A1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
phi2 . 1 is set
tt22 is Relation-like NAT -defined AllTermsOf S -valued Function-like finite abs (ar ((S -firstChar) . phi2)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
(s -TermEval) * A1 is non empty Relation-like NAT -defined U -valued Function-like finite (abs (ar b1)) + 0 -element len A1 -element FinSequence-like FinSubsequence-like finite-support FinSequence of U
len A1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
((s -TermEval) | (((rng hhh) /\ (OwnSymbolsOf u)) *)) * A1 is Relation-like NAT -defined U -valued Function-like finite finite-support Element of bool [:NAT,U:]
[:NAT,U:] is non empty non trivial Relation-like non finite V166() set
bool [:NAT,U:] is non empty non trivial non finite V166() set
s . b1 is Relation-like Function-like set
(s | ((rng hhh) /\ (OwnSymbolsOf u))) . b1 is Relation-like Function-like set
ss . r2 is Relation-like Function-like set
(s . b1) . ((s -TermEval) * A1) is set
(s . b1) . ((ss -TermEval) (*) (SubTerms phi2)) is set
(U -deltaInterpreter) . ((s -TermEval) * A1) is boolean set
(U -deltaInterpreter) . ((ss -TermEval) (*) (SubTerms phi2)) is boolean set
U is non empty set
U * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of U
U \/ BOOLEAN is non empty set
K546((U *),(U \/ BOOLEAN)) is non empty functional M31(U * ,U \/ BOOLEAN)
u is V51() V53() eligible Language-like
TheNorSymbOf u is non literal non low-compounding non relational non own Element of AllSymbolsOf u
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
the U3 of u is Element of the U1 of u
TheEqSymbOf u is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf u
the U2 of u is Element of the U1 of u
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
OwnSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
AllSymbolsOf u is non empty non trivial non finite V166() set
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
{ the U2 of u, the U3 of u} is non empty finite set
the U1 of u \ { the U2 of u, the U3 of u} is Element of bool the U1 of u
the U1 of u typed\ { the U2 of u, the U3 of u} is Element of bool the U1 of u
the adicity of u | (OwnSymbolsOf u) is Relation-like the U1 of u \ { the U3 of u} -defined OwnSymbolsOf u -defined the U1 of u \ { the U3 of u} -defined INT -valued Function-like Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf u,K546((U *),(U \/ BOOLEAN))
U -InterpretersOf u is non empty functional Element of bool (Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf u -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN))) : b₁ is u,U -interpreter-like } is set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
S is V51() V53() eligible Language-like
TheNorSymbOf S is non literal non low-compounding non relational non own Element of AllSymbolsOf S
AllSymbolsOf S is non empty non trivial non finite V166() set
the U1 of S is set
the U3 of S is Element of the U1 of S
TheEqSymbOf S is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf S
the U2 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 V166() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V166() set
the adicity of S | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined the U1 of S \ { the U3 of S} -defined INT -valued Function-like Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V166() set
bool (AllSymbolsOf S) is non empty non trivial non finite V166() set
{ 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
Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S,K546((U *),(U \/ BOOLEAN))
U -InterpretersOf S is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN))) : b₁ is S,U -interpreter-like } is set
(AllSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite V166() set
((AllSymbolsOf S) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf S) *)
u -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
[:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(AllSymbolsOf u) -pr1 is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total V233( AllSymbolsOf u) Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
[:(AllSymbolsOf u),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf u),(AllSymbolsOf u)) is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
MultPlace ((AllSymbolsOf u) -pr1) is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
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 V166() set
bool [:(((AllSymbolsOf S) *) \ {{}}),(AllSymbolsOf S):] is non empty non trivial non finite V166() 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 V233( AllSymbolsOf S) Element of bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):]
[:(AllSymbolsOf S),(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf S),(AllSymbolsOf S):],(AllSymbolsOf S):] is non empty non trivial non finite V166() set
K415((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):]
U -deltaInterpreter is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
2 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
[:(2 -tuples_on U),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on U),BOOLEAN:] is non empty set
[:(U *),(U *):] is non empty non trivial Relation-like non finite V166() set
U -concatenation is non empty Relation-like [:(U *),(U *):] -defined U * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233(U * ) Element of bool [:[:(U *),(U *):],(U *):]
[:[:(U *),(U *):],(U *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(U *),(U *):],(U *):] is non empty non trivial non finite V166() set
1 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
id (1 -tuples_on U) is non empty Relation-like non empty-yielding 1 -tuples_on U -defined 1 -tuples_on U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(1 -tuples_on U),(1 -tuples_on U):]
[:(1 -tuples_on U),(1 -tuples_on U):] is non empty Relation-like set
bool [:(1 -tuples_on U),(1 -tuples_on U):] is non empty set
(U -concatenation) .: (id (1 -tuples_on U)) is functional finite-membered FinSequence-membered Element of bool (U *)
bool (U *) is non empty non trivial non finite V166() set
chi (((U -concatenation) .: (id (1 -tuples_on U))),(2 -tuples_on U)) is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
AtomicFormulaSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
TheNorSymbOf u is set
{(TheNorSymbOf u)} is non empty trivial finite 1 -element set
(AllSymbolsOf u) \ {(TheNorSymbOf u)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
(AllSymbolsOf u) typed\ {(TheNorSymbOf u)} is Element of bool (AllSymbolsOf u)
AtomicFormulaSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
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 V166() Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V166() set
(AllSymbolsOf S) typed\ {(TheNorSymbOf S)} is Element of bool (AllSymbolsOf S)
h is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
h | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined OwnSymbolsOf u -defined OwnSymbolsOf u -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total Function-yielding V164() u,U -interpreter-like set
h null (OwnSymbolsOf u) is Relation-like (OwnSymbolsOf u) \/ (dom h) -defined (OwnSymbolsOf u) \/ (rng h) -valued Function-like set
dom h is set
(OwnSymbolsOf u) \/ (dom h) is non empty set
rng h is set
(OwnSymbolsOf u) \/ (rng h) is non empty set
h \typed/ (OwnSymbolsOf u) is Element of bool (h \/ (OwnSymbolsOf u))
h \/ (OwnSymbolsOf u) is non empty set
bool (h \/ (OwnSymbolsOf u)) is non empty set
G is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
G | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined OwnSymbolsOf S -defined Function-like Function-yielding V164() set
n is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
h -TruthEval n is boolean Element of BOOLEAN
h -AtomicEval n is boolean Element of BOOLEAN
h === is Relation-like Function-like Function-yielding V164() u,U -interpreter-like h -extension set
TheEqSymbOf u is Element of AtomicFormulaSymbolsOf u
(TheEqSymbOf u) .--> (U -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf u -defined {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf u)} is non empty trivial finite 1 -element set
{(TheEqSymbOf u)} --> (U -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued {(U -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:]
{(U -deltaInterpreter)} is non empty trivial functional finite 1 -element V165() V166() set
[:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty finite finite-membered set
h +* ((TheEqSymbOf u) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(u -firstChar) . n is low-compounding relational ofAtomicFormula Element of AllSymbolsOf u
(h ===) . ((u -firstChar) . n) is non empty Relation-like (abs (ar ((u -firstChar) . n))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . n,U
ar ((u -firstChar) . n) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of u . ((u -firstChar) . n) is set
abs (ar ((u -firstChar) . n)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((u -firstChar) . n))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms n is Relation-like NAT -defined (rng n) * -valued (TermSymbolsOf u) * -valued AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . n)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
rng n is non empty finite set
(rng n) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng n
TermSymbolsOf u is non empty set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
(TermSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf u
AllTermsOf u is non empty functional finite-membered FinSequence-membered AllSymbolsOf u -prefix u -prefix Element of bool ((AllSymbolsOf u) *)
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
((AllSymbolsOf u) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf u) *
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf u) *) *)
bool (((AllSymbolsOf u) *) *) is non empty non trivial non finite V166() set
h -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(h -TermEval) (*) (SubTerms n) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((h ===) . ((u -firstChar) . n)) . ((h -TermEval) (*) (SubTerms n)) is set
G -TermEval is non empty Relation-like AllTermsOf S -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),U:]
AllTermsOf S is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() set
S -termsOfMaxDepth is Relation-like Function-like set
rng (S -termsOfMaxDepth) is set
union (rng (S -termsOfMaxDepth)) is set
[:(AllTermsOf S),U:] is non empty Relation-like set
bool [:(AllTermsOf S),U:] is non empty set
bool (OwnSymbolsOf u) is non empty set
(rng n) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
(rng n) typed/\ (OwnSymbolsOf u) is finite Element of bool (rng n)
bool (rng n) is non empty finite finite-membered set
(rng n) /\ (OwnSymbolsOf u) is finite set
(rng n) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
hh is Element of bool (OwnSymbolsOf u)
the adicity of u | hh is Relation-like the U1 of u \ { the U3 of u} -defined hh -defined the U1 of u \ { the U3 of u} -defined INT -valued Function-like Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
( the adicity of u | (OwnSymbolsOf u)) | (rng n) is Relation-like the U1 of u \ { the U3 of u} -defined rng n -defined the U1 of u \ { the U3 of u} -defined INT -valued Function-like finite finite-support Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
the adicity of S | hh is Relation-like the U1 of S \ { the U3 of S} -defined hh -defined the U1 of S \ { the U3 of S} -defined INT -valued Function-like Element of bool [:( the U1 of S \ { the U3 of S}),INT:]
(G | (OwnSymbolsOf u)) | (rng n) is Relation-like rng n -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
h | hh is Relation-like hh -defined OwnSymbolsOf u -defined Function-like total Function-yielding V164() set
G | hh is Relation-like hh -defined OwnSymbolsOf S -defined Function-like Function-yielding V164() set
s is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
G -AtomicEval s is boolean Element of BOOLEAN
G === is Relation-like Function-like Function-yielding V164() S,U -interpreter-like G -extension set
TheEqSymbOf S is Element of AtomicFormulaSymbolsOf S
(TheEqSymbOf S) .--> (U -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf S -defined {(TheEqSymbOf S)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf S)} is non empty trivial finite 1 -element set
{(TheEqSymbOf S)} --> (U -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf S)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued {(U -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:]
[:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:] is non empty finite finite-membered set
G +* ((TheEqSymbOf S) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(S -firstChar) . s is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
(G ===) . ((S -firstChar) . s) is non empty Relation-like (abs (ar ((S -firstChar) . s))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . s,U
ar ((S -firstChar) . s) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of S . ((S -firstChar) . s) is set
abs (ar ((S -firstChar) . s)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((S -firstChar) . s))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms s is Relation-like NAT -defined (rng s) * -valued (TermSymbolsOf S) * -valued AllTermsOf S -valued Function-like finite abs (ar ((S -firstChar) . s)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
rng s is non empty finite set
(rng s) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng s
TermSymbolsOf S is non empty 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
(TermSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf S
AllTermsOf S is non empty functional finite-membered FinSequence-membered AllSymbolsOf S -prefix S -prefix Element of bool ((AllSymbolsOf S) *)
((AllSymbolsOf S) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf S) *
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) *)
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V166() set
(G -TermEval) (*) (SubTerms s) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((G ===) . ((S -firstChar) . s)) . ((G -TermEval) (*) (SubTerms s)) is set
G -TruthEval s is boolean Element of BOOLEAN
ss is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
G -TruthEval ss is boolean Element of BOOLEAN
G -AtomicEval ss is boolean Element of BOOLEAN
(S -firstChar) . ss is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
(G ===) . ((S -firstChar) . ss) is non empty Relation-like (abs (ar ((S -firstChar) . ss))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . ss,U
ar ((S -firstChar) . ss) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of S . ((S -firstChar) . ss) is set
abs (ar ((S -firstChar) . ss)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((S -firstChar) . ss))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms ss is Relation-like NAT -defined (rng ss) * -valued (TermSymbolsOf S) * -valued AllTermsOf S -valued Function-like finite abs (ar ((S -firstChar) . ss)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
rng ss is non empty finite set
(rng ss) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng ss
(G -TermEval) (*) (SubTerms ss) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((G ===) . ((S -firstChar) . ss)) . ((G -TermEval) (*) (SubTerms ss)) 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
G is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
G | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined OwnSymbolsOf u -defined OwnSymbolsOf u -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total Function-yielding V164() u,U -interpreter-like set
G null (OwnSymbolsOf u) is Relation-like (OwnSymbolsOf u) \/ (dom G) -defined (OwnSymbolsOf u) \/ (rng G) -valued Function-like set
dom G is set
(OwnSymbolsOf u) \/ (dom G) is non empty set
rng G is set
(OwnSymbolsOf u) \/ (rng G) is non empty set
G \typed/ (OwnSymbolsOf u) is Element of bool (G \/ (OwnSymbolsOf u))
G \/ (OwnSymbolsOf u) is non empty set
bool (G \/ (OwnSymbolsOf u)) is non empty set
n is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
n | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined OwnSymbolsOf S -defined Function-like Function-yielding V164() set
Enn is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h + 1 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
G -TruthEval Enn is boolean Element of BOOLEAN
rng Enn is non empty finite set
head Enn is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
SubWffsOf Enn is set
K74((SubWffsOf Enn)) is set
tail Enn is Relation-like NAT -defined AllSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (AllSymbolsOf u) *
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
K75((SubWffsOf Enn)) is set
(u -firstChar) . Enn is Element of AllSymbolsOf u
nE is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
G -TruthEval nE is boolean Element of BOOLEAN
s is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
n -TruthEval s is boolean Element of BOOLEAN
ss is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff h + 1 -wff wff exal Element of ((AllSymbolsOf u) *) \ {{}}
(u -firstChar) . ss is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
phi22 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
G . phi22 is non empty Relation-like (abs (ar phi22)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of phi22,U
ar phi22 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
the adicity of u . phi22 is set
abs (ar phi22) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
(abs (ar phi22)) -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
n . phi22 is Relation-like Function-like set
dom n is Element of bool (OwnSymbolsOf S)
bool (OwnSymbolsOf S) is non empty set
c₃₀ is own ofAtomicFormula Element of AllSymbolsOf S
ar c₃₀ is finite complex ext-real V40() V41() Element of INT
the adicity of S . c₃₀ is set
abs (ar c₃₀) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar c₃₀)) -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
n . c₃₀ is non empty Relation-like (abs (ar c₃₀)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of c₃₀,U
dom (n . c₃₀) is non empty functional finite-membered FinSequence-membered Element of bool ((abs (ar c₃₀)) -tuples_on U)
bool ((abs (ar c₃₀)) -tuples_on U) is non empty set
0 -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
phi2 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
<*phi2*> is non empty trivial Relation-like NAT -defined TermSymbolsOf S -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support 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})
bool ( the U1 of S \ { the U3 of S}) is non empty set
[1,phi2] is non empty set
{[1,phi2]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
<*phi2*> ^ s is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff h + 1 -wff 1 + (Depth s) -wff non Depth s -wff wff exal Element of ((AllSymbolsOf S) *) \ {{}}
Depth s is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (Depth s) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff h + 1 -wff wff exal Element of ((AllSymbolsOf S) *) \ {{}}
n -TruthEval b1 is boolean Element of BOOLEAN
<*phi22*> is non empty trivial Relation-like NAT -defined TermSymbolsOf u -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf u) *) \ {{}}
TermSymbolsOf u is non empty set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
[1,phi22] is non empty set
{[1,phi22]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
<*phi22*> ^ nE is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff h + 1 -wff 1 + (Depth nE) -wff non Depth nE -wff wff exal Element of ((AllSymbolsOf u) *) \ {{}}
Depth nE is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (Depth nE) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
tail ss is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued AllSymbolsOf u -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllSymbolsOf u) *
SubWffsOf ss is set
K75((SubWffsOf ss)) is set
(<*phi22*> ^ nE) ^ (tail ss) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(<*phi22*> ^ nE) null (tail ss) is Relation-like NAT -defined (tail ss) \/ (dom (<*phi22*> ^ nE)) -defined (tail ss) \/ (rng (<*phi22*> ^ nE)) -valued Function-like finite len (<*phi22*> ^ nE) -element FinSequence-like FinSubsequence-like finite-support set
dom (<*phi22*> ^ nE) is non empty finite set
(tail ss) \/ (dom (<*phi22*> ^ nE)) is non empty finite set
rng (<*phi22*> ^ nE) is non empty finite set
(tail ss) \/ (rng (<*phi22*> ^ nE)) is non empty finite set
len (<*phi22*> ^ nE) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(<*phi22*> ^ nE) \typed/ (tail ss) is Relation-like NAT -defined finite Element of bool ((<*phi22*> ^ nE) \/ (tail ss))
(<*phi22*> ^ nE) \/ (tail ss) is non empty Relation-like NAT -defined finite set
bool ((<*phi22*> ^ nE) \/ (tail ss)) is non empty finite finite-membered set
(tail ss) ^ (<*phi22*> ^ nE) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
G -TruthEval ss is boolean Element of BOOLEAN
c1 is Element of U
(phi22,c1) ReassignIn G is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> c1 is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> c1 is non empty Relation-like {{}} -defined U -valued {c1} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{c1}:]
{c1} is non empty trivial finite 1 -element set
[:{{}},{c1}:] is non empty Relation-like finite set
bool [:{{}},{c1}:] is non empty finite finite-membered set
phi22 .--> ({} .--> c1) is trivial Relation-like AllSymbolsOf u -defined {phi22} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{phi22} is non empty trivial finite 1 -element set
{phi22} --> ({} .--> c1) is non empty Relation-like {phi22} -defined {({} .--> c1)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{phi22},{({} .--> c1)}:]
{({} .--> c1)} is non empty trivial functional finite finite-membered 1 -element set
[:{phi22},{({} .--> c1)}:] is non empty Relation-like finite set
bool [:{phi22},{({} .--> c1)}:] is non empty finite finite-membered set
G +* (phi22 .--> ({} .--> c1)) is Relation-like Function-like Function-yielding V164() set
((phi22,c1) ReassignIn G) -TruthEval nE is boolean Element of BOOLEAN
(phi2,c1) ReassignIn n is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
phi2 .--> ({} .--> c1) is trivial Relation-like AllSymbolsOf S -defined {phi2} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{phi2} is non empty trivial finite 1 -element set
{phi2} --> ({} .--> c1) is non empty Relation-like {phi2} -defined {({} .--> c1)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{phi2},{({} .--> c1)}:]
[:{phi2},{({} .--> c1)}:] is non empty Relation-like finite set
bool [:{phi2},{({} .--> c1)}:] is non empty finite finite-membered set
n +* (phi2 .--> ({} .--> c1)) is Relation-like Function-like Function-yielding V164() set
b2 is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
b2 | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined OwnSymbolsOf u -defined OwnSymbolsOf u -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total Function-yielding V164() u,U -interpreter-like set
b2 null (OwnSymbolsOf u) is Relation-like (OwnSymbolsOf u) \/ (dom b2) -defined (OwnSymbolsOf u) \/ (rng b2) -valued Function-like set
dom b2 is set
(OwnSymbolsOf u) \/ (dom b2) is non empty set
rng b2 is set
(OwnSymbolsOf u) \/ (rng b2) is non empty set
b2 \typed/ (OwnSymbolsOf u) is Element of bool (b2 \/ (OwnSymbolsOf u))
b2 \/ (OwnSymbolsOf u) is non empty set
bool (b2 \/ (OwnSymbolsOf u)) is non empty set
(phi22 .--> ({} .--> c1)) | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined AllSymbolsOf u -defined Function-like constant finite Function-yielding V164() finite-support set
(G | (OwnSymbolsOf u)) +* ((phi22 .--> ({} .--> c1)) | (OwnSymbolsOf u)) is Relation-like Function-like Function-yielding V164() set
c2 is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
c2 | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined OwnSymbolsOf S -defined Function-like Function-yielding V164() set
b2 -TruthEval nE is boolean Element of BOOLEAN
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
c2 -TruthEval A1 is boolean Element of BOOLEAN
c1 is Element of U
(phi2,c1) ReassignIn n is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
{} .--> c1 is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> c1 is non empty Relation-like {{}} -defined U -valued {c1} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{c1}:]
{c1} is non empty trivial finite 1 -element set
[:{{}},{c1}:] is non empty Relation-like finite set
bool [:{{}},{c1}:] is non empty finite finite-membered set
phi2 .--> ({} .--> c1) is trivial Relation-like AllSymbolsOf S -defined {phi2} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{phi2} --> ({} .--> c1) is non empty Relation-like {phi2} -defined {({} .--> c1)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{phi2},{({} .--> c1)}:]
{({} .--> c1)} is non empty trivial functional finite finite-membered 1 -element set
[:{phi2},{({} .--> c1)}:] is non empty Relation-like finite set
bool [:{phi2},{({} .--> c1)}:] is non empty finite finite-membered set
n +* (phi2 .--> ({} .--> c1)) is Relation-like Function-like Function-yielding V164() set
((phi2,c1) ReassignIn n) -TruthEval s is boolean Element of BOOLEAN
(phi22,c1) ReassignIn G is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
phi22 .--> ({} .--> c1) is trivial Relation-like AllSymbolsOf u -defined {phi22} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{phi22} --> ({} .--> c1) is non empty Relation-like {phi22} -defined {({} .--> c1)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{phi22},{({} .--> c1)}:]
[:{phi22},{({} .--> c1)}:] is non empty Relation-like finite set
bool [:{phi22},{({} .--> c1)}:] is non empty finite finite-membered set
G +* (phi22 .--> ({} .--> c1)) is Relation-like Function-like Function-yielding V164() set
b2 is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
b2 | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined OwnSymbolsOf u -defined OwnSymbolsOf u -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total Function-yielding V164() u,U -interpreter-like set
b2 null (OwnSymbolsOf u) is Relation-like (OwnSymbolsOf u) \/ (dom b2) -defined (OwnSymbolsOf u) \/ (rng b2) -valued Function-like set
dom b2 is set
(OwnSymbolsOf u) \/ (dom b2) is non empty set
rng b2 is set
(OwnSymbolsOf u) \/ (rng b2) is non empty set
b2 \typed/ (OwnSymbolsOf u) is Element of bool (b2 \/ (OwnSymbolsOf u))
b2 \/ (OwnSymbolsOf u) is non empty set
bool (b2 \/ (OwnSymbolsOf u)) is non empty set
(phi22 .--> ({} .--> c1)) | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined AllSymbolsOf u -defined Function-like constant finite Function-yielding V164() finite-support set
(G | (OwnSymbolsOf u)) +* ((phi22 .--> ({} .--> c1)) | (OwnSymbolsOf u)) is Relation-like Function-like Function-yielding V164() set
c2 is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
c2 | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined OwnSymbolsOf S -defined Function-like Function-yielding V164() set
b2 -TruthEval nE is boolean Element of BOOLEAN
A1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
c2 -TruthEval A1 is boolean Element of BOOLEAN
ss is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff h + 1 -wff wff non exal Element of ((AllSymbolsOf u) *) \ {{}}
tail ss is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
SubWffsOf ss is set
K75((SubWffsOf ss)) is set
phi22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
G -TruthEval phi22 is boolean Element of BOOLEAN
c₃₀ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
n -TruthEval c₃₀ is boolean Element of BOOLEAN
<*(TheNorSymbOf S)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf S) *) \ {{}}
[1,(TheNorSymbOf S)] is non empty set
{[1,(TheNorSymbOf S)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
<*(TheNorSymbOf S)*> ^ s is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non exal Element of ((AllSymbolsOf S) *) \ {{}}
(<*(TheNorSymbOf S)*> ^ s) ^ c₃₀ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff non max ((Depth s),(Depth c₃₀)) -wff h + 1 -wff wff non exal Element of ((AllSymbolsOf S) *) \ {{}}
Depth s is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
Depth c₃₀ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
max ((Depth s),(Depth c₃₀)) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
phi2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff h + 1 -wff wff non exal Element of ((AllSymbolsOf S) *) \ {{}}
n -TruthEval phi2 is boolean Element of BOOLEAN
(u -firstChar) . ss is non relational Element of AllSymbolsOf u
((u -firstChar) . ss) \+\ (TheNorSymbOf u) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
((u -firstChar) . ss) \ (TheNorSymbOf u) is set
((u -firstChar) . ss) typed\ (TheNorSymbOf u) is Element of bool ((u -firstChar) . ss)
bool ((u -firstChar) . ss) is non empty set
((u -firstChar) . ss) \ (TheNorSymbOf u) is Element of bool ((u -firstChar) . ss)
(TheNorSymbOf u) \ ((u -firstChar) . ss) is set
(TheNorSymbOf u) typed\ ((u -firstChar) . ss) is Element of bool (TheNorSymbOf u)
bool (TheNorSymbOf u) is non empty set
(TheNorSymbOf u) \ ((u -firstChar) . ss) is Element of bool (TheNorSymbOf u)
(((u -firstChar) . ss) \ (TheNorSymbOf u)) \/ ((TheNorSymbOf u) \ ((u -firstChar) . ss)) is set
(S -firstChar) . phi2 is non relational Element of AllSymbolsOf S
((S -firstChar) . phi2) \+\ (TheNorSymbOf 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
((S -firstChar) . phi2) \ (TheNorSymbOf S) is set
((S -firstChar) . phi2) typed\ (TheNorSymbOf S) is Element of bool ((S -firstChar) . phi2)
bool ((S -firstChar) . phi2) is non empty set
((S -firstChar) . phi2) \ (TheNorSymbOf S) is Element of bool ((S -firstChar) . phi2)
(TheNorSymbOf S) \ ((S -firstChar) . phi2) is set
(TheNorSymbOf S) typed\ ((S -firstChar) . phi2) is Element of bool (TheNorSymbOf S)
bool (TheNorSymbOf S) is non empty set
(TheNorSymbOf S) \ ((S -firstChar) . phi2) is Element of bool (TheNorSymbOf S)
(((S -firstChar) . phi2) \ (TheNorSymbOf S)) \/ ((TheNorSymbOf S) \ ((S -firstChar) . phi2)) is set
<*((u -firstChar) . ss)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
[1,((u -firstChar) . ss)] is non empty set
{[1,((u -firstChar) . ss)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
<*((u -firstChar) . ss)*> ^ nE is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff Element of ((AllSymbolsOf u) *) \ {{}}
(<*((u -firstChar) . ss)*> ^ nE) ^ phi22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff Element of ((AllSymbolsOf u) *) \ {{}}
head phi2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
SubWffsOf phi2 is set
K74((SubWffsOf phi2)) is set
tail phi2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
K75((SubWffsOf phi2)) is set
G -TruthEval ss is boolean Element of BOOLEAN
head ss is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
K74((SubWffsOf ss)) is set
G -TruthEval (head ss) is boolean Element of BOOLEAN
G -TruthEval (tail ss) is boolean Element of BOOLEAN
(G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss)) is set
(G -TruthEval (head ss)) 'or' (G -TruthEval (tail ss)) is set
'not' (G -TruthEval (head ss)) is boolean set
1 - (G -TruthEval (head ss)) is set
'not' (G -TruthEval (tail ss)) is boolean set
1 - (G -TruthEval (tail ss)) is set
('not' (G -TruthEval (head ss))) '&' ('not' (G -TruthEval (tail ss))) is set
('not' (G -TruthEval (head ss))) * ('not' (G -TruthEval (tail ss))) is set
'not' (('not' (G -TruthEval (head ss))) '&' ('not' (G -TruthEval (tail ss)))) is boolean set
'not' ((G -TruthEval (head ss)) 'or' (G -TruthEval (tail ss))) is boolean set
(G -TruthEval ss) \+\ ((G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss))) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(G -TruthEval ss) \ ((G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss))) is set
(G -TruthEval ss) typed\ ((G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss))) is Element of bool (G -TruthEval ss)
bool (G -TruthEval ss) is non empty set
(G -TruthEval ss) \ ((G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss))) is Element of bool (G -TruthEval ss)
((G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss))) \ (G -TruthEval ss) is set
((G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss))) typed\ (G -TruthEval ss) is Element of bool ((G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss)))
bool ((G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss))) is non empty set
((G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss))) \ (G -TruthEval ss) is Element of bool ((G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss)))
((G -TruthEval ss) \ ((G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss)))) \/ (((G -TruthEval (head ss)) 'nor' (G -TruthEval (tail ss))) \ (G -TruthEval ss)) is set
n -TruthEval (head phi2) is boolean Element of BOOLEAN
n -TruthEval (tail phi2) is boolean Element of BOOLEAN
(n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2)) is set
(n -TruthEval (head phi2)) 'or' (n -TruthEval (tail phi2)) is set
'not' (n -TruthEval (head phi2)) is boolean set
1 - (n -TruthEval (head phi2)) is set
'not' (n -TruthEval (tail phi2)) is boolean set
1 - (n -TruthEval (tail phi2)) is set
('not' (n -TruthEval (head phi2))) '&' ('not' (n -TruthEval (tail phi2))) is set
('not' (n -TruthEval (head phi2))) * ('not' (n -TruthEval (tail phi2))) is set
'not' (('not' (n -TruthEval (head phi2))) '&' ('not' (n -TruthEval (tail phi2)))) is boolean set
'not' ((n -TruthEval (head phi2)) 'or' (n -TruthEval (tail phi2))) is boolean set
(n -TruthEval phi2) \+\ ((n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2))) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(n -TruthEval phi2) \ ((n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2))) is set
(n -TruthEval phi2) typed\ ((n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2))) is Element of bool (n -TruthEval phi2)
bool (n -TruthEval phi2) is non empty set
(n -TruthEval phi2) \ ((n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2))) is Element of bool (n -TruthEval phi2)
((n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2))) \ (n -TruthEval phi2) is set
((n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2))) typed\ (n -TruthEval phi2) is Element of bool ((n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2)))
bool ((n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2))) is non empty set
((n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2))) \ (n -TruthEval phi2) is Element of bool ((n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2)))
((n -TruthEval phi2) \ ((n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2)))) \/ (((n -TruthEval (head phi2)) 'nor' (n -TruthEval (tail phi2))) \ (n -TruthEval phi2)) is set
(G -TruthEval nE) 'nor' (G -TruthEval phi22) is set
(G -TruthEval nE) 'or' (G -TruthEval phi22) is set
'not' (G -TruthEval nE) is boolean set
1 - (G -TruthEval nE) is set
'not' (G -TruthEval phi22) is boolean set
1 - (G -TruthEval phi22) is set
('not' (G -TruthEval nE)) '&' ('not' (G -TruthEval phi22)) is set
('not' (G -TruthEval nE)) * ('not' (G -TruthEval phi22)) is set
'not' (('not' (G -TruthEval nE)) '&' ('not' (G -TruthEval phi22))) is boolean set
'not' ((G -TruthEval nE) 'or' (G -TruthEval phi22)) is boolean set
(n -TruthEval s) 'nor' (n -TruthEval c₃₀) is set
(n -TruthEval s) 'or' (n -TruthEval c₃₀) is set
'not' (n -TruthEval s) is boolean set
1 - (n -TruthEval s) is set
'not' (n -TruthEval c₃₀) is boolean set
1 - (n -TruthEval c₃₀) is set
('not' (n -TruthEval s)) '&' ('not' (n -TruthEval c₃₀)) is set
('not' (n -TruthEval s)) * ('not' (n -TruthEval c₃₀)) is set
'not' (('not' (n -TruthEval s)) '&' ('not' (n -TruthEval c₃₀))) is boolean set
'not' ((n -TruthEval s) 'or' (n -TruthEval c₃₀)) is boolean set
ss is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
n -TruthEval ss is boolean Element of BOOLEAN
n -AtomicEval ss is boolean Element of BOOLEAN
n === is Relation-like Function-like Function-yielding V164() S,U -interpreter-like n -extension set
TheEqSymbOf S is Element of AtomicFormulaSymbolsOf S
(TheEqSymbOf S) .--> (U -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf S -defined {(TheEqSymbOf S)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf S)} is non empty trivial finite 1 -element set
{(TheEqSymbOf S)} --> (U -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf S)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued {(U -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:]
{(U -deltaInterpreter)} is non empty trivial functional finite 1 -element V165() V166() set
[:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf S)},{(U -deltaInterpreter)}:] is non empty finite finite-membered set
n +* ((TheEqSymbOf S) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(S -firstChar) . ss is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
(n ===) . ((S -firstChar) . ss) is non empty Relation-like (abs (ar ((S -firstChar) . ss))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (S -firstChar) . ss,U
ar ((S -firstChar) . ss) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of S . ((S -firstChar) . ss) is set
abs (ar ((S -firstChar) . ss)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((S -firstChar) . ss))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms ss is Relation-like NAT -defined (rng ss) * -valued (TermSymbolsOf S) * -valued AllTermsOf S -valued Function-like finite abs (ar ((S -firstChar) . ss)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf S) *
rng ss is non empty finite set
(rng ss) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng ss
TermSymbolsOf S is non empty 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
(TermSymbolsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf S
AllTermsOf S is non empty functional finite-membered FinSequence-membered AllSymbolsOf S -prefix S -prefix Element of bool ((AllSymbolsOf S) *)
S -termsOfMaxDepth is Relation-like Function-like set
rng (S -termsOfMaxDepth) is set
union (rng (S -termsOfMaxDepth)) is set
((AllSymbolsOf S) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf S) *
(AllTermsOf S) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf S) *) *)
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite V166() set
n -TermEval is non empty Relation-like AllTermsOf S -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf S),U:]
AllTermsOf S is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf S -prefix S -prefix Element of K335((((AllSymbolsOf S) *) \ {{}}))
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite V166() set
[:(AllTermsOf S),U:] is non empty Relation-like set
bool [:(AllTermsOf S),U:] is non empty set
(n -TermEval) (*) (SubTerms ss) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((n ===) . ((S -firstChar) . ss)) . ((n -TermEval) (*) (SubTerms ss)) is set
0 * (h + 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
0 + (0 * (h + 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
0 + (h + 1) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
phi22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support h + 1 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
n -TruthEval phi22 is boolean Element of BOOLEAN
h is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
h | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined OwnSymbolsOf u -defined OwnSymbolsOf u -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total Function-yielding V164() u,U -interpreter-like set
h null (OwnSymbolsOf u) is Relation-like (OwnSymbolsOf u) \/ (dom h) -defined (OwnSymbolsOf u) \/ (rng h) -valued Function-like set
dom h is set
(OwnSymbolsOf u) \/ (dom h) is non empty set
rng h is set
(OwnSymbolsOf u) \/ (rng h) is non empty set
h \typed/ (OwnSymbolsOf u) is Element of bool (h \/ (OwnSymbolsOf u))
h \/ (OwnSymbolsOf u) is non empty set
bool (h \/ (OwnSymbolsOf u)) is non empty set
G is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
G | (OwnSymbolsOf u) is Relation-like OwnSymbolsOf u -defined OwnSymbolsOf S -defined Function-like Function-yielding V164() set
n is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
h -TruthEval n is boolean Element of BOOLEAN
Depth n is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth n) + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(u,0,n) is non empty Relation-like NAT -defined 0 \/ (dom n) -defined 0 \/ (rng n) -valued Function-like finite len n -element FinSequence-like FinSubsequence-like finite-support (Depth n) + 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
dom n is non empty finite set
0 \/ (dom n) is non empty finite set
rng n is non empty finite set
0 \/ (rng n) is non empty finite set
len n is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(Depth n) + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
n \typed/ 0 is Relation-like NAT -defined finite Element of bool (n \/ 0)
n \/ 0 is non empty Relation-like NAT -defined finite set
bool (n \/ 0) is non empty finite finite-membered set
n null 0 is Relation-like NAT -defined 0 \/ (dom n) -defined 0 \/ (rng n) -valued Function-like finite len n -element FinSequence-like FinSubsequence-like finite-support set
n ^ 0 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
0 ^ n is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
En is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support (Depth n) + 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
h -TruthEval En is boolean Element of BOOLEAN
nE is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Depth n -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
G -TruthEval nE is boolean Element of BOOLEAN
U is non empty set
U * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of U
U \/ BOOLEAN is non empty set
K546((U *),(U \/ BOOLEAN)) is non empty functional M31(U * ,U \/ BOOLEAN)
u is V51() V53() eligible Language-like
AllSymbolsOf u is non empty non trivial non finite V166() set
the U1 of u is set
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
((AllSymbolsOf u) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf u) *)
bool ((AllSymbolsOf u) *) is non empty non trivial non finite V166() set
((AllSymbolsOf u) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf u) *)
OwnSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
the U2 of u is Element of the U1 of u
the U3 of u is Element of the U1 of u
{ the U2 of u, the U3 of u} is non empty finite set
the U1 of u \ { the U2 of u, the U3 of u} is Element of bool the U1 of u
bool the U1 of u is non empty set
the U1 of u typed\ { the U2 of u, the U3 of u} is Element of bool the U1 of u
Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf u,K546((U *),(U \/ BOOLEAN))
U -InterpretersOf u is non empty functional Element of bool (Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf u -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf u),K546((U *),(U \/ BOOLEAN))) : b₁ is u,U -interpreter-like } is set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
rng S is non empty finite set
(rng S) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
(rng S) typed/\ (OwnSymbolsOf u) is finite Element of bool (rng S)
bool (rng S) is non empty finite finite-membered set
(rng S) /\ (OwnSymbolsOf u) is finite set
(rng S) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
bool (OwnSymbolsOf u) is non empty set
the adicity of u is non empty Relation-like the U1 of u \ { the U3 of u} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
{ the U3 of u} is non empty trivial finite 1 -element set
the U1 of u \ { the U3 of u} is non empty Element of bool the U1 of u
the U1 of u typed\ { the U3 of u} is Element of bool the U1 of u
[:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial Relation-like non finite V166() set
bool [:( the U1 of u \ { the U3 of u}),INT:] is non empty non trivial non finite V166() set
TheEqSymbOf u is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf u
AllSymbolsOf u is non empty non trivial non finite V166() set
u -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
[:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -firstChar is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
(AllSymbolsOf u) -pr1 is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total V233( AllSymbolsOf u) Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
[:(AllSymbolsOf u),(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
[:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):] is non empty non trivial non finite V166() set
K415((AllSymbolsOf u),(AllSymbolsOf u)) is non empty Relation-like [:(AllSymbolsOf u),(AllSymbolsOf u):] -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf u),(AllSymbolsOf u):],(AllSymbolsOf u):]
MultPlace ((AllSymbolsOf u) -pr1) is non empty Relation-like ((AllSymbolsOf u) *) \ {{}} -defined AllSymbolsOf u -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf u) *) \ {{}}),(AllSymbolsOf u):]
u -multiCat is non empty Relation-like ((AllSymbolsOf u) *) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):]
((AllSymbolsOf u) *) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of (AllSymbolsOf u) *
[:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
(AllSymbolsOf u) -multiCat is non empty Relation-like ((AllSymbolsOf u) *) * -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:(((AllSymbolsOf u) *) *),((AllSymbolsOf u) *):]
(AllSymbolsOf u) -concatenation is non empty Relation-like [:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233((AllSymbolsOf u) * ) Element of bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):]
[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
[:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:((AllSymbolsOf u) *),((AllSymbolsOf u) *):],((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
MultPlace ((AllSymbolsOf u) -concatenation) is non empty Relation-like (((AllSymbolsOf u) *) *) \ {{}} -defined (AllSymbolsOf u) * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding Element of bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):]
(((AllSymbolsOf u) *) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf u) *) *)
bool (((AllSymbolsOf u) *) *) is non empty non trivial non finite V166() set
(((AllSymbolsOf u) *) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool (((AllSymbolsOf u) *) *)
[:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial Relation-like non finite V166() set
bool [:((((AllSymbolsOf u) *) *) \ {{}}),((AllSymbolsOf u) *):] is non empty non trivial non finite V166() set
({} .--> {}) +* (MultPlace ((AllSymbolsOf u) -concatenation)) is non empty Relation-like Function-like Function-yielding V164() set
UU is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
III is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
AtomicFormulaSymbolsOf u is non empty Element of bool (AllSymbolsOf u)
TheNorSymbOf u is set
{(TheNorSymbOf u)} is non empty trivial finite 1 -element set
(AllSymbolsOf u) \ {(TheNorSymbOf u)} is non empty non trivial non finite V166() Element of bool (AllSymbolsOf u)
bool (AllSymbolsOf u) is non empty non trivial non finite V166() set
(AllSymbolsOf u) typed\ {(TheNorSymbOf u)} is Element of bool (AllSymbolsOf u)
X is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
rng X is non empty finite set
(rng X) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
(rng X) typed/\ (OwnSymbolsOf u) is finite Element of bool (rng X)
bool (rng X) is non empty finite finite-membered set
(rng X) /\ (OwnSymbolsOf u) is finite set
(rng X) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
UU | ((rng X) /\ (OwnSymbolsOf u)) is Relation-like (rng X) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
III | ((rng X) /\ (OwnSymbolsOf u)) is Relation-like (rng X) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
UU -TruthEval X is boolean Element of BOOLEAN
UU -AtomicEval X is boolean Element of BOOLEAN
UU === is Relation-like Function-like Function-yielding V164() u,U -interpreter-like UU -extension set
TheEqSymbOf u is Element of AtomicFormulaSymbolsOf u
U -deltaInterpreter is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
2 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
[:(2 -tuples_on U),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on U),BOOLEAN:] is non empty set
[:(U *),(U *):] is non empty non trivial Relation-like non finite V166() set
U -concatenation is non empty Relation-like [:(U *),(U *):] -defined U * -valued Function-like total quasi_total Function-yielding V164() FinSequence-yielding V233(U * ) Element of bool [:[:(U *),(U *):],(U *):]
[:[:(U *),(U *):],(U *):] is non empty non trivial Relation-like non finite V166() set
bool [:[:(U *),(U *):],(U *):] is non empty non trivial non finite V166() set
1 -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
id (1 -tuples_on U) is non empty Relation-like non empty-yielding 1 -tuples_on U -defined 1 -tuples_on U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Function-yielding V164() FinSequence-yielding Element of bool [:(1 -tuples_on U),(1 -tuples_on U):]
[:(1 -tuples_on U),(1 -tuples_on U):] is non empty Relation-like set
bool [:(1 -tuples_on U),(1 -tuples_on U):] is non empty set
(U -concatenation) .: (id (1 -tuples_on U)) is functional finite-membered FinSequence-membered Element of bool (U *)
bool (U *) is non empty non trivial non finite V166() set
chi (((U -concatenation) .: (id (1 -tuples_on U))),(2 -tuples_on U)) is non empty Relation-like 2 -tuples_on U -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on U),BOOLEAN:]
(TheEqSymbOf u) .--> (U -deltaInterpreter) is trivial Relation-like AtomicFormulaSymbolsOf u -defined {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{(TheEqSymbOf u)} is non empty trivial finite 1 -element set
{(TheEqSymbOf u)} --> (U -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf u)} -defined bool [:(2 -tuples_on U),BOOLEAN:] -valued {(U -deltaInterpreter)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:]
{(U -deltaInterpreter)} is non empty trivial functional finite 1 -element V165() V166() set
[:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty Relation-like finite set
bool [:{(TheEqSymbOf u)},{(U -deltaInterpreter)}:] is non empty finite finite-membered set
UU +* ((TheEqSymbOf u) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(u -firstChar) . X is low-compounding relational ofAtomicFormula Element of AllSymbolsOf u
(UU ===) . ((u -firstChar) . X) is non empty Relation-like (abs (ar ((u -firstChar) . X))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . X,U
ar ((u -firstChar) . X) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of u . ((u -firstChar) . X) is set
abs (ar ((u -firstChar) . 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 ((u -firstChar) . X))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms X is Relation-like NAT -defined (rng X) * -valued (TermSymbolsOf u) * -valued AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . X)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
(rng X) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng X
TermSymbolsOf u is non empty set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
(TermSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of TermSymbolsOf u
AllTermsOf u is non empty functional finite-membered FinSequence-membered AllSymbolsOf u -prefix u -prefix Element of bool ((AllSymbolsOf u) *)
u -termsOfMaxDepth is Relation-like Function-like set
rng (u -termsOfMaxDepth) is set
union (rng (u -termsOfMaxDepth)) is set
(AllTermsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() Element of bool (((AllSymbolsOf u) *) *)
UU -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
AllTermsOf u is non empty functional finite-membered FinSequence-membered V165() V166() AllSymbolsOf u -prefix u -prefix Element of K335((((AllSymbolsOf u) *) \ {{}}))
bool (((AllSymbolsOf u) *) \ {{}}) is non empty non trivial non finite V166() set
K335((((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() Element of bool (bool (((AllSymbolsOf u) *) \ {{}}))
bool (bool (((AllSymbolsOf u) *) \ {{}})) is non empty non trivial non finite V166() set
[:(AllTermsOf u),U:] is non empty Relation-like set
bool [:(AllTermsOf u),U:] is non empty set
(UU -TermEval) (*) (SubTerms X) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((UU ===) . ((u -firstChar) . X)) . ((UU -TermEval) (*) (SubTerms X)) is set
III -TruthEval X is boolean Element of BOOLEAN
III -AtomicEval X is boolean Element of BOOLEAN
III === is Relation-like Function-like Function-yielding V164() u,U -interpreter-like III -extension set
III +* ((TheEqSymbOf u) .--> (U -deltaInterpreter)) is Relation-like Function-like Function-yielding V164() set
(III ===) . ((u -firstChar) . X) is non empty Relation-like (abs (ar ((u -firstChar) . X))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . X,U
III -TermEval is non empty Relation-like AllTermsOf u -defined U -valued Function-like total quasi_total Element of bool [:(AllTermsOf u),U:]
(III -TermEval) (*) (SubTerms X) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((III ===) . ((u -firstChar) . X)) . ((III -TermEval) (*) (SubTerms X)) is set
I is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
rng I is non empty finite set
(rng I) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
(rng I) typed/\ (OwnSymbolsOf u) is finite Element of bool (rng I)
bool (rng I) is non empty finite finite-membered set
(rng I) /\ (OwnSymbolsOf u) is finite set
(rng I) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
UU | ((rng I) /\ (OwnSymbolsOf u)) is Relation-like (rng I) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
III | ((rng I) /\ (OwnSymbolsOf u)) is Relation-like (rng I) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
the adicity of u | ((rng I) /\ (OwnSymbolsOf u)) is Relation-like the U1 of u \ { the U3 of u} -defined (rng I) /\ (OwnSymbolsOf u) -defined the U1 of u \ { the U3 of u} -defined INT -valued Function-like finite finite-support Element of bool [:( the U1 of u \ { the U3 of u}),INT:]
UU -AtomicEval I is boolean Element of BOOLEAN
(u -firstChar) . I is low-compounding relational ofAtomicFormula Element of AllSymbolsOf u
(UU ===) . ((u -firstChar) . I) is non empty Relation-like (abs (ar ((u -firstChar) . I))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . I,U
ar ((u -firstChar) . I) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of u . ((u -firstChar) . I) is set
abs (ar ((u -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 ((u -firstChar) . I))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms I is Relation-like NAT -defined (rng I) * -valued (TermSymbolsOf u) * -valued AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . I)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
(rng I) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng I
(UU -TermEval) (*) (SubTerms I) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((UU ===) . ((u -firstChar) . I)) . ((UU -TermEval) (*) (SubTerms I)) is set
UU -TruthEval I is boolean Element of BOOLEAN
j is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf u -valued Function-like finite FinSequence-like FinSubsequence-like finite-support 0wff 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
III -AtomicEval j is boolean Element of BOOLEAN
(u -firstChar) . j is low-compounding relational ofAtomicFormula Element of AllSymbolsOf u
(III ===) . ((u -firstChar) . j) is non empty Relation-like (abs (ar ((u -firstChar) . j))) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (u -firstChar) . j,U
ar ((u -firstChar) . j) is non empty finite complex ext-real non positive negative V40() V41() Element of INT
the adicity of u . ((u -firstChar) . j) is set
abs (ar ((u -firstChar) . j)) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(abs (ar ((u -firstChar) . j))) -tuples_on U is non empty functional finite-membered FinSequence-membered V165() V166() FinSequenceSet of U
SubTerms j is Relation-like NAT -defined (rng j) * -valued (TermSymbolsOf u) * -valued AllTermsOf u -valued Function-like finite abs (ar ((u -firstChar) . j)) -element FinSequence-like FinSubsequence-like Function-yielding V164() FinSequence-yielding finite-support Element of (AllTermsOf u) *
rng j is non empty finite set
(rng j) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of rng j
(III -TermEval) (*) (SubTerms j) is Relation-like NAT -defined U -valued Function-like finite finite-support set
((III ===) . ((u -firstChar) . j)) . ((III -TermEval) (*) (SubTerms j)) is set
III -TruthEval j is boolean Element of BOOLEAN
UU is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
UU + 1 is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
III is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
X is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support UU + 1 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
rng I is non empty finite set
(rng I) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
(rng I) typed/\ (OwnSymbolsOf u) is finite Element of bool (rng I)
bool (rng I) is non empty finite finite-membered set
(rng I) /\ (OwnSymbolsOf u) is finite set
(rng I) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
III | ((rng I) /\ (OwnSymbolsOf u)) is Relation-like (rng I) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
X | ((rng I) /\ (OwnSymbolsOf u)) is Relation-like (rng I) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
III -TruthEval I is boolean Element of BOOLEAN
X -TruthEval I is boolean Element of BOOLEAN
j is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff UU + 1 -wff wff non exal Element of ((AllSymbolsOf u) *) \ {{}}
rng j is non empty finite set
(rng j) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
(rng j) typed/\ (OwnSymbolsOf u) is finite Element of bool (rng j)
bool (rng j) is non empty finite finite-membered set
(rng j) /\ (OwnSymbolsOf u) is finite set
(rng j) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
(u -firstChar) . j is non relational Element of AllSymbolsOf u
head j is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support UU -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
SubWffsOf j is set
K74((SubWffsOf j)) is set
tail j is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support UU -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
K75((SubWffsOf j)) is set
<*((u -firstChar) . j)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
[1,((u -firstChar) . j)] is non empty set
{[1,((u -firstChar) . j)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support UU -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
<*((u -firstChar) . j)*> ^ jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff Element of ((AllSymbolsOf u) *) \ {{}}
g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support UU -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
(<*((u -firstChar) . j)*> ^ jJ) ^ g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff Element of ((AllSymbolsOf u) *) \ {{}}
jJ ^ g is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Element of ((AllSymbolsOf u) *) \ {{}}
<*((u -firstChar) . j)*> ^ (jJ ^ g) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff Element of ((AllSymbolsOf u) *) \ {{}}
rng (jJ ^ g) is non empty finite set
rng g is non empty finite set
rng jJ is non empty finite set
bool ((rng j) /\ (OwnSymbolsOf u)) is non empty finite finite-membered set
(rng jJ) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
(rng jJ) typed/\ (OwnSymbolsOf u) is finite Element of bool (rng jJ)
bool (rng jJ) is non empty finite finite-membered set
(rng jJ) /\ (OwnSymbolsOf u) is finite set
(rng jJ) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
(rng g) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
(rng g) typed/\ (OwnSymbolsOf u) is finite Element of bool (rng g)
bool (rng g) is non empty finite finite-membered set
(rng g) /\ (OwnSymbolsOf u) is finite set
(rng g) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
III -TruthEval j is boolean Element of BOOLEAN
X -TruthEval j is boolean Element of BOOLEAN
III -TruthEval jJ is boolean Element of BOOLEAN
X -TruthEval jJ is boolean Element of BOOLEAN
III -TruthEval g is boolean Element of BOOLEAN
X -TruthEval g is boolean Element of BOOLEAN
h is finite Element of bool ((rng j) /\ (OwnSymbolsOf u))
III | h is Relation-like h -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
h null ((rng j) /\ (OwnSymbolsOf u)) is set
((rng j) /\ (OwnSymbolsOf u)) /\ h is finite Element of bool ((rng j) /\ (OwnSymbolsOf u))
((rng j) /\ (OwnSymbolsOf u)) typed/\ h is finite Element of bool ((rng j) /\ (OwnSymbolsOf u))
((rng j) /\ (OwnSymbolsOf u)) /\ h is finite set
((rng j) /\ (OwnSymbolsOf u)) /\typed h is finite Element of bool h
bool h is non empty finite finite-membered set
h \typed/ ((rng j) /\ (OwnSymbolsOf u)) is finite Element of bool (h \/ ((rng j) /\ (OwnSymbolsOf u)))
h \/ ((rng j) /\ (OwnSymbolsOf u)) is finite set
bool (h \/ ((rng j) /\ (OwnSymbolsOf u))) is non empty finite finite-membered set
III | (h null ((rng j) /\ (OwnSymbolsOf u))) is Relation-like h null ((rng j) /\ (OwnSymbolsOf u)) -defined OwnSymbolsOf u -defined Function-like Function-yielding V164() set
III | ((rng j) /\ (OwnSymbolsOf u)) is Relation-like (rng j) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
(III | ((rng j) /\ (OwnSymbolsOf u))) | h is Relation-like h -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
X | (h null ((rng j) /\ (OwnSymbolsOf u))) is Relation-like h null ((rng j) /\ (OwnSymbolsOf u)) -defined OwnSymbolsOf u -defined Function-like Function-yielding V164() set
G is finite Element of bool ((rng j) /\ (OwnSymbolsOf u))
III | G is Relation-like G -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
G null ((rng j) /\ (OwnSymbolsOf u)) is set
((rng j) /\ (OwnSymbolsOf u)) /\ G is finite Element of bool ((rng j) /\ (OwnSymbolsOf u))
((rng j) /\ (OwnSymbolsOf u)) typed/\ G is finite Element of bool ((rng j) /\ (OwnSymbolsOf u))
((rng j) /\ (OwnSymbolsOf u)) /\ G is finite set
((rng j) /\ (OwnSymbolsOf u)) /\typed G is finite Element of bool G
bool G is non empty finite finite-membered set
G \typed/ ((rng j) /\ (OwnSymbolsOf u)) is finite Element of bool (G \/ ((rng j) /\ (OwnSymbolsOf u)))
G \/ ((rng j) /\ (OwnSymbolsOf u)) is finite set
bool (G \/ ((rng j) /\ (OwnSymbolsOf u))) is non empty finite finite-membered set
III | (G null ((rng j) /\ (OwnSymbolsOf u))) is Relation-like G null ((rng j) /\ (OwnSymbolsOf u)) -defined OwnSymbolsOf u -defined Function-like Function-yielding V164() set
(III | ((rng j) /\ (OwnSymbolsOf u))) | G is Relation-like G -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
X | (G null ((rng j) /\ (OwnSymbolsOf u))) is Relation-like G null ((rng j) /\ (OwnSymbolsOf u)) -defined OwnSymbolsOf u -defined Function-like Function-yielding V164() set
(III -TruthEval jJ) 'nor' (III -TruthEval g) is set
(III -TruthEval jJ) 'or' (III -TruthEval g) is set
'not' (III -TruthEval jJ) is boolean set
1 - (III -TruthEval jJ) is set
'not' (III -TruthEval g) is boolean set
1 - (III -TruthEval g) is set
('not' (III -TruthEval jJ)) '&' ('not' (III -TruthEval g)) is set
('not' (III -TruthEval jJ)) * ('not' (III -TruthEval g)) is set
'not' (('not' (III -TruthEval jJ)) '&' ('not' (III -TruthEval g))) is boolean set
'not' ((III -TruthEval jJ) 'or' (III -TruthEval g)) is boolean set
(III -TruthEval j) \+\ ((III -TruthEval jJ) 'nor' (III -TruthEval g)) is set
(III -TruthEval j) \ ((III -TruthEval jJ) 'nor' (III -TruthEval g)) is set
(III -TruthEval j) typed\ ((III -TruthEval jJ) 'nor' (III -TruthEval g)) is Element of bool (III -TruthEval j)
bool (III -TruthEval j) is non empty set
(III -TruthEval j) \ ((III -TruthEval jJ) 'nor' (III -TruthEval g)) is Element of bool (III -TruthEval j)
((III -TruthEval jJ) 'nor' (III -TruthEval g)) \ (III -TruthEval j) is set
((III -TruthEval jJ) 'nor' (III -TruthEval g)) typed\ (III -TruthEval j) is Element of bool ((III -TruthEval jJ) 'nor' (III -TruthEval g))
bool ((III -TruthEval jJ) 'nor' (III -TruthEval g)) is non empty set
((III -TruthEval jJ) 'nor' (III -TruthEval g)) \ (III -TruthEval j) is Element of bool ((III -TruthEval jJ) 'nor' (III -TruthEval g))
((III -TruthEval j) \ ((III -TruthEval jJ) 'nor' (III -TruthEval g))) \/ (((III -TruthEval jJ) 'nor' (III -TruthEval g)) \ (III -TruthEval j)) is set
(X -TruthEval jJ) 'nor' (X -TruthEval g) is set
(X -TruthEval jJ) 'or' (X -TruthEval g) is set
'not' (X -TruthEval jJ) is boolean set
1 - (X -TruthEval jJ) is set
'not' (X -TruthEval g) is boolean set
1 - (X -TruthEval g) is set
('not' (X -TruthEval jJ)) '&' ('not' (X -TruthEval g)) is set
('not' (X -TruthEval jJ)) * ('not' (X -TruthEval g)) is set
'not' (('not' (X -TruthEval jJ)) '&' ('not' (X -TruthEval g))) is boolean set
'not' ((X -TruthEval jJ) 'or' (X -TruthEval g)) is boolean set
(X -TruthEval j) \+\ ((X -TruthEval jJ) 'nor' (X -TruthEval g)) is set
(X -TruthEval j) \ ((X -TruthEval jJ) 'nor' (X -TruthEval g)) is set
(X -TruthEval j) typed\ ((X -TruthEval jJ) 'nor' (X -TruthEval g)) is Element of bool (X -TruthEval j)
bool (X -TruthEval j) is non empty set
(X -TruthEval j) \ ((X -TruthEval jJ) 'nor' (X -TruthEval g)) is Element of bool (X -TruthEval j)
((X -TruthEval jJ) 'nor' (X -TruthEval g)) \ (X -TruthEval j) is set
((X -TruthEval jJ) 'nor' (X -TruthEval g)) typed\ (X -TruthEval j) is Element of bool ((X -TruthEval jJ) 'nor' (X -TruthEval g))
bool ((X -TruthEval jJ) 'nor' (X -TruthEval g)) is non empty set
((X -TruthEval jJ) 'nor' (X -TruthEval g)) \ (X -TruthEval j) is Element of bool ((X -TruthEval jJ) 'nor' (X -TruthEval g))
((X -TruthEval j) \ ((X -TruthEval jJ) 'nor' (X -TruthEval g))) \/ (((X -TruthEval jJ) 'nor' (X -TruthEval g)) \ (X -TruthEval j)) is set
j is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff wff exal Element of ((AllSymbolsOf u) *) \ {{}}
(u -firstChar) . j is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf u
head j is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf u) *) \ {{}}
SubWffsOf j is set
K74((SubWffsOf j)) is set
<*((u -firstChar) . j)*> is non empty trivial Relation-like NAT -defined TermSymbolsOf u -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support termal 0 -termal Element of ((AllSymbolsOf u) *) \ {{}}
TermSymbolsOf u is non empty set
the adicity of u " NAT is Element of bool ( the U1 of u \ { the U3 of u})
bool ( the U1 of u \ { the U3 of u}) is non empty set
[1,((u -firstChar) . j)] is non empty set
{[1,((u -firstChar) . j)]} is non empty trivial Relation-like Function-like constant finite 1 -element V165() V166() finite-support set
jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support UU -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
<*((u -firstChar) . j)*> ^ jJ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support non 0wff UU + 1 -wff 1 + (Depth jJ) -wff non Depth jJ -wff wff exal Element of ((AllSymbolsOf u) *) \ {{}}
Depth jJ is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
1 + (Depth jJ) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
tail j is empty trivial Relation-like non-empty empty-yielding NAT -defined {{}} -valued AllSymbolsOf u -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of (AllSymbolsOf u) *
(AllSymbolsOf u) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf u
K75((SubWffsOf j)) is set
(<*((u -firstChar) . j)*> ^ jJ) ^ (tail j) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(<*((u -firstChar) . j)*> ^ jJ) null (tail j) is Relation-like NAT -defined (tail j) \/ (dom (<*((u -firstChar) . j)*> ^ jJ)) -defined (tail j) \/ (rng (<*((u -firstChar) . j)*> ^ jJ)) -valued Function-like finite len (<*((u -firstChar) . j)*> ^ jJ) -element FinSequence-like FinSubsequence-like finite-support set
dom (<*((u -firstChar) . j)*> ^ jJ) is non empty finite set
(tail j) \/ (dom (<*((u -firstChar) . j)*> ^ jJ)) is non empty finite set
rng (<*((u -firstChar) . j)*> ^ jJ) is non empty finite set
(tail j) \/ (rng (<*((u -firstChar) . j)*> ^ jJ)) is non empty finite set
len (<*((u -firstChar) . j)*> ^ jJ) is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(<*((u -firstChar) . j)*> ^ jJ) \typed/ (tail j) is Relation-like NAT -defined finite Element of bool ((<*((u -firstChar) . j)*> ^ jJ) \/ (tail j))
(<*((u -firstChar) . j)*> ^ jJ) \/ (tail j) is non empty Relation-like NAT -defined finite set
bool ((<*((u -firstChar) . j)*> ^ jJ) \/ (tail j)) is non empty finite finite-membered set
(tail j) ^ (<*((u -firstChar) . j)*> ^ jJ) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
rng j is non empty finite set
bool (rng j) is non empty finite finite-membered set
rng jJ is non empty finite set
III -TruthEval j is boolean Element of BOOLEAN
g is Element of U
(((u -firstChar) . j),g) ReassignIn III is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> g is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> g is non empty Relation-like {{}} -defined U -valued {g} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{g}:]
{g} is non empty trivial finite 1 -element set
[:{{}},{g}:] is non empty Relation-like finite set
bool [:{{}},{g}:] is non empty finite finite-membered set
((u -firstChar) . j) .--> ({} .--> g) is trivial Relation-like AllSymbolsOf u -defined {((u -firstChar) . j)} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{((u -firstChar) . j)} is non empty trivial finite 1 -element set
{((u -firstChar) . j)} --> ({} .--> g) is non empty Relation-like {((u -firstChar) . j)} -defined {({} .--> g)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{((u -firstChar) . j)},{({} .--> g)}:]
{({} .--> g)} is non empty trivial functional finite finite-membered 1 -element set
[:{((u -firstChar) . j)},{({} .--> g)}:] is non empty Relation-like finite set
bool [:{((u -firstChar) . j)},{({} .--> g)}:] is non empty finite finite-membered set
III +* (((u -firstChar) . j) .--> ({} .--> g)) is Relation-like Function-like Function-yielding V164() set
((((u -firstChar) . j),g) ReassignIn III) -TruthEval jJ is boolean Element of BOOLEAN
(((u -firstChar) . j),g) ReassignIn X is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
X +* (((u -firstChar) . j) .--> ({} .--> g)) is Relation-like Function-like Function-yielding V164() set
G is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
(rng jJ) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
(rng jJ) typed/\ (OwnSymbolsOf u) is finite Element of bool (rng jJ)
bool (rng jJ) is non empty finite finite-membered set
(rng jJ) /\ (OwnSymbolsOf u) is finite set
(rng jJ) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
G | ((rng jJ) /\ (OwnSymbolsOf u)) is Relation-like (rng jJ) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
jJ is finite Element of bool (rng j)
jJ null (rng j) is set
(rng j) /\ jJ is finite Element of bool (rng j)
(rng j) typed/\ jJ is finite Element of bool (rng j)
(rng j) /\ jJ is finite set
(rng j) /\typed jJ is finite Element of bool jJ
bool jJ is non empty finite finite-membered set
jJ \typed/ (rng j) is finite Element of bool (jJ \/ (rng j))
jJ \/ (rng j) is non empty finite set
bool (jJ \/ (rng j)) is non empty finite finite-membered set
(jJ null (rng j)) /\ (OwnSymbolsOf u) is Element of bool (AllSymbolsOf u)
(jJ null (rng j)) typed/\ (OwnSymbolsOf u) is Element of bool (jJ null (rng j))
bool (jJ null (rng j)) is non empty set
(jJ null (rng j)) /\ (OwnSymbolsOf u) is set
(jJ null (rng j)) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
III | ((jJ null (rng j)) /\ (OwnSymbolsOf u)) is Relation-like (jJ null (rng j)) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like Function-yielding V164() set
jJ /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
jJ typed/\ (OwnSymbolsOf u) is finite Element of bool jJ
jJ /\ (OwnSymbolsOf u) is finite set
jJ /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
(((u -firstChar) . j) .--> ({} .--> g)) | (jJ /\ (OwnSymbolsOf u)) is Relation-like jJ /\ (OwnSymbolsOf u) -defined AllSymbolsOf u -defined Function-like constant finite Function-yielding V164() finite-support set
(III | ((jJ null (rng j)) /\ (OwnSymbolsOf u))) +* ((((u -firstChar) . j) .--> ({} .--> g)) | (jJ /\ (OwnSymbolsOf u))) is Relation-like Function-like Function-yielding V164() set
(rng j) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
(rng j) typed/\ (OwnSymbolsOf u) is finite Element of bool (rng j)
(rng j) /\ (OwnSymbolsOf u) is finite set
(rng j) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
jJ /\ ((rng j) /\ (OwnSymbolsOf u)) is finite Element of bool (AllSymbolsOf u)
jJ typed/\ ((rng j) /\ (OwnSymbolsOf u)) is finite Element of bool jJ
jJ /\ ((rng j) /\ (OwnSymbolsOf u)) is finite set
jJ /\typed ((rng j) /\ (OwnSymbolsOf u)) is finite Element of bool ((rng j) /\ (OwnSymbolsOf u))
bool ((rng j) /\ (OwnSymbolsOf u)) is non empty finite finite-membered set
III | (jJ /\ ((rng j) /\ (OwnSymbolsOf u))) is Relation-like jJ /\ ((rng j) /\ (OwnSymbolsOf u)) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
(III | (jJ /\ ((rng j) /\ (OwnSymbolsOf u)))) +* ((((u -firstChar) . j) .--> ({} .--> g)) | (jJ /\ (OwnSymbolsOf u))) is Relation-like Function-like finite Function-yielding V164() finite-support set
III | ((rng j) /\ (OwnSymbolsOf u)) is Relation-like (rng j) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
(III | ((rng j) /\ (OwnSymbolsOf u))) | jJ is Relation-like jJ -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
((III | ((rng j) /\ (OwnSymbolsOf u))) | jJ) +* ((((u -firstChar) . j) .--> ({} .--> g)) | (jJ /\ (OwnSymbolsOf u))) is Relation-like Function-like finite Function-yielding V164() finite-support set
((rng j) /\ (OwnSymbolsOf u)) /\ jJ is finite Element of bool (rng j)
((rng j) /\ (OwnSymbolsOf u)) typed/\ jJ is finite Element of bool ((rng j) /\ (OwnSymbolsOf u))
((rng j) /\ (OwnSymbolsOf u)) /\ jJ is finite set
((rng j) /\ (OwnSymbolsOf u)) /\typed jJ is finite Element of bool jJ
X | (((rng j) /\ (OwnSymbolsOf u)) /\ jJ) is Relation-like ((rng j) /\ (OwnSymbolsOf u)) /\ jJ -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
(X | (((rng j) /\ (OwnSymbolsOf u)) /\ jJ)) +* ((((u -firstChar) . j) .--> ({} .--> g)) | (jJ /\ (OwnSymbolsOf u))) is Relation-like Function-like finite Function-yielding V164() finite-support set
((rng j) /\ jJ) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
((rng j) /\ jJ) typed/\ (OwnSymbolsOf u) is finite Element of bool ((rng j) /\ jJ)
bool ((rng j) /\ jJ) is non empty finite finite-membered set
((rng j) /\ jJ) /\ (OwnSymbolsOf u) is finite set
((rng j) /\ jJ) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
X | (((rng j) /\ jJ) /\ (OwnSymbolsOf u)) is Relation-like ((rng j) /\ jJ) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
(X | (((rng j) /\ jJ) /\ (OwnSymbolsOf u))) +* ((((u -firstChar) . j) .--> ({} .--> g)) | (jJ /\ (OwnSymbolsOf u))) is Relation-like Function-like finite Function-yielding V164() finite-support set
n is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
n | ((rng jJ) /\ (OwnSymbolsOf u)) is Relation-like (rng jJ) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
n -TruthEval jJ is boolean Element of BOOLEAN
X -TruthEval j is boolean Element of BOOLEAN
g is Element of U
(((u -firstChar) . j),g) ReassignIn X is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
{} .--> g is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> g is non empty Relation-like {{}} -defined U -valued {g} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{g}:]
{g} is non empty trivial finite 1 -element set
[:{{}},{g}:] is non empty Relation-like finite set
bool [:{{}},{g}:] is non empty finite finite-membered set
((u -firstChar) . j) .--> ({} .--> g) is trivial Relation-like AllSymbolsOf u -defined {((u -firstChar) . j)} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{((u -firstChar) . j)} --> ({} .--> g) is non empty Relation-like {((u -firstChar) . j)} -defined {({} .--> g)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{((u -firstChar) . j)},{({} .--> g)}:]
{({} .--> g)} is non empty trivial functional finite finite-membered 1 -element set
[:{((u -firstChar) . j)},{({} .--> g)}:] is non empty Relation-like finite set
bool [:{((u -firstChar) . j)},{({} .--> g)}:] is non empty finite finite-membered set
X +* (((u -firstChar) . j) .--> ({} .--> g)) is Relation-like Function-like Function-yielding V164() set
((((u -firstChar) . j),g) ReassignIn X) -TruthEval jJ is boolean Element of BOOLEAN
(((u -firstChar) . j),g) ReassignIn III is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
III +* (((u -firstChar) . j) .--> ({} .--> g)) is Relation-like Function-like Function-yielding V164() set
G is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
G | ((rng jJ) /\ (OwnSymbolsOf u)) is Relation-like (rng jJ) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
(((u -firstChar) . j) .--> ({} .--> g)) | (jJ /\ (OwnSymbolsOf u)) is Relation-like jJ /\ (OwnSymbolsOf u) -defined AllSymbolsOf u -defined Function-like constant finite Function-yielding V164() finite-support set
(III | ((jJ null (rng j)) /\ (OwnSymbolsOf u))) +* ((((u -firstChar) . j) .--> ({} .--> g)) | (jJ /\ (OwnSymbolsOf u))) is Relation-like Function-like Function-yielding V164() set
(III | (jJ /\ ((rng j) /\ (OwnSymbolsOf u)))) +* ((((u -firstChar) . j) .--> ({} .--> g)) | (jJ /\ (OwnSymbolsOf u))) is Relation-like Function-like finite Function-yielding V164() finite-support set
((III | ((rng j) /\ (OwnSymbolsOf u))) | jJ) +* ((((u -firstChar) . j) .--> ({} .--> g)) | (jJ /\ (OwnSymbolsOf u))) is Relation-like Function-like finite Function-yielding V164() finite-support set
(X | (((rng j) /\ (OwnSymbolsOf u)) /\ jJ)) +* ((((u -firstChar) . j) .--> ({} .--> g)) | (jJ /\ (OwnSymbolsOf u))) is Relation-like Function-like finite Function-yielding V164() finite-support set
(X | (((rng j) /\ jJ) /\ (OwnSymbolsOf u))) +* ((((u -firstChar) . j) .--> ({} .--> g)) | (jJ /\ (OwnSymbolsOf u))) is Relation-like Function-like finite Function-yielding V164() finite-support set
n is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
n | ((rng jJ) /\ (OwnSymbolsOf u)) is Relation-like (rng jJ) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
G -TruthEval jJ is boolean Element of BOOLEAN
UU is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
UU | ((rng S) /\ (OwnSymbolsOf u)) is Relation-like (rng S) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
III is Relation-like OwnSymbolsOf u -defined Function-like total Function-yielding V164() u,U -interpreter-like Element of U -InterpretersOf u
III | ((rng S) /\ (OwnSymbolsOf u)) is Relation-like (rng S) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
UU -TruthEval S is boolean Element of BOOLEAN
III -TruthEval S is boolean Element of BOOLEAN
Depth S is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(Depth S) + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(u,0,S) is non empty Relation-like NAT -defined 0 \/ (dom S) -defined 0 \/ (rng S) -valued Function-like finite len S -element FinSequence-like FinSubsequence-like finite-support (Depth S) + 0 -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
dom S is non empty finite set
0 \/ (dom S) is non empty finite set
0 \/ (rng S) is non empty finite set
len S is non empty epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real positive non negative V40() V41() Element of NAT
(Depth S) + 0 is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
S \typed/ 0 is Relation-like NAT -defined finite Element of bool (S \/ 0)
S \/ 0 is non empty Relation-like NAT -defined finite set
bool (S \/ 0) is non empty finite finite-membered set
S null 0 is Relation-like NAT -defined 0 \/ (dom S) -defined 0 \/ (rng S) -valued Function-like finite len S -element FinSequence-like FinSubsequence-like finite-support set
S ^ 0 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
0 ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support Depth S -wff wff Element of ((AllSymbolsOf u) *) \ {{}}
rng I is non empty finite set
(rng I) /\ (OwnSymbolsOf u) is finite Element of bool (AllSymbolsOf u)
(rng I) typed/\ (OwnSymbolsOf u) is finite Element of bool (rng I)
bool (rng I) is non empty finite finite-membered set
(rng I) /\ (OwnSymbolsOf u) is finite set
(rng I) /\typed (OwnSymbolsOf u) is Element of bool (OwnSymbolsOf u)
UU | ((rng I) /\ (OwnSymbolsOf u)) is Relation-like (rng I) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
III | ((rng I) /\ (OwnSymbolsOf u)) is Relation-like (rng I) /\ (OwnSymbolsOf u) -defined OwnSymbolsOf u -defined Function-like finite Function-yielding V164() finite-support set
U is set
u is non empty set
u * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of u
u \/ BOOLEAN is non empty set
K546((u *),(u \/ BOOLEAN)) is non empty functional M31(u * ,u \/ BOOLEAN)
S is Element of u
l is V51() V53() eligible Language-like
AllSymbolsOf l is non empty non trivial non finite V166() set
the U1 of l is set
OwnSymbolsOf l is non empty Element of bool (AllSymbolsOf l)
AllSymbolsOf l is non empty non trivial non finite V166() set
bool (AllSymbolsOf l) is non empty non trivial non finite V166() set
the U2 of l is Element of the U1 of l
the U3 of l is Element of the U1 of l
{ the U2 of l, the U3 of l} is non empty finite set
the U1 of l \ { the U2 of l, the U3 of l} is Element of bool the U1 of l
bool the U1 of l is non empty set
the U1 of l typed\ { the U2 of l, the U3 of l} is Element of bool the U1 of l
Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf l,K546((u *),(u \/ BOOLEAN))
u -InterpretersOf l is non empty functional Element of bool (Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf l -defined K546((u *),(u \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf l),K546((u *),(u \/ BOOLEAN))) : b₁ is l,u -interpreter-like } is set
II is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf l
i is Relation-like OwnSymbolsOf l -defined Function-like total Function-yielding V164() l,u -interpreter-like Element of u -InterpretersOf l
(II,S) ReassignIn i is Relation-like OwnSymbolsOf l -defined Function-like total Function-yielding V164() l,u -interpreter-like Element of u -InterpretersOf l
{} .--> S is trivial Relation-like {{}} -defined u -valued Function-like one-to-one constant finite finite-support set
{{}} --> S is non empty Relation-like {{}} -defined u -valued {S} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{S}:]
{S} is non empty trivial finite 1 -element set
[:{{}},{S}:] is non empty Relation-like finite set
bool [:{{}},{S}:] is non empty finite finite-membered set
II .--> ({} .--> S) is trivial Relation-like AllSymbolsOf l -defined {II} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{II} is non empty trivial finite 1 -element set
{II} --> ({} .--> S) is non empty Relation-like {II} -defined {({} .--> S)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{II},{({} .--> S)}:]
{({} .--> S)} is non empty trivial functional finite finite-membered 1 -element set
[:{II},{({} .--> S)}:] is non empty Relation-like finite set
bool [:{II},{({} .--> S)}:] is non empty finite finite-membered set
i +* (II .--> ({} .--> S)) is Relation-like Function-like Function-yielding V164() set
(AllSymbolsOf l) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of AllSymbolsOf l
((AllSymbolsOf l) *) \ {{}} is non empty non trivial functional non finite finite-membered FinSequence-membered V165() V166() Element of bool ((AllSymbolsOf l) *)
bool ((AllSymbolsOf l) *) is non empty non trivial non finite V166() set
((AllSymbolsOf l) *) typed\ {{}} is functional finite-membered FinSequence-membered Element of bool ((AllSymbolsOf l) *)
III is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support wff Element of ((AllSymbolsOf l) *) \ {{}}
rng III is non empty finite set
bool (rng III) is non empty finite finite-membered set
(rng III) /\ (OwnSymbolsOf l) is finite Element of bool (AllSymbolsOf l)
(rng III) typed/\ (OwnSymbolsOf l) is finite Element of bool (rng III)
(rng III) /\ (OwnSymbolsOf l) is finite set
(rng III) /\typed (OwnSymbolsOf l) is Element of bool (OwnSymbolsOf l)
bool (OwnSymbolsOf l) is non empty set
bool U is non empty set
{III} is non empty trivial functional finite finite-membered 1 -element FinSequence-membered V165() V166() Element of bool (((AllSymbolsOf l) *) \ {{}})
bool (((AllSymbolsOf l) *) \ {{}}) is non empty non trivial non finite V166() set
i -TruthEval III is boolean Element of BOOLEAN
I is Element of bool U
U /\ I is Element of bool U
U typed/\ I is Element of bool U
U /\ I is set
U /\typed I is Element of bool I
bool I is non empty set
I null U is set
I \typed/ U is Element of bool (I \/ U)
I \/ U is set
bool (I \/ U) is non empty set
X is finite Element of bool (rng III)
{II} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf l)
bool (AllSymbolsOf l) is non empty non trivial non finite V166() set
dom (II .--> ({} .--> S)) is trivial finite Element of bool {II}
bool {II} is non empty finite finite-membered set
i | X is Relation-like X -defined OwnSymbolsOf l -defined Function-like finite Function-yielding V164() finite-support set
(II .--> ({} .--> S)) | X is Relation-like X -defined AllSymbolsOf l -defined Function-like constant finite Function-yielding V164() finite-support set
(i | X) +* ((II .--> ({} .--> S)) | X) is Relation-like Function-like finite Function-yielding V164() finite-support set
(i | X) +* {} is Relation-like Function-like finite Function-yielding V164() finite-support set
((II,S) ReassignIn i) | X is Relation-like X -defined OwnSymbolsOf l -defined Function-like finite Function-yielding V164() finite-support set
((II,S) ReassignIn i) -TruthEval III is boolean Element of BOOLEAN
U is non empty set
[:U,U:] is non empty Relation-like set
bool [:U,U:] is non empty set
U * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of U
U \/ BOOLEAN is non empty set
K546((U *),(U \/ BOOLEAN)) is non empty functional M31(U * ,U \/ BOOLEAN)
u is Element of U
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite V166() set
the U1 of S is set
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite V166() set
bool (AllSymbolsOf S) is non empty non trivial non finite V166() 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
Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S,K546((U *),(U \/ BOOLEAN))
U -InterpretersOf S is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined K546((U *),(U \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),K546((U *),(U \/ BOOLEAN))) : b₁ is S,U -interpreter-like } is set
l is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf S
E is Relation-like U -defined U -valued total quasi_total reflexive symmetric transitive Element of bool [:U,U:]
Class E is non empty V165() V166() a_partition of U
(U,E) is non empty Relation-like non empty-yielding U -defined Class E -valued Function-like total quasi_total onto Element of bool [:U,(Class E):]
[:U,(Class E):] is non empty Relation-like set
bool [:U,(Class E):] is non empty set
(U,E) . u is non empty Element of Class E
i is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like (S,U,E) Element of U -InterpretersOf S
(S,U,E,i) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S, Class E -interpreter-like Element of (Class E) -InterpretersOf S
(Class E) * is non empty non trivial functional non finite finite-membered FinSequence-membered V166() FinSequenceSet of Class E
(Class E) \/ BOOLEAN is non empty set
K546(((Class E) *),((Class E) \/ BOOLEAN)) is non empty functional M31((Class E) * ,(Class E) \/ BOOLEAN)
Funcs ((OwnSymbolsOf S),K546(((Class E) *),((Class E) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S,K546(((Class E) *),((Class E) \/ BOOLEAN))
(Class E) -InterpretersOf S is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),K546(((Class E) *),((Class E) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf S),K546(((Class E) *),((Class E) \/ BOOLEAN)))) is non empty set
{ b₁ where b₁ is Relation-like OwnSymbolsOf S -defined K546(((Class E) *),((Class E) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V164() Element of Funcs ((OwnSymbolsOf S),K546(((Class E) *),((Class E) \/ BOOLEAN))) : b₁ is S, Class E -interpreter-like } is set
(l,((U,E) . u)) ReassignIn (S,U,E,i) is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S, Class E -interpreter-like Element of (Class E) -InterpretersOf S
{} .--> ((U,E) . u) is trivial Relation-like {{}} -defined Class E -valued Function-like one-to-one constant finite finite-support set
{{}} --> ((U,E) . u) is non empty Relation-like non-empty non empty-yielding {{}} -defined Class E -valued {((U,E) . u)} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{((U,E) . u)}:]
{((U,E) . u)} is non empty trivial finite 1 -element V165() V166() set
[:{{}},{((U,E) . u)}:] is non empty Relation-like finite set
bool [:{{}},{((U,E) . u)}:] is non empty finite finite-membered set
l .--> ({} .--> ((U,E) . u)) is trivial Relation-like AllSymbolsOf S -defined {l} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} is non empty trivial finite 1 -element set
{l} --> ({} .--> ((U,E) . u)) is non empty Relation-like {l} -defined {({} .--> ((U,E) . u))} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({} .--> ((U,E) . u))}:]
{({} .--> ((U,E) . u))} is non empty trivial functional finite finite-membered 1 -element set
[:{l},{({} .--> ((U,E) . u))}:] is non empty Relation-like finite set
bool [:{l},{({} .--> ((U,E) . u))}:] is non empty finite finite-membered set
(S,U,E,i) +* (l .--> ({} .--> ((U,E) . u))) is Relation-like Function-like Function-yielding V164() set
(l,u) ReassignIn i is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
{} .--> u is trivial Relation-like {{}} -defined U -valued Function-like one-to-one constant finite finite-support set
{{}} --> u is non empty Relation-like {{}} -defined U -valued {u} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{u}:]
{u} is non empty trivial finite 1 -element set
[:{{}},{u}:] is non empty Relation-like finite set
bool [:{{}},{u}:] is non empty finite finite-membered set
l .--> ({} .--> u) is trivial Relation-like AllSymbolsOf S -defined {l} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} --> ({} .--> u) is non empty Relation-like {l} -defined {({} .--> u)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({} .--> u)}:]
{({} .--> u)} is non empty trivial functional finite finite-membered 1 -element set
[:{l},{({} .--> u)}:] is non empty Relation-like finite set
bool [:{l},{({} .--> u)}:] is non empty finite finite-membered set
i +* (l .--> ({} .--> u)) is Relation-like Function-like Function-yielding V164() set
(S,U,E,((l,u) ReassignIn i)) is Relation-like OwnSymbolsOf S -defined Function-like set
bool U is non empty set
I is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S, Class E -interpreter-like Element of (Class E) -InterpretersOf S
X is non empty Element of Class E
(l,X) ReassignIn I is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S, Class E -interpreter-like Element of (Class E) -InterpretersOf S
{} .--> X is trivial Relation-like {{}} -defined Class E -valued Function-like one-to-one constant finite finite-support set
{{}} --> X is non empty Relation-like non-empty non empty-yielding {{}} -defined Class E -valued {X} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{X}:]
{X} is non empty trivial finite 1 -element V165() V166() set
[:{{}},{X}:] is non empty Relation-like finite set
bool [:{{}},{X}:] is non empty finite finite-membered set
l .--> ({} .--> X) is trivial Relation-like AllSymbolsOf S -defined {l} -defined Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} --> ({} .--> X) is non empty Relation-like {l} -defined {({} .--> X)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({} .--> X)}:]
{({} .--> X)} is non empty trivial functional finite finite-membered 1 -element set
[:{l},{({} .--> X)}:] is non empty Relation-like finite set
bool [:{l},{({} .--> X)}:] is non empty finite finite-membered set
I +* (l .--> ({} .--> X)) is Relation-like Function-like Function-yielding V164() set
j is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S,U -interpreter-like Element of U -InterpretersOf S
(S,U,E,j) is Relation-like OwnSymbolsOf S -defined Function-like set
Jj is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V164() S, Class E -interpreter-like Element of (Class E) -InterpretersOf S
dom Jj is Element of bool (OwnSymbolsOf S)
bool (OwnSymbolsOf S) is non empty set
jJ is Relation-like Function-like set
dom jJ is set
{{}} --> u is non empty Relation-like {{}} -defined U -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},U:]
[:{{}},U:] is non empty Relation-like set
bool [:{{}},U:] is non empty set
l .--> ({{}} --> u) is trivial Relation-like AllSymbolsOf S -defined {l} -defined bool [:{{}},U:] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} --> ({{}} --> u) is non empty Relation-like non-empty non empty-yielding {l} -defined bool [:{{}},U:] -valued {({{}} --> u)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({{}} --> u)}:]
{({{}} --> u)} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{l},{({{}} --> u)}:] is non empty Relation-like finite set
bool [:{l},{({{}} --> u)}:] is non empty finite finite-membered set
{{}} --> X is non empty Relation-like non-empty non empty-yielding {{}} -defined Class E -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},(Class E):]
[:{{}},(Class E):] is non empty Relation-like set
bool [:{{}},(Class E):] is non empty set
l .--> ({{}} --> X) is trivial Relation-like AllSymbolsOf S -defined {l} -defined bool [:{{}},(Class E):] -valued Function-like one-to-one constant finite Function-yielding V164() finite-support set
{l} --> ({{}} --> X) is non empty Relation-like non-empty non empty-yielding {l} -defined bool [:{{}},(Class E):] -valued {({{}} --> X)} -valued Function-like constant finite total quasi_total Function-yielding V164() finite-support Element of bool [:{l},{({{}} --> X)}:]
{({{}} --> X)} is non empty trivial functional finite finite-membered 1 -element V165() V166() set
[:{l},{({{}} --> X)}:] is non empty Relation-like finite set
bool [:{l},{({{}} --> X)}:] is non empty finite finite-membered set
ar l 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of INT
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 V166() set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite V166() set
the adicity of S . l is set
abs (ar l) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support Element of NAT
0 -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
[:(0 -tuples_on U),(0 -tuples_on U):] is non empty Relation-like set
bool [:(0 -tuples_on U),(0 -tuples_on U):] is non empty set
n is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() set
(U,E,n) is Relation-like n -tuples_on U -defined n -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:(n -tuples_on U),(n -tuples_on U):]
n -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
[:(n -tuples_on U),(n -tuples_on U):] is non empty Relation-like set
bool [:(n -tuples_on U),(n -tuples_on U):] is non empty set
(U,U,E,n) is Relation-like n -tuples_on U -defined n -tuples_on U -valued total quasi_total Element of bool [:(n -tuples_on U),(n -tuples_on U):]
Seg n is finite n -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 <= n ) } is set
{ [b₁,b₂] where b₁, b₂ is Relation-like NAT -defined U -valued Function-like finite n -element FinSequence-like FinSubsequence-like finite-support Element of n -tuples_on U : for b₃ being set holds
( not b₃ in Seg n or [(b₁ . b₃),(b₂ . b₃)] in E ) } is set
(U,n,E) is non empty Relation-like non empty-yielding n -tuples_on (Class E) -defined Class (U,E,n) -valued Function-like total quasi_total Element of bool [:(n -tuples_on (Class E)),(Class (U,E,n)):]
n -tuples_on (Class E) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class E
Class (U,E,n) is non empty V165() V166() a_partition of n -tuples_on U
[:(n -tuples_on (Class E)),(Class (U,E,n)):] is non empty Relation-like set
bool [:(n -tuples_on (Class E)),(Class (U,E,n)):] is non empty set
(U,E) ~ is Relation-like Class E -defined U -valued total quasi_total Element of bool [:(Class E),U:]
[:(Class E),U:] is non empty Relation-like set
bool [:(Class E),U:] is non empty set
((Class E),U,((U,E) ~),n) is Relation-like n -tuples_on (Class E) -defined n -tuples_on U -valued total quasi_total Element of bool [:(n -tuples_on (Class E)),(n -tuples_on U):]
[:(n -tuples_on (Class E)),(n -tuples_on U):] is non empty Relation-like set
bool [:(n -tuples_on (Class E)),(n -tuples_on U):] is non empty set
{ [b₁,b₂] where b₁ is Relation-like NAT -defined Class E -valued Function-like finite n -element FinSequence-like FinSubsequence-like finite-support Element of n -tuples_on (Class E), b₂ is Relation-like NAT -defined U -valued Function-like finite n -element FinSequence-like FinSubsequence-like finite-support Element of n -tuples_on U : for b₃ being set holds
( not b₃ in Seg n or [(b₁ . b₃),(b₂ . b₃)] in (U,E) ~ ) } is set
((n -tuples_on U),(U,E,n)) is non empty Relation-like non empty-yielding n -tuples_on U -defined Class (U,E,n) -valued Function-like total quasi_total onto Element of bool [:(n -tuples_on U),(Class (U,E,n)):]
[:(n -tuples_on U),(Class (U,E,n)):] is non empty Relation-like set
bool [:(n -tuples_on U),(Class (U,E,n)):] is non empty set
((Class E),U,((U,E) ~),n) * ((n -tuples_on U),(U,E,n)) is Relation-like n -tuples_on (Class E) -defined Class (U,E,n) -valued total quasi_total Element of bool [:(n -tuples_on (Class E)),(Class (U,E,n)):]
dom (l .--> ({{}} --> u)) is trivial finite Element of bool {l}
bool {l} is non empty finite finite-membered set
{l} is non empty trivial finite 1 -element Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite V166() set
dom (l .--> ({{}} --> X)) is trivial finite Element of bool {l}
Enn is Relation-like 0 -tuples_on U -defined 0 -tuples_on U -valued total quasi_total reflexive symmetric transitive Element of bool [:(0 -tuples_on U),(0 -tuples_on U):]
dom (U,E) is non empty Element of bool U
{{}} --> ((U,E) . u) is non empty Relation-like non-empty non empty-yielding {{}} -defined Class E -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},(Class E):]
dom ({{}} --> ((U,E) . u)) is non empty trivial functional finite finite-membered 1 -element V166() Element of bool {{}}
bool {{}} is non empty finite finite-membered set
dom ({{}} --> u) is non empty trivial functional finite finite-membered 1 -element V166() Element of bool {{}}
(id {{}}) \+\ ({} .--> {}) 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 finite-membered cardinal {} -element complex ext-real non positive non negative V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V164() V166() V192() FinSequence-yielding finite-support set
(id {{}}) \ ({} .--> {}) is Relation-like empty-yielding {{}} -defined {{}} -valued finite set
(id {{}}) typed\ ({} .--> {}) is Relation-like empty-yielding {{}} -defined {{}} -valued Function-like finite Function-yielding V164() finite-support Element of bool (id {{}})
(id {{}}) \ ({} .--> {}) is Relation-like empty-yielding {{}} -defined {{}} -valued Function-like finite Function-yielding V164() finite-support Element of bool (id {{}})
({} .--> {}) \ (id {{}}) is Relation-like {{}} -defined finite set
({} .--> {}) typed\ (id {{}}) is trivial Relation-like {{}} -defined Function-like constant finite finite-support Element of bool ({} .--> {})
bool ({} .--> {}) is non empty finite finite-membered set
({} .--> {}) \ (id {{}}) is trivial Relation-like {{}} -defined Function-like constant finite finite-support Element of bool ({} .--> {})
((id {{}}) \ ({} .--> {})) \/ (({} .--> {}) \ (id {{}})) is Relation-like {{}} -defined finite set
[:(n -tuples_on U),U:] is non empty Relation-like set
bool [:(n -tuples_on U),U:] is non empty set
hh is Relation-like Function-like (Enn,E) set
s is set
(S,U,E,j) . s is set
j . l is non empty Relation-like (abs (ar l)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of l,U
(abs (ar l)) -tuples_on U is non empty functional finite-membered FinSequence-membered V166() FinSequenceSet of U
(S,U,l,E,(j . l)) is set
((n -tuples_on U),U,(U,E,n),E,(j . l)) is Relation-like Class (U,E,n) -defined Class E -valued Element of bool [:(Class (U,E,n)),(Class E):]
[:(Class (U,E,n)),(Class E):] is non empty Relation-like set
bool [:(Class (U,E,n)),(Class E):] is non empty set
bool (n -tuples_on U) is non empty set
{ [b₁,b₂] where b₁ is non empty Element of Class (U,E,n), b₂ is non empty Element of Class E : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in j . l ) } is set
(U,n,E) * ((n -tuples_on U),U,(U,E,n),E,(j . l)) is Relation-like n -tuples_on (Class E) -defined Class E -valued Element of bool [:(n -tuples_on (Class E)),(Class E):]
[:(n -tuples_on (Class E)),(Class E):] is non empty Relation-like set
bool [:(n -tuples_on (Class E)),(Class E):] is non empty set
(l .--> ({{}} --> u)) . l is Relation-like Function-like set
((n -tuples_on U),U,(U,E,n),E,((l .--> ({{}} --> u)) . l)) is Relation-like Class (U,E,n) -defined Class E -valued Element of bool [:(Class (U,E,n)),(Class E):]
{ [b₁,b₂] where b₁ is non empty Element of Class (U,E,n), b₂ is non empty Element of Class E : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in (l .--> ({{}} --> u)) . l ) } is set
(U,n,E) * ((n -tuples_on U),U,(U,E,n),E,((l .--> ({{}} --> u)) . l)) is Relation-like n -tuples_on (Class E) -defined Class E -valued Element of bool [:(n -tuples_on (Class E)),(Class E):]
((n -tuples_on U),U,(U,E,n),E,({{}} --> u)) is Relation-like Class (U,E,n) -defined Class E -valued Element of bool [:(Class (U,E,n)),(Class E):]
{ [b₁,b₂] where b₁ is non empty Element of Class (U,E,n), b₂ is non empty Element of Class E : ex b₃, b₄ being set st
( b₃ in b₁ & b₄ in b₂ & [b₃,b₄] in {{}} --> u ) } is set
((n -tuples_on U),U,(U,E,n),E,({{}} --> u)) (*) (U,n,E) is Relation-like n -tuples_on (Class E) -defined Class E -valued set
hhh is non empty Relation-like n -tuples_on U -defined U -valued Function-like total quasi_total ((U,E,n),E) Element of bool [:(n -tuples_on U),U:]
(U,E) * hhh is non empty Relation-like non empty-yielding n -tuples_on U -defined Class E -valued Function-like total quasi_total Element of bool [:(n -tuples_on U),(Class E):]
[:(n -tuples_on U),(Class E):] is non empty Relation-like set
bool [:(n -tuples_on U),(Class E):] is non empty set
((Class E),U,((U,E) ~),n) * ((U,E) * hhh) is Relation-like n -tuples_on (Class E) -defined Class E -valued total quasi_total Element of bool [:(n -tuples_on (Class E)),(Class E):]
((U,E) * hhh) (*) (id {{}}) is Relation-like {{}} -defined Class E -valued Function-like finite finite-support set
({{}} --> ((U,E) . u)) * ({{}} --> {}) is non empty Relation-like non-empty non empty-yielding {{}} -defined Class E -valued Function-like finite total quasi_total finite-support Element of bool [:{{}},(Class E):]
({} .--> ((U,E) . u)) . {} is set
{{}} --> (({} .--> ((U,E) . u)) . {}) is non empty Relation-like {{}} -defined {(({} .--> ((U,E) . u)) . {})} -valued Function-like constant finite total quasi_total finite-support Element of bool [:{{}},{(({} .--> ((U,E) . u)) . {})}:]
{(({} .--> ((U,E) . u)) . {})} is non empty trivial finite 1 -element set
[:{{}},{(({} .--> ((U,E) . u)) . {})}:] is non empty Relation-like finite set
bool [:{{}},{(({} .--> ((U,E) . u)) . {})}:] is non empty finite finite-membered set
Jj . s is Relation-like Function-like set
(l .--> ({{}} --> X)) . l is Relation-like Function-like set
Jj . s is Relation-like Function-like set
I . s is Relation-like Function-like set
ss is own ofAtomicFormula Element of AllSymbolsOf S
i . ss is non empty Relation-like (abs (ar ss)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total (S,U,ss,E) Interpreter of ss,U
ar ss is finite complex ext-real V40() V41() Element of INT
the adicity of S . ss is set
abs (ar ss) is epsilon-transitive epsilon-connected ordinal natural finite cardinal complex ext-real non negative V40() V41() Element of NAT
(abs (ar ss)) -tuples_on U is non empty functional finite-membered FinSequence-membered FinSequenceSet of U
(S,U,ss,E,(i . ss)) is non empty Relation-like (abs (ar ss)) -tuples_on (Class E) -defined (Class E) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of ss, Class E
(abs (ar ss)) -tuples_on (Class E) is non empty functional finite-membered FinSequence-membered FinSequenceSet of Class E
j . ss is non empty Relation-like (abs (ar ss)) -tuples_on U -defined U \/ BOOLEAN -valued Function-like total quasi_total Interpreter of ss,U
(S,U,ss,E,(j . ss)) is set
(S,U,E,j) . ss is set
(S,U,E,j) . s is set