REAL is non empty non trivial non finite non empty-membered set
NAT is non empty non trivial V4() V5() V6() non finite cardinal limit_cardinal non empty-membered countable denumerable Element of bool REAL
bool REAL is non empty non trivial non finite non empty-membered set
BOOLEAN is non empty set
NAT is non empty non trivial V4() V5() V6() non finite cardinal limit_cardinal non empty-membered countable denumerable set
bool NAT is non empty non trivial non finite non empty-membered set
bool NAT is non empty non trivial non finite non empty-membered set
COMPLEX is non empty non trivial non finite non empty-membered set
RAT is non empty non trivial non finite non empty-membered set
INT is non empty non trivial non finite non empty-membered set
{} is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
{{}} is non empty trivial functional finite V36() 1 -element empty-membered with_common_domain countable set
1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
{} * is non empty functional V36() FinSequence-membered FinSequenceSet of {}
[:{{}},NAT:] is non empty non trivial Relation-like non finite non empty-membered set
[{},{}] is non empty V26() set
{[{},{}]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
[:{{}},NAT:] \ {[{},{}]} is non empty non trivial Relation-like {{}} -defined NAT -valued non finite non empty-membered Element of bool [:{{}},NAT:]
bool [:{{}},NAT:] is non empty non trivial non finite non empty-membered set
[:{{}},NAT:] typed\ {[{},{}]} is Relation-like {{}} -defined NAT -valued Element of bool [:{{}},NAT:]
NAT \/ ([:{{}},NAT:] \ {[{},{}]}) is non empty non trivial non finite non empty-membered set
[:REAL,REAL:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:REAL,REAL:] is non empty non trivial non finite non empty-membered set
K281() is V47() V75() L8()
the U1 of K281() is set
K286() is V47() L8()
K287() is V47() V75() M13(K286())
K288() is V47() V75() V97() V154() M16(K286(),K287())
K290() is V47() V75() V97() V99() V101() L8()
K291() is V47() V75() V97() V154() M13(K290())
2 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
{{},1} is non empty finite V36() countable set
[:COMPLEX,COMPLEX:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:COMPLEX,COMPLEX:] is non empty non trivial non finite non empty-membered set
0 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of NAT
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
3 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
proj1 {} is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined NAT -defined {{}} -valued {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
proj2 {} is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined NAT -defined {{}} -valued {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
len {} is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of NAT
Seg 1 is non empty trivial finite 1 -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= 1 ) } is set
{1} is non empty trivial finite V36() 1 -element with_non-empty_elements non empty-membered countable Element of bool NAT
- 2 is non empty complex ext-real non positive negative finite V40() V41() countable set
TRUE is boolean Element of BOOLEAN
FALSE is boolean Element of BOOLEAN
X is set
C is set
phi is set
Funcs (C,phi) is functional set
bool (Funcs (C,phi)) is non empty set
[:C,phi:] is Relation-like set
bool [:C,phi:] is non empty set
bool (bool [:C,phi:]) is non empty set
bool [:C,phi:] is non empty Element of bool (bool [:C,phi:])
X is V51() V53() eligible Language-like
TermSymbolsOf X is non empty set
the U1 of X is set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
C is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ C) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
{} .--> {} is non empty trivial Relation-like {{}} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() Cardinal-yielding countable V209() set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant total quasi_total finite Function-yielding V156() Cardinal-yielding countable V209() Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite countable set
bool [:{{}},{{}}:] is non empty finite V36() countable set
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
Y is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
<*Y*> is non empty trivial Relation-like non empty-yielding NAT -defined AllTermsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() FinSequence of AllTermsOf X
[1,Y] is non empty V26() set
{[1,Y]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
<*phii*> is non empty trivial Relation-like non empty-yielding NAT -defined AllTermsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() FinSequence of AllTermsOf X
[1,phii] is non empty V26() set
{[1,phii]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*Y*> ^ <*phii*> is non empty Relation-like non empty-yielding NAT -defined AllTermsOf X -valued Function-like finite 1 + 1 -element 1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() FinSequence of AllTermsOf X
1 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
1 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
H is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
H * is non empty functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
psi is Relation-like NAT -defined AllTermsOf X -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
m is Relation-like NAT -defined H -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V156() countable V209() Element of H *
abs (- 2) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
- (- 2) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
HH is ofAtomicFormula Element of AllSymbolsOf X
ar HH is complex ext-real finite V40() V41() countable Element of INT
the adicity of X . HH is set
abs (ar HH) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(X -multiCat) . m is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
(X -multiCat) . psi is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
a is non empty set
D2 is Element of a
<*D2*> is non empty trivial Relation-like NAT -defined a -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() FinSequence of a
[1,D2] is non empty V26() set
{[1,D2]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
sub1 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() FinSequence of AllSymbolsOf X
HC is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() FinSequence of AllSymbolsOf X
sub1 ^ HC is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() FinSequence of AllSymbolsOf X
sub2 is non empty Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() FinSequence of AllSymbolsOf X
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
<*Y,phii*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V209() set
<*Y*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
<*phii*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
<*Y*> ^ <*phii*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element 1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
((AllSymbolsOf X) -multiCat) . <*Y,phii*> is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() set
Y ^ phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
C ^ phi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ (C ^ phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
X is V51() V53() eligible Language-like
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
X is V51() V53() eligible Language-like
(X) is set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
the functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X) is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[ the functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X), the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}] is non empty V26() Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
X is V51() V53() eligible Language-like
(X) is non empty set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
DD is set
FF is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X)
D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[FF,D] is non empty V26() Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool (AllFormulasOf X) is non empty Element of bool (bool (AllFormulasOf X))
bool (bool (AllFormulasOf X)) is non empty set
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like bool (AllFormulasOf X) -defined (AllSymbolsOf X) * -valued non finite non empty-membered Element of bool [:(bool (AllFormulasOf X)),((AllSymbolsOf X) *):]
[:(bool (AllFormulasOf X)),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(bool (AllFormulasOf X)),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
bool [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty set
C is Relation-like Element of bool (X)
C is Element of (X)
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
the (X) Element of (X) is (X) Element of (X)
bool (X) is non empty set
the Relation-like (X) Element of bool (X) is Relation-like (X) Element of bool (X)
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
the (X) Element of (X) is (X) Element of (X)
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty set
the Relation-like (X) Element of bool (X) is Relation-like (X) Element of bool (X)
X is set
C is set
Funcs (X,C) is functional set
bool (Funcs (X,C)) is non empty set
phi is functional Element of bool (Funcs (X,C))
union phi is Relation-like set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
union C is Relation-like set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
union C is Relation-like set
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
DD is Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):]
FF is non empty Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of bool [:(bool (X)),(bool (X)):]
D is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
Y is Relation-like (X) Element of bool (X)
D . Y is Relation-like (X) Element of bool (X)
{Y} is non empty trivial finite 1 -element countable Element of bool (bool (X))
bool (bool (X)) is non empty set
(union C) .: {Y} is set
union ((union C) .: {Y}) is set
DD is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
FF is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
D is non empty Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of bool [:(bool (X)),(bool (X)):]
phii is Relation-like (X) Element of bool (X)
D . phii is Relation-like (X) Element of bool (X)
{phii} is non empty trivial finite 1 -element countable set
(union C) .: {phii} is set
union ((union C) .: {phii}) is set
Y is non empty Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of bool [:(bool (X)),(bool (X)):]
Y . phii is Relation-like (X) Element of bool (X)
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
[:(bool (C)),(bool (C)):] is non empty Relation-like set
bool [:(bool (C)),(bool (C)):] is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,phi) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
dom (C,phi) is Element of bool (bool (C))
bool (bool (C)) is non empty set
proj2 (C,phi) is set
iter ((C,phi),X) is Relation-like Function-like set
proj1 (iter ((C,phi),X)) is set
(dom (C,phi)) \/ (proj2 (C,phi)) is set
S is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
dom S is Element of bool (bool (C))
iter (S,X) is Relation-like Function-like set
proj1 (iter (S,X)) is set
DD is Relation-like (C) Element of bool (C)
FF is (C) set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
(X,C) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
iter ((X,C),phi) is Relation-like Function-like set
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
(X,C) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{ (iter ((X,C),b1)) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
[:(bool (X)),(bool (X)):] is non empty Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):]
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
bool [:(bool (X)),(bool (X)):] is non empty set
bool (bool [:(bool (X)),(bool (X)):]) is non empty set
FF is set
D is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
iter ((X,C),D) is Relation-like Function-like set
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
bool [:(bool (X)),(bool (X)):] is non empty Element of bool (bool [:(bool (X)),(bool (X)):])
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
id (bool (X)) is non empty Relation-like bool (X) -defined bool (X) -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:(bool (X)),(bool (X)):]
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
S is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
DD is Relation-like (X) Element of bool (X)
S . DD is Relation-like (X) Element of bool (X)
FF is Relation-like (X) Element of bool (X)
S . FF is Relation-like (X) Element of bool (X)
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
id (bool (X)) is non empty Relation-like bool (X) -defined bool (X) -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:(bool (X)),(bool (X)):]
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
phi is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
{C} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
S is Relation-like (X) Element of bool (X)
DD is Relation-like (X) Element of bool (X)
FF is Relation-like Function-like set
Y is Relation-like Function-like set
D is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
D . S is Relation-like (X) Element of bool (X)
D . DD is Relation-like (X) Element of bool (X)
FF . S is set
Y . DD is set
S is functional Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
the Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X))) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
{ the Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
phi is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is set
phi is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
S is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is set
S is set
[phi,S] is non empty V26() set
{[phi,S]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
DD is non empty V26() set
DD `1 is set
DD `2 is set
{DD} is non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable set
[phi,S] is non empty V26() set
{[phi,S]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
[phi,S] is non empty V26() set
{[phi,S]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
DD is set
DD `1 is set
DD `2 is set
{DD} is non empty trivial finite 1 -element countable set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}} : (<*(TheEqSymbOf X)*> ^ b1) ^ b2 is (X,C,phi) } is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
X is set
C is set
phi is set
S is V51() V53() eligible Language-like
(S) is non empty Relation-like set
AllFormulasOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
the U1 of S is set
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf S) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf S), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}} : b1 is finite } is set
bool (S) is non empty Element of bool (bool (S))
bool (S) is non empty set
bool (bool (S)) is non empty set
Funcs ((bool (S)),(bool (S))) is non empty functional FUNCTION_DOMAIN of bool (S), bool (S)
bool (Funcs ((bool (S)),(bool (S)))) is non empty set
DD is functional Element of bool (Funcs ((bool (S)),(bool (S))))
FF is set
FF `1 is set
FF `2 is set
{FF} is non empty trivial finite 1 -element countable set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is set
(X,C,phi) is set
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}} : (<*(TheEqSymbOf X)*> ^ b1) ^ b2 is (X,C,phi) } is set
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
[:(AllTermsOf X),(AllTermsOf X):] is non empty Relation-like set
bool [:(AllTermsOf X),(AllTermsOf X):] is non empty set
S is set
DD is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
FF is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
[DD,FF] is non empty V26() Element of [:(((AllSymbolsOf X) *) \ {{}}),(((AllSymbolsOf X) *) \ {{}}):]
[:(((AllSymbolsOf X) *) \ {{}}),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
<*(TheEqSymbOf X)*> ^ DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ DD) ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
Y is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
[D,Y] is non empty V26() Element of [:(AllTermsOf X),(AllTermsOf X):]
[:(AllTermsOf X),(AllTermsOf X):] is non empty Relation-like non empty-yielding ((AllSymbolsOf X) *) \ {{}} -defined ((AllSymbolsOf X) *) \ {{}} -valued Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(((AllSymbolsOf X) *) \ {{}}),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
phi is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
S is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
phi \/ S is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[(phi \/ S),C] is non empty V26() Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
FF is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
[FF,C] is non empty V26() Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
(X) is non empty Relation-like set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[C,phi] is non empty V26() set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
S is functional finite V36() FinSequence-membered countable Element of bool ((AllSymbolsOf X) *)
[S,phi] is non empty V26() Element of [:(bool ((AllSymbolsOf X) *)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool ((AllSymbolsOf X) *)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
X is V51() V53() eligible Language-like
{} /\ X is Relation-like functional finite countable set
{} typed/\ X is empty trivial non proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {}
bool {} is non empty finite V36() countable set
{} /\typed X is Element of bool X
bool X is non empty set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty set
S is Relation-like (X) Element of bool (X)
DD is set
X is V51() V53() eligible Language-like
X is V51() V53() eligible Language-like
C is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
C is (X) (X) Element of (X)
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C,phi,X) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C,phi) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,phi),X) is Relation-like Function-like set
S is set
(C,phi,X) . S is set
[:(bool (C)),(bool (C)):] is non empty Relation-like set
bool [:(bool (C)),(bool (C)):] is non empty set
FF is non empty Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of bool [:(bool (C)),(bool (C)):]
dom FF is non empty Element of bool (bool (C))
bool (bool (C)) is non empty set
FF . S is set
FF is non empty Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of bool [:(bool (C)),(bool (C)):]
D is Relation-like (C) Element of bool (C)
FF . D is Relation-like (C) Element of bool (C)
X is V51() V53() eligible Language-like
phi is (X) set
C is set
phi /\ C is set
phi typed/\ C is Element of bool phi
bool phi is non empty set
phi /\typed C is Element of bool C
bool C is non empty set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
DD is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
S is set
(X,C) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X,C) [*] is Relation-like bool (X) -defined bool (X) -valued reflexive transitive Element of bool [:(bool (X)),(bool (X)):]
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
{S} is non empty trivial finite 1 -element countable set
((X,C) [*]) .: {S} is Element of bool (bool (X))
bool (bool (X)) is non empty set
union (((X,C) [*]) .: {S}) is Relation-like (X) Element of bool (X)
(X,C,phi) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
iter ((X,C),phi) is Relation-like Function-like set
(X,C,phi) . S is (X) set
Y is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is set
S is set
phi \ S is Element of bool phi
bool phi is non empty set
phi typed\ S is Element of bool phi
DD is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is set
S is set
phi \ S is Element of bool phi
bool phi is non empty set
phi typed\ S is Element of bool phi
phi \/ S is set
DD is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is set
S is set
phi /\ S is set
phi typed/\ S is Element of bool phi
bool phi is non empty set
phi /\typed S is Element of bool S
bool S is non empty set
DD is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
phi is set
bool phi is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
S is Element of bool phi
DD is set
FF is set
FF `1 is set
FF `2 is set
{FF} is non empty trivial finite 1 -element countable set
X is V51() V53() eligible Language-like
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
C is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[C,phi] is non empty V26() Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
(X) is non empty Relation-like set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
FF is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{C} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[{C},phi] is non empty V26() Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf X
{DD} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (AllFormulasOf X)
FF is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
[FF,phi] is non empty V26() (X) (X) Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
D is set
{C,phi} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[{C,phi},S] is non empty V26() Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf X
{FF} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (AllFormulasOf X)
D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf X
{D} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (AllFormulasOf X)
{FF} \/ {D} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (AllFormulasOf X)
Y is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
[Y,phi] is non empty V26() (X) (X) Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
{FF,D} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (AllFormulasOf X)
phii is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
S is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{C} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
S \/ {C} is non empty functional finite V36() with_non-empty_elements non empty-membered countable set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[(S \/ {C}),phi] is non empty V26() set
FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf X
{FF} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (AllFormulasOf X)
S \/ {FF} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (AllFormulasOf X)
D is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
[D,phi] is non empty V26() (X) (X) Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
Y is set
X is set
{X} is non empty trivial finite 1 -element countable set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
[:(bool (C)),(bool (C)):] is non empty Relation-like bool (C) -defined bool (C) -valued Element of bool [:(bool (C)),(bool (C)):]
[:(bool (C)),(bool (C)):] is non empty Relation-like set
bool [:(bool (C)),(bool (C)):] is non empty set
bool [:(bool (C)),(bool (C)):] is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,phi) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C,phi) . X is set
{ (b1 .: {X}) where b1 is Relation-like bool (C) -defined bool (C) -valued Element of bool [:(bool (C)),(bool (C)):] : b1 in phi } is set
union { (b1 .: {X}) where b1 is Relation-like bool (C) -defined bool (C) -valued Element of bool [:(bool (C)),(bool (C)):] : b1 in phi } is set
union (union { (b1 .: {X}) where b1 is Relation-like bool (C) -defined bool (C) -valued Element of bool [:(bool (C)),(bool (C)):] : b1 in phi } ) is set
bool (bool [:(bool (C)),(bool (C)):]) is non empty set
D is Relation-like (C) Element of bool (C)
(C,phi) . D is Relation-like (C) Element of bool (C)
Y is Element of bool (bool [:(bool (C)),(bool (C)):])
union Y is Relation-like bool (C) -defined bool (C) -valued Element of bool [:(bool (C)),(bool (C)):]
{D} is non empty trivial finite 1 -element countable Element of bool (bool (C))
bool (bool (C)) is non empty set
(union Y) .: {D} is Element of bool (bool (C))
union ((union Y) .: {D}) is Relation-like (C) Element of bool (C)
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{C} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X,{C}) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
dom C is Element of bool (bool (X))
bool (bool (X)) is non empty set
dom (X,{C}) is Element of bool (bool (X))
S is set
C . S is set
{(C . S)} is non empty trivial finite 1 -element countable set
union {(C . S)} is set
Im (C,S) is set
{S} is non empty trivial finite 1 -element countable set
C .: {S} is finite countable set
union (Im (C,S)) is set
union {C} is Relation-like set
(union {C}) .: {S} is set
union ((union {C}) .: {S}) is set
(X,{C}) . S is set
X is set
{X} is non empty trivial finite 1 -element countable set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S is Relation-like (C) Element of bool (C)
(C,phi) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C,phi) is Element of bool (bool [:(bool (C)),(bool (C)):])
[:(bool (C)),(bool (C)):] is non empty Relation-like bool (C) -defined bool (C) -valued Element of bool [:(bool (C)),(bool (C)):]
[:(bool (C)),(bool (C)):] is non empty Relation-like set
bool [:(bool (C)),(bool (C)):] is non empty set
bool [:(bool (C)),(bool (C)):] is non empty set
bool (bool [:(bool (C)),(bool (C)):]) is non empty set
{ (iter ((C,phi),b1)) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
(C,phi) [*] is Relation-like bool (C) -defined bool (C) -valued reflexive transitive Element of bool [:(bool (C)),(bool (C)):]
[:(bool (C)),(bool (C)):] is non empty Relation-like set
bool [:(bool (C)),(bool (C)):] is non empty set
{S} is non empty trivial finite 1 -element countable Element of bool (bool (C))
((C,phi) [*]) .: {S} is Element of bool (bool (C))
bool (bool (C)) is non empty set
union (((C,phi) [*]) .: {S}) is Relation-like (C) Element of bool (C)
phii is set
proj2 (C,phi) is set
dom (C,phi) is Element of bool (bool (C))
union (C,phi) is Relation-like bool (C) -defined bool (C) -valued Element of bool [:(bool (C)),(bool (C)):]
{ (b1 .: {S}) where b1 is Relation-like bool (C) -defined bool (C) -valued Element of bool [:(bool (C)),(bool (C)):] : b1 in (C,phi) } is set
union { (b1 .: {S}) where b1 is Relation-like bool (C) -defined bool (C) -valued Element of bool [:(bool (C)),(bool (C)):] : b1 in (C,phi) } is set
psi is set
H is Relation-like bool (C) -defined bool (C) -valued Element of bool [:(bool (C)),(bool (C)):]
H .: {S} is Element of bool (bool (C))
m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
iter ((C,phi),m) is Relation-like Function-like set
proj1 (iter ((C,phi),m)) is set
Im ((iter ((C,phi),m)),S) is set
{S} is non empty trivial finite 1 -element countable set
(iter ((C,phi),m)) .: {S} is finite countable set
(iter ((C,phi),m)) . S is set
{((iter ((C,phi),m)) . S)} is non empty trivial finite 1 -element countable set
(C,phi,m) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C,phi,m) . S is Relation-like (C) Element of bool (C)
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is set
{C} is non empty trivial finite 1 -element countable set
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
S is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
(phi,S,X) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
(phi,S) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
iter ((phi,S),X) is Relation-like Function-like set
(phi,S,X) . C is (phi) set
(phi,S) [*] is Relation-like bool (phi) -defined bool (phi) -valued reflexive transitive Element of bool [:(bool (phi)),(bool (phi)):]
[:(bool (phi)),(bool (phi)):] is non empty Relation-like set
bool [:(bool (phi)),(bool (phi)):] is non empty set
((phi,S) [*]) .: {C} is Element of bool (bool (phi))
bool (bool (phi)) is non empty set
union (((phi,S) [*]) .: {C}) is Relation-like (phi) Element of bool (phi)
proj1 (iter ((phi,S),X)) is set
{(iter ((phi,S),X))} is non empty trivial functional finite 1 -element with_common_domain countable set
union {(iter ((phi,S),X))} is Relation-like set
(iter ((phi,S),X)) . C is set
{((iter ((phi,S),X)) . C)} is non empty trivial finite 1 -element countable set
union {((iter ((phi,S),X)) . C)} is set
Im ((iter ((phi,S),X)),C) is set
(iter ((phi,S),X)) .: {C} is finite countable set
union (Im ((iter ((phi,S),X)),C)) is set
Y is Relation-like Function-like set
Y .: {C} is finite countable set
union (Y .: {C}) is set
phii is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
iter ((phi,S),phii) is Relation-like Function-like set
(phi,S) is Element of bool (bool [:(bool (phi)),(bool (phi)):])
[:(bool (phi)),(bool (phi)):] is non empty Relation-like bool (phi) -defined bool (phi) -valued Element of bool [:(bool (phi)),(bool (phi)):]
[:(bool (phi)),(bool (phi)):] is non empty Relation-like set
bool [:(bool (phi)),(bool (phi)):] is non empty set
bool [:(bool (phi)),(bool (phi)):] is non empty set
bool (bool [:(bool (phi)),(bool (phi)):]) is non empty set
{ (iter ((phi,S),b1)) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
union (phi,S) is Relation-like bool (phi) -defined bool (phi) -valued Element of bool [:(bool (phi)),(bool (phi)):]
(union (phi,S)) .: {C} is Element of bool (bool (phi))
union ((union (phi,S)) .: {C}) is Relation-like (phi) Element of bool (phi)
proj2 (phi,S) is set
dom (phi,S) is Element of bool (bool (phi))
X is set
{X} is non empty trivial finite 1 -element countable set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,phi) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C,phi) [*] is Relation-like bool (C) -defined bool (C) -valued reflexive transitive Element of bool [:(bool (C)),(bool (C)):]
[:(bool (C)),(bool (C)):] is non empty Relation-like set
bool [:(bool (C)),(bool (C)):] is non empty set
((C,phi) [*]) .: {X} is Element of bool (bool (C))
bool (bool (C)) is non empty set
union (((C,phi) [*]) .: {X}) is Relation-like (C) Element of bool (C)
{ ((C,phi,b1) . X) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
union { ((C,phi,b1) . X) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
dom ((C,phi) [*]) is Element of bool (bool (C))
{X} /\ (dom ((C,phi) [*])) is finite countable Element of bool (bool (C))
{X} typed/\ (dom ((C,phi) [*])) is trivial finite countable Element of bool {X}
bool {X} is non empty finite V36() countable set
{X} /\ (dom ((C,phi) [*])) is finite countable set
{X} /\typed (dom ((C,phi) [*])) is Element of bool (dom ((C,phi) [*]))
bool (dom ((C,phi) [*])) is non empty set
((C,phi) [*]) .: {} is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (bool (C))
psi is set
H is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(C,phi,H) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,phi),H) is Relation-like Function-like set
(C,phi,H) . X is (C) set
dom (C,phi,H) is Element of bool (bool (C))
union {{}} is Relation-like finite countable set
phii is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
union phii is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
psi is set
H is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(C,phi,H) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,phi),H) is Relation-like Function-like set
(C,phi,H) . X is (C) set
psi is set
{psi} is non empty trivial finite 1 -element countable set
phii is Relation-like (C) Element of bool (C)
H is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(C,phi,H) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,phi),H) is Relation-like Function-like set
(C,phi,H) . phii is Relation-like (C) Element of bool (C)
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is set
{C} is non empty trivial finite 1 -element countable set
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
S is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
(phi,S,X) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
(phi,S) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
iter ((phi,S),X) is Relation-like Function-like set
(phi,S,X) . C is (phi) set
(phi,S) [*] is Relation-like bool (phi) -defined bool (phi) -valued reflexive transitive Element of bool [:(bool (phi)),(bool (phi)):]
[:(bool (phi)),(bool (phi)):] is non empty Relation-like set
bool [:(bool (phi)),(bool (phi)):] is non empty set
((phi,S) [*]) .: {C} is Element of bool (bool (phi))
bool (bool (phi)) is non empty set
union (((phi,S) [*]) .: {C}) is Relation-like (phi) Element of bool (phi)
{ ((phi,S,b1) . C) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
union { ((phi,S,b1) . C) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
psi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(phi,S,psi) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
iter ((phi,S),psi) is Relation-like Function-like set
(phi,S,psi) . C is (phi) set
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is set
{C} is non empty trivial finite 1 -element countable set
phi is set
S is V51() V53() eligible Language-like
(S) is non empty Relation-like set
AllFormulasOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
the U1 of S is set
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf S) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf S), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}} : b1 is finite } is set
bool (S) is non empty Element of bool (bool (S))
bool (S) is non empty set
bool (bool (S)) is non empty set
Funcs ((bool (S)),(bool (S))) is non empty functional FUNCTION_DOMAIN of bool (S), bool (S)
bool (Funcs ((bool (S)),(bool (S)))) is non empty set
DD is functional Element of bool (Funcs ((bool (S)),(bool (S))))
(S,DD) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
(S,DD) [*] is Relation-like bool (S) -defined bool (S) -valued reflexive transitive Element of bool [:(bool (S)),(bool (S)):]
[:(bool (S)),(bool (S)):] is non empty Relation-like set
bool [:(bool (S)),(bool (S)):] is non empty set
{phi} is non empty trivial finite 1 -element countable set
((S,DD) [*]) .: {phi} is Element of bool (bool (S))
bool (bool (S)) is non empty set
union (((S,DD) [*]) .: {phi}) is Relation-like (S) Element of bool (S)
(S,DD,X) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
iter ((S,DD),X) is Relation-like Function-like set
(S,DD,X) . phi is (S) set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
(X,C) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
phi is functional Element of bool (Funcs ((bool (X)),(bool (X))))
(X,phi) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
S is Relation-like (X) Element of bool (X)
(X,C) . S is Relation-like (X) Element of bool (X)
DD is Relation-like (X) Element of bool (X)
(X,phi) . DD is Relation-like (X) Element of bool (X)
union C is Relation-like set
union phi is Relation-like set
[:(bool (X)),(bool (X)):] is non empty Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):]
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
bool [:(bool (X)),(bool (X)):] is non empty set
{S} is non empty trivial finite 1 -element countable Element of bool (bool (X))
{ (b1 .: {S}) where b1 is Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):] : b1 in C } is set
{DD} is non empty trivial finite 1 -element countable Element of bool (bool (X))
{ (b1 .: {DD}) where b1 is Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):] : b1 in phi } is set
union { (b1 .: {S}) where b1 is Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):] : b1 in C } is set
union (union { (b1 .: {S}) where b1 is Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):] : b1 in C } ) is set
union { (b1 .: {DD}) where b1 is Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):] : b1 in phi } is set
union (union { (b1 .: {DD}) where b1 is Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):] : b1 in phi } ) is set
HC is set
a is set
D2 is set
sub1 is Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):]
sub1 .: {S} is Element of bool (bool (X))
bool (bool (X)) is non empty set
sub2 is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
Im (sub2,S) is set
{S} is non empty trivial finite 1 -element countable set
sub2 .: {S} is finite countable set
dom sub2 is Element of bool (bool (X))
sub2 . S is Relation-like (X) Element of bool (X)
{(sub2 . S)} is non empty trivial finite 1 -element countable Element of bool (bool (X))
inf is Relation-like Function-like set
inf . DD is set
inf is Relation-like Function-like set
inf . DD is set
inf is Relation-like Function-like set
inf . DD is set
U is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
dom U is Element of bool (bool (X))
Im (U,DD) is set
{DD} is non empty trivial finite 1 -element countable set
U .: {DD} is finite countable set
U . DD is Relation-like (X) Element of bool (X)
{(U . DD)} is non empty trivial finite 1 -element countable Element of bool (bool (X))
{{(U . DD)}} is non empty trivial finite V36() 1 -element with_non-empty_elements non empty-membered countable Element of bool (bool (bool (X)))
bool (bool (bool (X))) is non empty set
{(inf . DD)} is non empty trivial finite 1 -element countable set
{{(inf . DD)}} is non empty trivial finite V36() 1 -element with_non-empty_elements non empty-membered countable set
union {{(inf . DD)}} is non empty finite countable set
union {(inf . DD)} is set
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,phi,X) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C,phi) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,phi),X) is Relation-like Function-like set
S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,S,X) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C,S) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,S),X) is Relation-like Function-like set
DD is Relation-like (C) Element of bool (C)
(C,phi,X) . DD is Relation-like (C) Element of bool (C)
FF is Relation-like (C) Element of bool (C)
(C,S,X) . FF is Relation-like (C) Element of bool (C)
(C,phi,0) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,phi),0) is Relation-like Function-like set
(C,phi,0) . DD is Relation-like (C) Element of bool (C)
(C,S,0) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,S),0) is Relation-like Function-like set
(C,S,0) . FF is Relation-like (C) Element of bool (C)
(iter ((C,phi),0)) . DD is set
field (C,phi) is set
proj1 (C,phi) is set
proj2 (C,phi) is set
(proj1 (C,phi)) \/ (proj2 (C,phi)) is set
id (field (C,phi)) is Relation-like field (C,phi) -defined field (C,phi) -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:(field (C,phi)),(field (C,phi)):]
[:(field (C,phi)),(field (C,phi)):] is Relation-like set
bool [:(field (C,phi)),(field (C,phi)):] is non empty set
(id (field (C,phi))) . DD is set
id (bool (C)) is non empty Relation-like bool (C) -defined bool (C) -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:(bool (C)),(bool (C)):]
[:(bool (C)),(bool (C)):] is non empty Relation-like set
bool [:(bool (C)),(bool (C)):] is non empty set
(id (bool (C))) . DD is Relation-like (C) Element of bool (C)
(iter ((C,S),0)) . FF is set
field (C,S) is set
proj1 (C,S) is set
proj2 (C,S) is set
(proj1 (C,S)) \/ (proj2 (C,S)) is set
id (field (C,S)) is Relation-like field (C,S) -defined field (C,S) -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:(field (C,S)),(field (C,S)):]
[:(field (C,S)),(field (C,S)):] is Relation-like set
bool [:(field (C,S)),(field (C,S)):] is non empty set
(id (field (C,S))) . FF is set
(id (bool (C))) . FF is Relation-like (C) Element of bool (C)
m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C,phi,m) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,phi),m) is Relation-like Function-like set
(C,phi,m) . DD is Relation-like (C) Element of bool (C)
(C,S,m) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,S),m) is Relation-like Function-like set
(C,S,m) . FF is Relation-like (C) Element of bool (C)
m + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(C,phi,(m + 1)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,phi),(m + 1)) is Relation-like Function-like set
(C,phi,(m + 1)) . DD is Relation-like (C) Element of bool (C)
(C,S,(m + 1)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,S),(m + 1)) is Relation-like Function-like set
(C,S,(m + 1)) . FF is Relation-like (C) Element of bool (C)
proj1 (iter ((C,phi),m)) is set
proj1 (iter ((C,S),m)) is set
(iter ((C,phi),m)) * (C,phi) is Relation-like bool (C) -valued Function-like set
((iter ((C,phi),m)) * (C,phi)) . DD is set
seqt is Relation-like (C) Element of bool (C)
(C,phi) . seqt is Relation-like (C) Element of bool (C)
(iter ((C,S),m)) * (C,S) is Relation-like bool (C) -valued Function-like set
((iter ((C,S),m)) * (C,S)) . FF is set
HH is Relation-like (C) Element of bool (C)
(C,S) . HH is Relation-like (C) Element of bool (C)
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,phi,X) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C,phi) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,phi),X) is Relation-like Function-like set
S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,S,X) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C,S) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,S),X) is Relation-like Function-like set
DD is (C) set
(C,phi,X) . DD is (C) set
FF is (C) set
(C,S,X) . FF is (C) set
D is Relation-like (C) Element of bool (C)
(C,phi,X) . D is Relation-like (C) Element of bool (C)
Y is Relation-like (C) Element of bool (C)
(C,S,X) . Y is Relation-like (C) Element of bool (C)
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is set
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
S is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
(phi,S,X) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
(phi,S) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
iter ((phi,S),X) is Relation-like Function-like set
(phi,S,X) . C is (phi) set
DD is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
(phi,DD,X) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
(phi,DD) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
iter ((phi,DD),X) is Relation-like Function-like set
(phi,DD,X) . C is (phi) set
phii is Relation-like (phi) Element of bool (phi)
(phi,S,X) . phii is Relation-like (phi) Element of bool (phi)
(phi,DD,X) . phii is Relation-like (phi) Element of bool (phi)
dom (phi,S,X) is Element of bool (bool (phi))
bool (bool (phi)) is non empty set
dom (phi,DD,X) is Element of bool (bool (phi))
X is set
{X} is non empty trivial finite 1 -element countable set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,phi) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C,phi) [*] is Relation-like bool (C) -defined bool (C) -valued reflexive transitive Element of bool [:(bool (C)),(bool (C)):]
[:(bool (C)),(bool (C)):] is non empty Relation-like set
bool [:(bool (C)),(bool (C)):] is non empty set
((C,phi) [*]) .: {X} is Element of bool (bool (C))
bool (bool (C)) is non empty set
union (((C,phi) [*]) .: {X}) is Relation-like (C) Element of bool (C)
S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,S) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C,S) [*] is Relation-like bool (C) -defined bool (C) -valued reflexive transitive Element of bool [:(bool (C)),(bool (C)):]
((C,S) [*]) .: {X} is Element of bool (bool (C))
union (((C,S) [*]) .: {X}) is Relation-like (C) Element of bool (C)
{ ((C,phi,b1) . X) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
{ ((C,S,b1) . X) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
union { ((C,phi,b1) . X) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
union { ((C,S,b1) . X) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
m is set
seqt is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(C,phi,seqt) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,phi),seqt) is Relation-like Function-like set
(C,phi,seqt) . X is (C) set
(C,S,seqt) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
iter ((C,S),seqt) is Relation-like Function-like set
(C,S,seqt) . X is (C) set
X is set
C is set
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
S is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
DD is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
(phi,S) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
(phi,DD) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
(phi,S) [*] is Relation-like bool (phi) -defined bool (phi) -valued reflexive transitive Element of bool [:(bool (phi)),(bool (phi)):]
[:(bool (phi)),(bool (phi)):] is non empty Relation-like set
bool [:(bool (phi)),(bool (phi)):] is non empty set
{C} is non empty trivial finite 1 -element countable set
((phi,S) [*]) .: {C} is Element of bool (bool (phi))
bool (bool (phi)) is non empty set
union (((phi,S) [*]) .: {C}) is Relation-like (phi) Element of bool (phi)
(phi,DD) [*] is Relation-like bool (phi) -defined bool (phi) -valued reflexive transitive Element of bool [:(bool (phi)),(bool (phi)):]
((phi,DD) [*]) .: {C} is Element of bool (bool (phi))
union (((phi,DD) [*]) .: {C}) is Relation-like (phi) Element of bool (phi)
X is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
phi is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{phi} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (C)),(bool (C))))
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
S is Relation-like (C) Element of bool (C)
phi . S is Relation-like (C) Element of bool (C)
(C,{phi}) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C,{phi}) [*] is Relation-like bool (C) -defined bool (C) -valued reflexive transitive Element of bool [:(bool (C)),(bool (C)):]
[:(bool (C)),(bool (C)):] is non empty Relation-like set
bool [:(bool (C)),(bool (C)):] is non empty set
dom phi is Element of bool (bool (C))
bool (bool (C)) is non empty set
{(phi . S)} is non empty trivial finite 1 -element countable Element of bool (bool (C))
Im (phi,S) is set
{S} is non empty trivial finite 1 -element countable set
phi .: {S} is finite countable set
{S} is non empty trivial finite 1 -element countable Element of bool (bool (C))
phi .: {S} is finite countable set
((C,{phi}) [*]) .: {S} is Element of bool (bool (C))
union {(phi . S)} is Relation-like (C) Element of bool (C)
union (((C,{phi}) [*]) .: {S}) is Relation-like (C) Element of bool (C)
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
X + C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
phi is set
S is V51() V53() eligible Language-like
(S) is non empty Relation-like set
AllFormulasOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
the U1 of S is set
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf S) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf S), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}} : b1 is finite } is set
bool (S) is non empty Element of bool (bool (S))
bool (S) is non empty set
bool (bool (S)) is non empty set
Funcs ((bool (S)),(bool (S))) is non empty functional FUNCTION_DOMAIN of bool (S), bool (S)
bool (Funcs ((bool (S)),(bool (S)))) is non empty set
DD is functional Element of bool (Funcs ((bool (S)),(bool (S))))
(S,DD) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
iter ((S,DD),X) is Relation-like Function-like set
FF is functional Element of bool (Funcs ((bool (S)),(bool (S))))
DD \/ FF is functional Element of bool (Funcs ((bool (S)),(bool (S))))
(S,FF) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
iter ((S,FF),C) is Relation-like Function-like set
(S,(DD \/ FF)) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
iter ((S,(DD \/ FF)),(X + C)) is Relation-like Function-like set
D is (S) set
(iter ((S,FF),C)) . D is set
Y is (S) set
(iter ((S,DD),X)) . Y is set
(iter ((S,(DD \/ FF)),(X + C))) . Y is set
(S,DD,X) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
(S,DD,X) . Y is (S) set
(S,(DD \/ FF),X) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
iter ((S,(DD \/ FF)),X) is Relation-like Function-like set
(S,(DD \/ FF),X) . Y is (S) set
proj1 (iter ((S,(DD \/ FF)),X)) is set
(S,FF,C) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
(S,FF,C) . D is (S) set
(S,(DD \/ FF),C) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
iter ((S,(DD \/ FF)),C) is Relation-like Function-like set
(S,(DD \/ FF),C) . D is (S) set
(S,(DD \/ FF),(X + C)) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
(S,(DD \/ FF),(X + C)) . Y is (S) set
phii is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
iter ((S,(DD \/ FF)),phii) is Relation-like Function-like set
psi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
iter ((S,(DD \/ FF)),psi) is Relation-like Function-like set
(iter ((S,(DD \/ FF)),phii)) * (iter ((S,(DD \/ FF)),psi)) is Relation-like Function-like set
((iter ((S,(DD \/ FF)),phii)) * (iter ((S,(DD \/ FF)),psi))) . Y is set
(iter ((S,(DD \/ FF)),X)) . Y is set
(S,(DD \/ FF),C) . ((iter ((S,(DD \/ FF)),X)) . Y) is (S) set
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
X + C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
phi is set
{phi} is non empty trivial finite 1 -element countable set
S is set
DD is set
FF is V51() V53() eligible Language-like
(FF) is non empty Relation-like set
AllFormulasOf FF is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf FF -prefix FF -prefix Element of bool (((AllSymbolsOf FF) *) \ {{}})
AllSymbolsOf FF is non empty non trivial non finite non empty-membered set
the U1 of FF is set
AllSymbolsOf FF is non empty non trivial non finite non empty-membered set
(AllSymbolsOf FF) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf FF
((AllSymbolsOf FF) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf FF) *)
bool ((AllSymbolsOf FF) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf FF) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf FF) *)
bool (((AllSymbolsOf FF) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf FF) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf FF
((AllSymbolsOf FF) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf FF) *)
bool ((AllSymbolsOf FF) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf FF) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf FF) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf FF) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf FF) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf FF), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf FF) *) \ {{}} : b1 is finite } is set
bool (FF) is non empty Element of bool (bool (FF))
bool (FF) is non empty set
bool (bool (FF)) is non empty set
Funcs ((bool (FF)),(bool (FF))) is non empty functional FUNCTION_DOMAIN of bool (FF), bool (FF)
bool (Funcs ((bool (FF)),(bool (FF)))) is non empty set
D is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
Y is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
D \/ Y is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
(FF,D) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
(FF,Y) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
(FF,(D \/ Y)) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
(FF,D,X) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
iter ((FF,D),X) is Relation-like Function-like set
(FF,D,X) . S is (FF) set
(FF,Y,C) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
iter ((FF,Y),C) is Relation-like Function-like set
(FF,Y,C) . {phi} is (FF) set
dom (FF,D,X) is Element of bool (bool (FF))
bool (bool (FF)) is non empty set
HC is (FF) (FF) Element of (FF)
{HC} is non empty trivial Relation-like finite 1 -element countable (FF) Element of bool (FF)
HH is Relation-like (FF) Element of bool (FF)
(iter ((FF,D),X)) . HH is set
{DD} is non empty trivial finite 1 -element countable set
(iter ((FF,Y),C)) . {HC} is set
iter ((FF,(D \/ Y)),(X + C)) is Relation-like Function-like set
(iter ((FF,(D \/ Y)),(X + C))) . HH is set
(FF,(D \/ Y),(X + C)) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
(FF,(D \/ Y),(X + C)) . S is (FF) set
X is set
C is V51() V53() eligible Language-like
TermSymbolsOf C is non empty set
the U1 of C is set
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phi is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheEqSymbOf C)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
S is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
[phi,S] is non empty V26() Element of [:(((AllSymbolsOf C) *) \ {{}}),(((AllSymbolsOf C) *) \ {{}}):]
[:(((AllSymbolsOf C) *) \ {{}}),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
(<*(TheEqSymbOf C)*> ^ phi) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
DD is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,DD,X) is Relation-like AllTermsOf C -defined AllTermsOf C -valued Element of bool [:(AllTermsOf C),(AllTermsOf C):]
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
[:(AllTermsOf C),(AllTermsOf C):] is non empty Relation-like set
bool [:(AllTermsOf C),(AllTermsOf C):] is non empty set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} : (<*(TheEqSymbOf C)*> ^ b1) ^ b2 is (C,DD,X) } is set
Y is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
phii is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
[Y,phii] is non empty V26() Element of [:(((AllSymbolsOf C) *) \ {{}}),(((AllSymbolsOf C) *) \ {{}}):]
<*(TheEqSymbOf C)*> ^ Y is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ Y) ^ phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
C is (X) (X) set
C `2 is set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
S is (X) (X) Element of (X)
DD is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X)
FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[DD,FF] is non empty V26() Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
X is set
C is set
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
S is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
FF is set
FF `1 is set
FF `2 is set
{FF} is non empty trivial finite 1 -element countable set
D is Relation-like (phi) Element of bool (phi)
Y is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
phii is (phi) (phi) Element of (phi)
phii `2 is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
S is set
DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
FF is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{S} is non empty trivial finite 1 -element countable set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
S is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X)
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
the functional V36() FinSequence-membered with_non-empty_elements (X,C) Element of bool (AllFormulasOf X) is functional V36() FinSequence-membered with_non-empty_elements (X,C) Element of bool (AllFormulasOf X)
C is V51() V53() eligible Language-like
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like (X) Element of bool (X)
S is (X) (X) Element of (X)
[phi,S] is non empty V26() Element of [:(bool (X)),(X):]
DD is Relation-like (X) Element of bool (X)
FF is (X) (X) Element of (X)
[DD,FF] is non empty V26() Element of [:(bool (X)),(X):]
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
phi is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
C is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
{ b1 where b1 is (X) (X) Element of (X) : [a1,b1] in C } is set
phi is set
{ b1 where b1 is (X) (X) Element of (X) : [phi,b1] in C } is set
S is set
DD is (X) (X) Element of (X)
[phi,DD] is non empty V26() set
phi is set
{ b1 where b1 is (X) (X) Element of (X) : [phi,b1] in C } is set
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
phi is non empty Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of bool [:(bool (X)),(bool (X)):]
S is set
phi . S is set
{ b1 where b1 is (X) (X) Element of (X) : [S,b1] in C } is set
S is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
DD is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{ b1 where b1 is (X) (X) Element of (X) : [a1,b1] in C } is set
FF is set
S . FF is set
DD . FF is set
{ b1 where b1 is (X) (X) Element of (X) : [FF,b1] in C } is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty set
bool (X) is non empty Element of bool (bool (X))
bool (bool (X)) is non empty set
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
C is Relation-like (X) Element of bool (X)
phi is (X) (X) Element of (X)
[C,phi] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
S is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,S) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X,S) . C is Relation-like (X) Element of bool (X)
{ b1 where b1 is (X) (X) Element of (X) : [C,b1] in S } is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
C is (X) set
phi is (X) (X) set
[C,phi] is non empty V26() set
DD is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,DD) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X,DD)} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X,{(X,DD)}) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X,{(X,DD)},1) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
iter ((X,{(X,DD)}),1) is Relation-like Function-like set
phii is (X) (X) Element of (X)
Y is Relation-like (X) Element of bool (X)
(X,{(X,DD)},1) . Y is Relation-like (X) Element of bool (X)
X is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
phi is (C) set
[phi,X] is non empty V26() set
DD is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,DD) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
(C,DD) . phi is set
[:(bool (C)),(bool (C)):] is non empty Relation-like set
bool [:(bool (C)),(bool (C)):] is non empty set
D is Relation-like (C) Element of bool (C)
{ b1 where b1 is (C) (C) Element of (C) : [D,b1] in DD } is set
FF is non empty Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of bool [:(bool (C)),(bool (C)):]
FF . D is Relation-like (C) Element of bool (C)
phii is (C) (C) Element of (C)
[D,phii] is non empty V26() Element of [:(bool (C)),(C):]
phii is (C) (C) Element of (C)
X is set
C is set
[C,X] is non empty V26() set
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
[:(bool (phi)),(phi):] is non empty Relation-like set
bool [:(bool (phi)),(phi):] is non empty set
DD is Relation-like bool (phi) -defined (phi) -valued Element of bool [:(bool (phi)),(phi):]
(phi,DD) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
(phi,DD) . C is set
[:(bool (phi)),(bool (phi)):] is non empty Relation-like set
bool [:(bool (phi)),(bool (phi)):] is non empty set
FF is non empty Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of bool [:(bool (phi)),(bool (phi)):]
dom FF is non empty Element of bool (bool (phi))
bool (bool (phi)) is non empty set
D is Relation-like (phi) Element of bool (phi)
(phi,DD) . D is Relation-like (phi) Element of bool (phi)
[D,X] is non empty V26() set
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
TermSymbolsOf X is non empty set
the U1 of X is set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
C is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ C) ^ C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[{},((<*(TheEqSymbOf X)*> ^ C) ^ C)] is non empty V26() set
{[{},((<*(TheEqSymbOf X)*> ^ C) ^ C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
X -termsOfMaxDepth is non empty Relation-like NAT -defined bool (((AllSymbolsOf X) *) \ {{}}) -valued Function-like total quasi_total Element of bool [:NAT,(bool (((AllSymbolsOf X) *) \ {{}})):]
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
[:NAT,(bool (((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (((AllSymbolsOf X) *) \ {{}})):] is non empty non trivial non finite non empty-membered set
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
{} .--> {} is non empty trivial Relation-like {{}} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() Cardinal-yielding countable V209() set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant total quasi_total finite Function-yielding V156() Cardinal-yielding countable V209() Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite countable set
bool [:{{}},{{}}:] is non empty finite V36() countable set
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(X,{},D) is non empty V26() (X) (X) Element of (X)
phii is (X) (X) Element of (X)
phii `1 is set
phii `2 is set
Y is Relation-like (X) Element of bool (X)
[Y,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . Y is Relation-like (X) Element of bool (X)
{phii} is non empty trivial Relation-like finite 1 -element countable (X) Element of bool (X)
psi is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like (X) Element of bool (X)
phi is Relation-like (X) Element of bool (X)
Y is set
(X) . C is Relation-like (X) Element of bool (X)
[C,Y] is non empty V26() set
phii is (X) (X) Element of (X)
phii `1 is set
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
phii `2 is set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
psi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ psi) ^ psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[phi,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
(X) . phi is Relation-like (X) Element of bool (X)
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,phi,X) is Relation-like AllTermsOf C -defined AllTermsOf C -valued Element of bool [:(AllTermsOf C),(AllTermsOf C):]
[:(AllTermsOf C),(AllTermsOf C):] is non empty Relation-like set
bool [:(AllTermsOf C),(AllTermsOf C):] is non empty set
TermSymbolsOf C is non empty set
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} : (<*(TheEqSymbOf C)*> ^ b1) ^ b2 is (C,phi,X) } is set
Y is set
phii is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheEqSymbOf C)*> ^ phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ phii) ^ phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[{},((<*(TheEqSymbOf C)*> ^ phii) ^ phii)] is non empty V26() set
{[{},((<*(TheEqSymbOf C)*> ^ phii) ^ phii)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C,{(C)}, {} ) (C,{(C)}) set
X \ {} is Element of bool X
bool X is non empty set
X typed\ {} is Element of bool X
{} \ (X \ {}) is empty trivial non proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {}
{} typed\ (X \ {}) is empty trivial non proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {}
X \/ {} is set
[phii,phii] is non empty V26() Element of [:(((AllSymbolsOf C) *) \ {{}}),(((AllSymbolsOf C) *) \ {{}}):]
[:(((AllSymbolsOf C) *) \ {{}}),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
dom (C,phi,X) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllTermsOf C)
bool (AllTermsOf C) is non empty set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like (X) Element of bool (X)
phi is Relation-like (X) Element of bool (X)
Y is set
(X) . C is Relation-like (X) Element of bool (X)
phii is (X) (X) Element of (X)
[C,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
phii `1 is set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phii `2 is set
psi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
H is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ psi) ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
{((<*(TheEqSymbOf X)*> ^ psi) ^ H)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
<*(TheEqSymbOf X)*> ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ H) ^ psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[phi,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . phi is Relation-like (X) Element of bool (X)
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,phi,X) is Relation-like AllTermsOf C -defined AllTermsOf C -valued Element of bool [:(AllTermsOf C),(AllTermsOf C):]
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
[:(AllTermsOf C),(AllTermsOf C):] is non empty Relation-like set
bool [:(AllTermsOf C),(AllTermsOf C):] is non empty set
TermSymbolsOf C is non empty set
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} : (<*(TheEqSymbOf C)*> ^ b1) ^ b2 is (C,phi,X) } is set
field (C,phi,X) is set
proj1 (C,phi,X) is set
proj2 (C,phi,X) is set
(proj1 (C,phi,X)) \/ (proj2 (C,phi,X)) is set
(AllTermsOf C) \/ (AllTermsOf C) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) \ {{}})
psi is set
H is set
m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf C
seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf C
HH is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheEqSymbOf C)*> ^ HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
HC is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ HH) ^ HC is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheEqSymbOf C)*> ^ HC is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ HC) ^ HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
a is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
{a} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf C) *) \ {{}})
D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
[{a},D2] is non empty V26() (C) (C) Element of [:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):]
[:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
sub1 is (C) (C) Element of (C)
sub1 `1 is set
sub1 `2 is set
sub2 is Relation-like (C) Element of bool (C)
[sub2,sub1] is non empty V26() Element of [:(bool (C)),(C):]
(C) . sub2 is Relation-like (C) Element of bool (C)
{sub1} is non empty trivial Relation-like finite 1 -element countable (C) Element of bool (C)
[psi,H] is non empty V26() set
inf is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
U is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
[inf,U] is non empty V26() Element of [:(((AllSymbolsOf C) *) \ {{}}),(((AllSymbolsOf C) *) \ {{}}):]
[:(((AllSymbolsOf C) *) \ {{}}),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
<*(TheEqSymbOf C)*> ^ inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ inf) ^ U is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[H,psi] is non empty V26() set
X is V51() V53() eligible Language-like
TermSymbolsOf X is non empty set
the U1 of X is set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
DD is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
S is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ phi) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
{((<*(TheEqSymbOf X)*> ^ phi) ^ S)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
DD \/ {((<*(TheEqSymbOf X)*> ^ phi) ^ S)} is non empty functional finite V36() with_non-empty_elements non empty-membered countable set
C is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ C) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[(DD \/ {((<*(TheEqSymbOf X)*> ^ phi) ^ S)}),((<*(TheEqSymbOf X)*> ^ C) ^ S)] is non empty V26() set
(X) is non empty Relation-like set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(<*(TheEqSymbOf X)*> ^ C) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[DD,((<*(TheEqSymbOf X)*> ^ C) ^ phi)] is non empty V26() Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
{[DD,((<*(TheEqSymbOf X)*> ^ C) ^ phi)]} is non empty trivial Relation-like non empty-yielding bool (AllFormulasOf X) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() Element of bool [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
Y is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
{Y} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
H is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
DD \/ H is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
m is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
psi is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
[m,psi] is non empty V26() (X) (X) Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
phii is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
[DD,phii] is non empty V26() (X) (X) Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
HH is (X) (X) Element of (X)
{HH} is non empty trivial Relation-like finite 1 -element countable (X) Element of bool (X)
HC is Relation-like (X) Element of bool (X)
seqt is (X) (X) Element of (X)
seqt `1 is set
DD \/ {Y} is non empty functional finite V36() with_non-empty_elements non empty-membered countable set
HH `1 is set
(HH `1) \/ {Y} is non empty set
HH `2 is set
seqt `2 is set
[HC,seqt] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
a is set
X is V51() V53() eligible Language-like
TermSymbolsOf X is non empty set
the U1 of X is set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
S is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ phi) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
{DD,((<*(TheEqSymbOf X)*> ^ phi) ^ S)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
C is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ C) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[{DD,((<*(TheEqSymbOf X)*> ^ phi) ^ S)},((<*(TheEqSymbOf X)*> ^ C) ^ S)] is non empty V26() Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
{DD} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
(<*(TheEqSymbOf X)*> ^ C) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[{DD},((<*(TheEqSymbOf X)*> ^ C) ^ phi)] is non empty V26() Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
{[{DD},((<*(TheEqSymbOf X)*> ^ C) ^ phi)]} is non empty trivial Relation-like non empty-yielding bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() Element of bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf X
{psi} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (AllFormulasOf X)
H is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
[H,((<*(TheEqSymbOf X)*> ^ C) ^ phi)] is non empty V26() Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
{[H,((<*(TheEqSymbOf X)*> ^ C) ^ phi)]} is non empty trivial Relation-like non empty-yielding bool (AllFormulasOf X) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() Element of bool [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
{((<*(TheEqSymbOf X)*> ^ phi) ^ S)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
H \/ {((<*(TheEqSymbOf X)*> ^ phi) ^ S)} is non empty functional finite V36() with_non-empty_elements non empty-membered countable set
[(H \/ {((<*(TheEqSymbOf X)*> ^ phi) ^ S)}),((<*(TheEqSymbOf X)*> ^ C) ^ S)] is non empty V26() (X) (1,X,{(X)},{[H,((<*(TheEqSymbOf X)*> ^ C) ^ phi)]}) (X) set
m is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
phi is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{C} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
phi \/ {C} is non empty functional finite V36() with_non-empty_elements non empty-membered countable set
[(phi \/ {C}),C] is non empty V26() (X) (X) set
(X) is non empty Relation-like set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
DD is (X) (X) Element of (X)
DD `2 is set
DD `1 is set
FF is Relation-like (X) Element of bool (X)
[FF,DD] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
D is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{C,phi} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[{C,phi},C] is non empty V26() (X) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf X
{FF} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (AllFormulasOf X)
D is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
{C} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
D \/ {C} is non empty functional finite V36() with_non-empty_elements non empty-membered countable set
[(D \/ {C}),C] is non empty V26() (X) (1,X,{(X)}, {} ) (X) set
Y is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{C} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[{C},C] is non empty V26() (X) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
S is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
S \/ {C} is non empty functional finite V36() with_non-empty_elements non empty-membered countable set
[(S \/ {C}),C] is non empty V26() (X) (1,X,{(X)}, {} ) (X) set
DD is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{C} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[{C},C] is non empty V26() (X) (1,X,{(X)}, {} ) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
[:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
{[{C},C]} is non empty trivial Relation-like non empty-yielding bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() Element of bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
phi is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like (X) Element of bool (X)
phi is Relation-like (X) Element of bool (X)
Y is set
(X) . C is Relation-like (X) Element of bool (X)
phii is (X) (X) Element of (X)
[C,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
phii `2 is set
phii `1 is set
[phi,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . phi is Relation-like (X) Element of bool (X)
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like (X) Element of bool (X)
phi is Relation-like (X) Element of bool (X)
Y is set
(X) . C is Relation-like (X) Element of bool (X)
phii is (X) (X) Element of (X)
[C,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
phii `1 is set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phii `2 is set
seqt is set
seqt `1 is set
H is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
m is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ H) ^ m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
{((<*(TheEqSymbOf X)*> ^ H) ^ m)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(seqt `1) \/ {((<*(TheEqSymbOf X)*> ^ H) ^ m)} is non empty set
seqt `2 is set
psi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ psi) ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ psi) ^ m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[phi,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . phi is Relation-like (X) Element of bool (X)
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like (X) Element of bool (X)
phi is Relation-like (X) Element of bool (X)
Y is set
(X) . C is Relation-like (X) Element of bool (X)
phii is (X) (X) Element of (X)
[C,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
phii `1 is set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phii `2 is set
psi is low-compounding ofAtomicFormula Element of AllSymbolsOf X
ar psi is non empty complex ext-real finite V40() V41() countable Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X . psi is set
abs (ar psi) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
Seg (abs (ar psi)) is non empty finite abs (ar psi) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar psi) ) } is set
[:(Seg (abs (ar psi))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg (abs (ar psi))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
H is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar psi) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
m is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar psi) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar psi)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar psi)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar psi))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = H & b3 = m ) } is set
psi -compound H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*psi*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,psi] is non empty V26() set
{[1,psi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
{} .--> {} is non empty trivial Relation-like {{}} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() Cardinal-yielding countable V209() set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant total quasi_total finite Function-yielding V156() Cardinal-yielding countable V209() Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite countable set
bool [:{{}},{{}}:] is non empty finite V36() countable set
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
(X -multiCat) . H is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*psi*> ^ ((X -multiCat) . H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
<*(TheEqSymbOf X)*> ^ (psi -compound H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
psi -compound m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(X -multiCat) . m is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*psi*> ^ ((X -multiCat) . m) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(<*(TheEqSymbOf X)*> ^ (psi -compound H)) ^ (psi -compound m) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[phi,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . phi is Relation-like (X) Element of bool (X)
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like (X) Element of bool (X)
phi is Relation-like (X) Element of bool (X)
Y is set
(X) . C is Relation-like (X) Element of bool (X)
phii is (X) (X) Element of (X)
[C,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
phii `1 is set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phii `2 is set
psi is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
ar psi is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X . psi is set
abs (ar psi) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
H is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar psi) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
psi -compound H is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
<*psi*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,psi] is non empty V26() set
{[1,psi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
{} .--> {} is non empty trivial Relation-like {{}} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() Cardinal-yielding countable V209() set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant total quasi_total finite Function-yielding V156() Cardinal-yielding countable V209() Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite countable set
bool [:{{}},{{}}:] is non empty finite V36() countable set
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
(X -multiCat) . H is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*psi*> ^ ((X -multiCat) . H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{(psi -compound H)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
Seg (abs (ar psi)) is non empty finite abs (ar psi) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar psi) ) } is set
[:(Seg (abs (ar psi))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg (abs (ar psi))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
m is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar psi) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar psi)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar psi)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar psi))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = H & b3 = m ) } is set
{(psi -compound H)} \/ { ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar psi)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar psi)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar psi))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = H & b3 = m ) } is non empty set
psi -compound m is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
(X -multiCat) . m is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*psi*> ^ ((X -multiCat) . m) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
[phi,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . phi is Relation-like (X) Element of bool (X)
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional (X) Element of bool (Funcs ((bool (X)),(bool (X))))
phi is functional (X) Element of bool (Funcs ((bool (X)),(bool (X))))
C \/ phi is functional Element of bool (Funcs ((bool (X)),(bool (X))))
DD is Relation-like (X) Element of bool (X)
FF is Relation-like (X) Element of bool (X)
D is Relation-like Function-like set
D . DD is set
psi is Relation-like Function-like set
psi . FF is set
psi is Relation-like Function-like set
psi . FF is set
DD is functional Element of bool (Funcs ((bool (X)),(bool (X))))
X is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,phi,X) is Relation-like AllTermsOf C -defined AllTermsOf C -valued Element of bool [:(AllTermsOf C),(AllTermsOf C):]
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
[:(AllTermsOf C),(AllTermsOf C):] is non empty Relation-like set
bool [:(AllTermsOf C),(AllTermsOf C):] is non empty set
TermSymbolsOf C is non empty set
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} : (<*(TheEqSymbOf C)*> ^ b1) ^ b2 is (C,phi,X) } is set
field (C,phi,X) is set
proj1 (C,phi,X) is set
proj2 (C,phi,X) is set
(proj1 (C,phi,X)) \/ (proj2 (C,phi,X)) is set
(AllTermsOf C) \/ (AllTermsOf C) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) \ {{}})
H is set
m is set
seqt is set
HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf C
HC is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf C
a is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf C
D2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheEqSymbOf C)*> ^ D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
sub1 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ D2) ^ sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheEqSymbOf C)*> ^ sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
sub2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ sub1) ^ sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ D2) ^ sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
{inf} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf C) *) \ {{}})
[{inf},((<*(TheEqSymbOf C)*> ^ D2) ^ sub1)] is non empty V26() Element of [:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):]
[:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
{[{inf},((<*(TheEqSymbOf C)*> ^ D2) ^ sub1)]} is non empty trivial Relation-like non empty-yielding bool (((AllSymbolsOf C) *) \ {{}}) -defined ((AllSymbolsOf C) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() Element of bool [:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):]
bool [:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
{inf,((<*(TheEqSymbOf C)*> ^ sub1) ^ sub2)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
[{inf,((<*(TheEqSymbOf C)*> ^ sub1) ^ sub2)},((<*(TheEqSymbOf C)*> ^ D2) ^ sub2)] is non empty V26() (C) (1,C,{(C)},{[{inf},((<*(TheEqSymbOf C)*> ^ D2) ^ sub1)]}) (C) Element of [:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):]
[{inf},inf] is non empty V26() (C) (1,C,{(C)}, {} ) (C) Element of [:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):]
{[{inf},inf]} is non empty trivial Relation-like non empty-yielding bool (((AllSymbolsOf C) *) \ {{}}) -defined ((AllSymbolsOf C) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() (C,{(C)}, {} ) (C,{(C)}) Element of bool [:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):]
U is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
{inf,U} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
II1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
[{inf,U},II1] is non empty V26() (C) (C) Element of [:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):]
1 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
{[{inf,U},II1]} is non empty trivial Relation-like non empty-yielding bool (((AllSymbolsOf C) *) \ {{}}) -defined ((AllSymbolsOf C) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() Element of bool [:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):]
{U} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf C) *) \ {{}})
{inf} \/ {U} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
[H,m] is non empty V26() set
[m,seqt] is non empty V26() set
bool X is non empty set
II2 is Element of bool X
I2 is Element of bool X
II2 \/ I2 is Element of bool X
I1 is Element of bool X
[H,seqt] is non empty V26() set
X is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
[:(AllTermsOf C),(AllTermsOf C):] is non empty Relation-like set
bool [:(AllTermsOf C),(AllTermsOf C):] is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,phi,X) is Relation-like AllTermsOf C -defined AllTermsOf C -valued Element of bool [:(AllTermsOf C),(AllTermsOf C):]
TermSymbolsOf C is non empty set
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} : (<*(TheEqSymbOf C)*> ^ b1) ^ b2 is (C,phi,X) } is set
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} /\ phi is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} typed/\ phi is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
{(C)} /\ phi is functional finite countable set
{(C)} /\typed phi is functional Element of bool phi
bool phi is non empty set
{(C)} /\ phi is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} typed/\ phi is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
{(C)} /\ phi is functional finite countable set
{(C)} /\typed phi is functional Element of bool phi
X is V51() V53() eligible Language-like
TermSymbolsOf X is non empty set
the U1 of X is set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
C is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ C) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
C is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
X is V51() V53() eligible Language-like
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
Seg C is non empty finite C -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= C ) } is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(Seg C),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg C),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phi is Relation-like NAT -defined AllTermsOf X -valued Function-like finite C -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
S is Relation-like NAT -defined AllTermsOf X -valued Function-like finite C -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg C, b2, b3 is non empty Relation-like non-empty non empty-yielding Seg C -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg C),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = phi & b3 = S ) } is set
C is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
X is V51() V53() eligible Language-like
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
phi is Relation-like NAT -defined AllTermsOf X -valued Function-like finite C -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
S is Relation-like NAT -defined AllTermsOf X -valued Function-like finite C -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
(X,C,phi,S) is set
Seg C is non empty finite C -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= C ) } is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
[:(Seg C),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg C),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg C, b2, b3 is non empty Relation-like non-empty non empty-yielding Seg C -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg C),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = phi & b3 = S ) } is set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
psi is set
m is non empty Relation-like non-empty non empty-yielding Seg C -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg C),(((AllSymbolsOf X) *) \ {{}}):]
H is Element of Seg C
m . H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ (m . H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
seqt is non empty Relation-like non-empty non empty-yielding Seg C -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg C),(((AllSymbolsOf X) *) \ {{}}):]
seqt . H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ (m . H)) ^ (seqt . H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
C -tuples_on (AllTermsOf X) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf X
Funcs ((Seg C),(AllTermsOf X)) is non empty functional FUNCTION_DOMAIN of Seg C, AllTermsOf X
[:(Seg C),(AllTermsOf X):] is non empty Relation-like set
bool [:(Seg C),(AllTermsOf X):] is non empty set
HH is non empty Relation-like non-empty non empty-yielding Seg C -defined AllTermsOf X -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg C),(AllTermsOf X):]
HH . H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
HC is non empty Relation-like non-empty non empty-yielding Seg C -defined AllTermsOf X -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg C),(AllTermsOf X):]
HC . H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
a is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ a is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ a) ^ D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
sub1 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
C is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
X is V51() V53() eligible Language-like
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
phi is Relation-like NAT -defined AllTermsOf X -valued Function-like finite C -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
S is Relation-like NAT -defined AllTermsOf X -valued Function-like finite C -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
(X,C,phi,S) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X)
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
Seg C is non empty finite C -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= C ) } is set
[:(Seg C),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg C),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg C, b2, b3 is non empty Relation-like non-empty non empty-yielding Seg C -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg C),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = phi & b3 = S ) } is set
C -tuples_on (AllTermsOf X) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf X
Funcs ((Seg C),(AllTermsOf X)) is non empty functional FUNCTION_DOMAIN of Seg C, AllTermsOf X
[:(Seg C),(AllTermsOf X):] is non empty Relation-like set
bool [:(Seg C),(AllTermsOf X):] is non empty set
Y is non empty Relation-like non-empty non empty-yielding Seg C -defined AllTermsOf X -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg C),(AllTermsOf X):]
phii is non empty Relation-like non-empty non empty-yielding Seg C -defined AllTermsOf X -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg C),(AllTermsOf X):]
{ H1(b1) where b1 is Element of Seg C : b1 in Seg C } is set
m is set
HH is non empty Relation-like non-empty non empty-yielding Seg C -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg C),(((AllSymbolsOf X) *) \ {{}}):]
seqt is Element of Seg C
HH . seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ (HH . seqt) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
HC is non empty Relation-like non-empty non empty-yielding Seg C -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg C),(((AllSymbolsOf X) *) \ {{}}):]
HC . seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ (HH . seqt)) ^ (HC . seqt) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
H is finite countable set
bool H is non empty finite V36() countable set
m is finite countable Element of bool H
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
C is low-compounding ofAtomicFormula Element of AllSymbolsOf X
ar C is non empty complex ext-real finite V40() V41() countable Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X . C is set
abs (ar C) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
FF is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar C) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
D is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar C) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
(X,(abs (ar C)),FF,D) is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
Seg (abs (ar C)) is non empty finite abs (ar C) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar C) ) } is set
[:(Seg (abs (ar C))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg (abs (ar C))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar C)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar C)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar C))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = FF & b3 = D ) } is set
C -compound FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*C*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,C] is non empty V26() set
{[1,C]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
{} .--> {} is non empty trivial Relation-like {{}} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() Cardinal-yielding countable V209() set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant total quasi_total finite Function-yielding V156() Cardinal-yielding countable V209() Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite countable set
bool [:{{}},{{}}:] is non empty finite V36() countable set
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
(X -multiCat) . FF is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*C*> ^ ((X -multiCat) . FF) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
<*(TheEqSymbOf X)*> ^ (C -compound FF) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
C -compound D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(X -multiCat) . D is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*C*> ^ ((X -multiCat) . D) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(<*(TheEqSymbOf X)*> ^ (C -compound FF)) ^ (C -compound D) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[(X,(abs (ar C)),FF,D),((<*(TheEqSymbOf X)*> ^ (C -compound FF)) ^ (C -compound D))] is non empty V26() Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
{[(X,(abs (ar C)),FF,D),((<*(TheEqSymbOf X)*> ^ (C -compound FF)) ^ (C -compound D))]} is non empty trivial Relation-like non empty-yielding bool (AllFormulasOf X) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() Element of bool [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
Y is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
Y -compound FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*Y*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,Y] is non empty V26() set
{[1,Y]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*Y*> ^ ((X -multiCat) . FF) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
Y -compound D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*Y*> ^ ((X -multiCat) . D) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
phii is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
psi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ phii) ^ psi is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[(X,(abs (ar C)),FF,D),H] is non empty V26() (X) (X) Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
m is (X) (X) Element of (X)
m `1 is set
m `2 is set
seqt is Relation-like (X) Element of bool (X)
[seqt,m] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
(X) . seqt is Relation-like (X) Element of bool (X)
{m} is non empty trivial Relation-like finite 1 -element countable (X) Element of bool (X)
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
ar C is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X . C is set
abs (ar C) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
D is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar C) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
Y is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar C) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
(X,(abs (ar C)),D,Y) is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
Seg (abs (ar C)) is non empty finite abs (ar C) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar C) ) } is set
[:(Seg (abs (ar C))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg (abs (ar C))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar C)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar C)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar C))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = D & b3 = Y ) } is set
C -compound D is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
<*C*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,C] is non empty V26() set
{[1,C]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
{} .--> {} is non empty trivial Relation-like {{}} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() Cardinal-yielding countable V209() set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant total quasi_total finite Function-yielding V156() Cardinal-yielding countable V209() Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite countable set
bool [:{{}},{{}}:] is non empty finite V36() countable set
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
(X -multiCat) . D is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*C*> ^ ((X -multiCat) . D) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{(C -compound D)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,(abs (ar C)),D,Y) \/ {(C -compound D)} is non empty functional finite V36() with_non-empty_elements non empty-membered countable set
C -compound Y is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
(X -multiCat) . Y is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*C*> ^ ((X -multiCat) . Y) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
[((X,(abs (ar C)),D,Y) \/ {(C -compound D)}),(C -compound Y)] is non empty V26() (X) (X) set
{[((X,(abs (ar C)),D,Y) \/ {(C -compound D)}),(C -compound Y)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phii is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf X
{H} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (AllFormulasOf X)
(X,(abs (ar C)),D,Y) \/ {H} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (AllFormulasOf X)
m is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X)
psi is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
[m,psi] is non empty V26() Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
seqt is (X) (X) Element of (X)
seqt `1 is set
{(C -compound D)} \/ (X,(abs (ar C)),D,Y) is non empty functional finite V36() with_non-empty_elements non empty-membered countable set
seqt `2 is set
HH is Relation-like (X) Element of bool (X)
[HH,seqt] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
(X) . HH is Relation-like (X) Element of bool (X)
{seqt} is non empty trivial Relation-like finite 1 -element countable (X) Element of bool (X)
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
C is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
ar C is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X . C is set
abs (ar C) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
phi is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar C) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
S is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar C) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
(X,(abs (ar C)),phi,S) is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
Seg (abs (ar C)) is non empty finite abs (ar C) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar C) ) } is set
[:(Seg (abs (ar C))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg (abs (ar C))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar C)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar C)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar C))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = phi & b3 = S ) } is set
C -compound phi is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
<*C*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,C] is non empty V26() set
{[1,C]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
{} .--> {} is non empty trivial Relation-like {{}} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() Cardinal-yielding countable V209() set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined INT -valued {{}} -valued Function-like constant total quasi_total finite Function-yielding V156() Cardinal-yielding countable V209() Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is non empty Relation-like finite countable set
bool [:{{}},{{}}:] is non empty finite V36() countable set
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
(X -multiCat) . phi is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*C*> ^ ((X -multiCat) . phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{(C -compound phi)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
(X,(abs (ar C)),phi,S) \/ {(C -compound phi)} is non empty functional finite V36() with_non-empty_elements non empty-membered countable set
C -compound S is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
(X -multiCat) . S is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*C*> ^ ((X -multiCat) . S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
[((X,(abs (ar C)),phi,S) \/ {(C -compound phi)}),(C -compound S)] is non empty V26() (X) (X) set
{[((X,(abs (ar C)),phi,S) \/ {(C -compound phi)}),(C -compound S)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
X is set
C is set
phi is set
[C,phi] is non empty V26() set
S is V51() V53() eligible Language-like
(S) is non empty Relation-like set
AllFormulasOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
the U1 of S is set
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf S) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf S), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}} : b1 is finite } is set
bool (S) is non empty Element of bool (bool (S))
bool (S) is non empty set
bool (bool (S)) is non empty set
Funcs ((bool (S)),(bool (S))) is non empty functional FUNCTION_DOMAIN of bool (S), bool (S)
bool (Funcs ((bool (S)),(bool (S)))) is non empty set
AllTermsOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite non empty-membered set
S -termsOfMaxDepth is Relation-like Function-like set
proj2 (S -termsOfMaxDepth) is set
union (proj2 (S -termsOfMaxDepth)) is set
(((AllSymbolsOf S) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf S) *) \ {{}}
(AllTermsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf S) *) \ {{}}) *)
bool ((((AllSymbolsOf S) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
DD is functional Element of bool (Funcs ((bool (S)),(bool (S))))
(S,DD,X) is Relation-like AllTermsOf S -defined AllTermsOf S -valued 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
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 countable 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 non empty-membered set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite non empty-membered 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
TheEqSymbOf S is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf S
the U2 of S is Element of the U1 of S
<*(TheEqSymbOf S)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(TheEqSymbOf S)] is non empty V26() set
{[1,(TheEqSymbOf S)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf S) *) \ {{}} : (<*(TheEqSymbOf S)*> ^ b1) ^ b2 is (S,DD,X) } is set
FF is low-compounding ofAtomicFormula Element of AllSymbolsOf S
ar FF is non empty complex ext-real finite V40() V41() countable Element of INT
the adicity of S . FF is set
abs (ar FF) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar FF)) -placesOf (S,DD,X) is Relation-like (abs (ar FF)) -tuples_on (AllTermsOf S) -defined (abs (ar FF)) -tuples_on (AllTermsOf S) -valued Element of bool [:((abs (ar FF)) -tuples_on (AllTermsOf S)),((abs (ar FF)) -tuples_on (AllTermsOf S)):]
(abs (ar FF)) -tuples_on (AllTermsOf S) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf S
[:((abs (ar FF)) -tuples_on (AllTermsOf S)),((abs (ar FF)) -tuples_on (AllTermsOf S)):] is non empty Relation-like set
bool [:((abs (ar FF)) -tuples_on (AllTermsOf S)),((abs (ar FF)) -tuples_on (AllTermsOf S)):] is non empty set
(abs (ar FF)) -placesOf (S,DD,X) is Relation-like (abs (ar FF)) -tuples_on (AllTermsOf S) -defined (abs (ar FF)) -tuples_on (AllTermsOf S) -valued Element of bool [:((abs (ar FF)) -tuples_on (AllTermsOf S)),((abs (ar FF)) -tuples_on (AllTermsOf S)):]
Seg (abs (ar FF)) is non empty finite abs (ar FF) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar FF) ) } is set
{ [b1,b2] where b1, b2 is Relation-like NAT -defined AllTermsOf S -valued Function-like finite abs (ar FF) -element FinSequence-like FinSubsequence-like countable V209() Element of (abs (ar FF)) -tuples_on (AllTermsOf S) : for b3 being set holds
( not b3 in Seg (abs (ar FF)) or [(b1 . b3),(b2 . b3)] in (S,DD,X) ) } is set
S -cons is non empty Relation-like [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):]
[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial non finite non empty-membered set
K295((AllSymbolsOf S)) is non empty Relation-like [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):]
HC is non empty Relation-like non empty-yielding NAT -defined AllTermsOf S -valued Function-like finite abs (ar FF) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (abs (ar FF)) -tuples_on (AllTermsOf S)
a is non empty Relation-like non empty-yielding NAT -defined AllTermsOf S -valued Function-like finite abs (ar FF) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (abs (ar FF)) -tuples_on (AllTermsOf S)
[HC,a] is non empty V26() Element of [:((abs (ar FF)) -tuples_on (AllTermsOf S)),((abs (ar FF)) -tuples_on (AllTermsOf S)):]
D2 is non empty Relation-like non empty-yielding NAT -defined AllTermsOf S -valued Function-like finite abs (ar FF) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (abs (ar FF)) -tuples_on (AllTermsOf S)
sub1 is non empty Relation-like non empty-yielding NAT -defined AllTermsOf S -valued Function-like finite abs (ar FF) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (abs (ar FF)) -tuples_on (AllTermsOf S)
sub2 is Relation-like NAT -defined AllTermsOf S -valued Function-like finite abs (ar FF) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf S) *
U is Relation-like NAT -defined AllTermsOf S -valued Function-like finite abs (ar FF) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf S) *
inf is Relation-like NAT -defined AllTermsOf S -valued Function-like finite abs (ar FF) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf S) *
II1 is Relation-like NAT -defined AllTermsOf S -valued Function-like finite abs (ar FF) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf S) *
(S,(abs (ar FF)),U,II1) is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf S)
[:(Seg (abs (ar FF))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg (abs (ar FF))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
{ ((<*(TheEqSymbOf S)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar FF)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar FF)) -defined ((AllSymbolsOf S) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar FF))),(((AllSymbolsOf S) *) \ {{}}):] : ( b2 = U & b3 = II1 ) } is set
Funcs ((Seg (abs (ar FF))),(AllTermsOf S)) is non empty functional FUNCTION_DOMAIN of Seg (abs (ar FF)), AllTermsOf S
[:(Seg (abs (ar FF))),(AllTermsOf S):] is non empty Relation-like set
bool [:(Seg (abs (ar FF))),(AllTermsOf S):] is non empty set
c26 is set
I1 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar FF)) -defined ((AllSymbolsOf S) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar FF))),(((AllSymbolsOf S) *) \ {{}}):]
I02 is Element of Seg (abs (ar FF))
I1 . I02 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}}
<*(TheEqSymbOf S)*> ^ (I1 . I02) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}}
I2 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar FF)) -defined ((AllSymbolsOf S) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar FF))),(((AllSymbolsOf S) *) \ {{}}):]
I2 . I02 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}}
(<*(TheEqSymbOf S)*> ^ (I1 . I02)) ^ (I2 . I02) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}}
I2 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar FF)) -defined AllTermsOf S -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar FF))),(AllTermsOf S):]
I2 . I02 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf S
I1 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar FF)) -defined AllTermsOf S -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar FF))),(AllTermsOf S):]
I1 . I02 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf S
X1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf S
X2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf S
[(I2 . I02),(I1 . I02)] is non empty V26() Element of [:(AllTermsOf S),(AllTermsOf S):]
X22 is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf S) *) \ {{}}
<*(TheEqSymbOf S)*> ^ X22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}}
U is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf S) *) \ {{}}
(<*(TheEqSymbOf S)*> ^ X22) ^ U is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
AtomicFormulaSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite non empty-membered set
TheNorSymbOf S is set
{(TheNorSymbOf S)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf S) \ {(TheNorSymbOf S)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) typed\ {(TheNorSymbOf S)} is Element of bool (AllSymbolsOf S)
{((<*(TheEqSymbOf S)*> ^ X22) ^ U)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf S) *) \ {{}})
X is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,phi,X) is Relation-like AllTermsOf C -defined AllTermsOf C -valued Element of bool [:(AllTermsOf C),(AllTermsOf C):]
[:(AllTermsOf C),(AllTermsOf C):] is non empty Relation-like set
bool [:(AllTermsOf C),(AllTermsOf C):] is non empty set
TermSymbolsOf C is non empty set
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} : (<*(TheEqSymbOf C)*> ^ b1) ^ b2 is (C,phi,X) } is set
S is low-compounding ofAtomicFormula Element of AllSymbolsOf C
X -freeInterpreter S is non empty Relation-like (abs (ar S)) -tuples_on (AllTermsOf C) -defined (AllTermsOf C) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of S, AllTermsOf C
ar S is non empty complex ext-real finite V40() V41() countable Element of INT
the adicity of C . S is set
abs (ar S) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar S)) -tuples_on (AllTermsOf C) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf C
(AllTermsOf C) \/ BOOLEAN is non empty set
H is non relational termal own ofAtomicFormula Element of AllSymbolsOf C
m is set
seqt is set
[m,seqt] is non empty V26() set
(abs (ar S)) -placesOf (C,phi,X) is Relation-like (abs (ar S)) -tuples_on (AllTermsOf C) -defined (abs (ar S)) -tuples_on (AllTermsOf C) -valued Element of bool [:((abs (ar S)) -tuples_on (AllTermsOf C)),((abs (ar S)) -tuples_on (AllTermsOf C)):]
[:((abs (ar S)) -tuples_on (AllTermsOf C)),((abs (ar S)) -tuples_on (AllTermsOf C)):] is non empty Relation-like set
bool [:((abs (ar S)) -tuples_on (AllTermsOf C)),((abs (ar S)) -tuples_on (AllTermsOf C)):] is non empty set
(abs (ar S)) -placesOf (C,phi,X) is Relation-like (abs (ar S)) -tuples_on (AllTermsOf C) -defined (abs (ar S)) -tuples_on (AllTermsOf C) -valued Element of bool [:((abs (ar S)) -tuples_on (AllTermsOf C)),((abs (ar S)) -tuples_on (AllTermsOf C)):]
Seg (abs (ar S)) is non empty finite abs (ar S) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar S) ) } is set
{ [b1,b2] where b1, b2 is Relation-like NAT -defined AllTermsOf C -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like countable V209() Element of (abs (ar S)) -tuples_on (AllTermsOf C) : for b3 being set holds
( not b3 in Seg (abs (ar S)) or [(b1 . b3),(b2 . b3)] in (C,phi,X) ) } is set
(((AllSymbolsOf C) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf C) *) \ {{}}
(AllTermsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf C) *) \ {{}}) *)
bool ((((AllSymbolsOf C) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
HH is Relation-like NAT -defined AllTermsOf C -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf C) *
HC is Relation-like NAT -defined AllTermsOf C -valued Function-like finite abs (ar S) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf C) *
(C,(abs (ar S)),HH,HC) is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf C)
[:(Seg (abs (ar S))),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg (abs (ar S))),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
{ ((<*(TheEqSymbOf C)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar S)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar S)) -defined ((AllSymbolsOf C) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar S))),(((AllSymbolsOf C) *) \ {{}}):] : ( b2 = HH & b3 = HC ) } is set
H -compound HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
<*H*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,H] is non empty V26() set
{[1,H]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
((AllSymbolsOf C) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf C) *
C -multiCat is non empty Relation-like ((AllSymbolsOf C) *) * -defined (AllSymbolsOf C) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf C) *) *),((AllSymbolsOf C) *):]
((AllSymbolsOf C) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf C) *
[:(((AllSymbolsOf C) *) *),((AllSymbolsOf C) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf C) *) *),((AllSymbolsOf C) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) -multiCat is non empty Relation-like ((AllSymbolsOf C) *) * -defined (AllSymbolsOf C) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf C) *) *),((AllSymbolsOf C) *):]
K295((AllSymbolsOf C)) is non empty Relation-like [:((AllSymbolsOf C) *),((AllSymbolsOf C) *):] -defined (AllSymbolsOf C) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf C) *),((AllSymbolsOf C) *):],((AllSymbolsOf C) *):]
[:((AllSymbolsOf C) *),((AllSymbolsOf C) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf C) *),((AllSymbolsOf C) *):],((AllSymbolsOf C) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf C) *),((AllSymbolsOf C) *):],((AllSymbolsOf C) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf C)) is non empty Relation-like (((AllSymbolsOf C) *) *) \ {{}} -defined (AllSymbolsOf C) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf C) *) *) \ {{}}),((AllSymbolsOf C) *):]
(((AllSymbolsOf C) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) *)
bool (((AllSymbolsOf C) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf C) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf C) *) *)
[:((((AllSymbolsOf C) *) *) \ {{}}),((AllSymbolsOf C) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf C) *) *) \ {{}}),((AllSymbolsOf C) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf C))) is non empty Relation-like Function-like Function-yielding V156() set
(C -multiCat) . HH is Relation-like NAT -defined AllSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf C) *
<*H*> ^ ((C -multiCat) . HH) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
H -compound HC is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
(C -multiCat) . HC is Relation-like NAT -defined AllSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf C) *
<*H*> ^ ((C -multiCat) . HC) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
bool X is non empty set
D2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheEqSymbOf C)*> ^ D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
sub1 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ D2) ^ sub1 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf C) *) \ {{}}
AtomicFormulaSymbolsOf C is non empty Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
TheNorSymbOf C is set
{(TheNorSymbOf C)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf C) \ {(TheNorSymbOf C)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) typed\ {(TheNorSymbOf C)} is Element of bool (AllSymbolsOf C)
[(C,(abs (ar S)),HH,HC),((<*(TheEqSymbOf C)*> ^ D2) ^ sub1)] is non empty V26() (C) (C) Element of [:(bool (AllFormulasOf C)),(((AllSymbolsOf C) *) \ {{}}):]
[:(bool (AllFormulasOf C)),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
{[(C,(abs (ar S)),HH,HC),((<*(TheEqSymbOf C)*> ^ D2) ^ sub1)]} is non empty trivial Relation-like non empty-yielding bool (AllFormulasOf C) -defined ((AllSymbolsOf C) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() Element of bool [:(bool (AllFormulasOf C)),(((AllSymbolsOf C) *) \ {{}}):]
bool [:(bool (AllFormulasOf C)),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
sub2 is Element of bool X
(X -freeInterpreter S) . HH is set
(X -freeInterpreter S) . HC is set
(X -freeInterpreter S) . m is set
(X -freeInterpreter S) . seqt is set
[((X -freeInterpreter S) . m),((X -freeInterpreter S) . seqt)] is non empty V26() set
X is set
C is set
phi is set
[C,phi] is non empty V26() set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
the U1 of S is set
(S) is non empty Relation-like set
AllFormulasOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf S) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf S), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}} : b1 is finite } is set
bool (S) is non empty Element of bool (bool (S))
bool (S) is non empty set
bool (bool (S)) is non empty set
Funcs ((bool (S)),(bool (S))) is non empty functional FUNCTION_DOMAIN of bool (S), bool (S)
bool (Funcs ((bool (S)),(bool (S)))) is non empty set
(S) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total (S) Element of Funcs ((bool (S)),(bool (S)))
(S) is Relation-like bool (S) -defined (S) -valued Element of bool [:(bool (S)),(S):]
[:(bool (S)),(S):] is non empty Relation-like set
bool [:(bool (S)),(S):] is non empty set
(S,(S)) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
{(S)} is non empty trivial functional finite 1 -element with_common_domain countable (S) Element of bool (Funcs ((bool (S)),(bool (S))))
AllTermsOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite non empty-membered set
S -termsOfMaxDepth is Relation-like Function-like set
proj2 (S -termsOfMaxDepth) is set
union (proj2 (S -termsOfMaxDepth)) is set
DD is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
ar DD is non empty complex ext-real non positive negative finite V40() V41() countable 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 Element of the U1 of S
{ the U3 of S} is non empty trivial finite 1 -element countable 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 non empty-membered set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of S . DD is set
abs (ar DD) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
DD -compound is non empty Relation-like non-empty non empty-yielding (((AllSymbolsOf S) *) \ {{}}) * -defined ((AllSymbolsOf S) *) \ {{}} -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):]
(((AllSymbolsOf S) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf S) *) *)
((AllSymbolsOf S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf S) *
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite non empty-membered set
[:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
(DD -compound) . C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(DD -compound) . phi is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
FF is functional Element of bool (Funcs ((bool (S)),(bool (S))))
(S,FF,X) is Relation-like AllTermsOf S -defined AllTermsOf S -valued 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
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
TheEqSymbOf S is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf S
the U2 of S is Element of the U1 of S
<*(TheEqSymbOf S)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(TheEqSymbOf S)] is non empty V26() set
{[1,(TheEqSymbOf S)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf S) *) \ {{}} : (<*(TheEqSymbOf S)*> ^ b1) ^ b2 is (S,FF,X) } is set
(abs (ar DD)) -placesOf (S,FF,X) is Relation-like (abs (ar DD)) -tuples_on (AllTermsOf S) -defined (abs (ar DD)) -tuples_on (AllTermsOf S) -valued Element of bool [:((abs (ar DD)) -tuples_on (AllTermsOf S)),((abs (ar DD)) -tuples_on (AllTermsOf S)):]
(abs (ar DD)) -tuples_on (AllTermsOf S) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf S
[:((abs (ar DD)) -tuples_on (AllTermsOf S)),((abs (ar DD)) -tuples_on (AllTermsOf S)):] is non empty Relation-like set
bool [:((abs (ar DD)) -tuples_on (AllTermsOf S)),((abs (ar DD)) -tuples_on (AllTermsOf S)):] is non empty set
(abs (ar DD)) -placesOf (S,FF,X) is Relation-like (abs (ar DD)) -tuples_on (AllTermsOf S) -defined (abs (ar DD)) -tuples_on (AllTermsOf S) -valued Element of bool [:((abs (ar DD)) -tuples_on (AllTermsOf S)),((abs (ar DD)) -tuples_on (AllTermsOf S)):]
Seg (abs (ar DD)) is non empty finite abs (ar DD) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar DD) ) } is set
{ [b1,b2] where b1, b2 is Relation-like NAT -defined AllTermsOf S -valued Function-like finite abs (ar DD) -element FinSequence-like FinSubsequence-like countable V209() Element of (abs (ar DD)) -tuples_on (AllTermsOf S) : for b3 being set holds
( not b3 in Seg (abs (ar DD)) or [(b1 . b3),(b2 . b3)] in (S,FF,X) ) } is set
(((AllSymbolsOf S) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf S) *) \ {{}}
(AllTermsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf S) *) \ {{}}) *)
bool ((((AllSymbolsOf S) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
HH is Relation-like NAT -defined AllTermsOf S -valued Function-like finite abs (ar DD) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf S) *
HC is Relation-like NAT -defined AllTermsOf S -valued Function-like finite abs (ar DD) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf S) *
(S,(abs (ar DD)),HH,HC) is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf S)
[:(Seg (abs (ar DD))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg (abs (ar DD))),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
{ ((<*(TheEqSymbOf S)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar DD)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar DD)) -defined ((AllSymbolsOf S) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar DD))),(((AllSymbolsOf S) *) \ {{}}):] : ( b2 = HH & b3 = HC ) } is set
AtomicFormulaSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite non empty-membered set
TheNorSymbOf S is set
{(TheNorSymbOf S)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf S) \ {(TheNorSymbOf S)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf S)
bool (AllSymbolsOf S) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) typed\ {(TheNorSymbOf S)} is Element of bool (AllSymbolsOf S)
DD -compound HH is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
<*DD*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}}
[1,DD] is non empty V26() set
{[1,DD]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
S -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
((AllSymbolsOf S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf S) *
[:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) -multiCat is non empty Relation-like ((AllSymbolsOf S) *) * -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf S) *) *),((AllSymbolsOf S) *):]
K295((AllSymbolsOf S)) is non empty Relation-like [:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):]
[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf S) *),((AllSymbolsOf S) *):],((AllSymbolsOf S) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf S)) is non empty Relation-like (((AllSymbolsOf S) *) *) \ {{}} -defined (AllSymbolsOf S) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):]
(((AllSymbolsOf S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf S) *) *)
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf S) *) *)
[:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf S) *) *) \ {{}}),((AllSymbolsOf S) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf S))) is non empty Relation-like Function-like Function-yielding V156() set
(S -multiCat) . HH is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf S) *
<*DD*> ^ ((S -multiCat) . HH) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
DD -compound HC is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
(S -multiCat) . HC is Relation-like NAT -defined AllSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf S) *
<*DD*> ^ ((S -multiCat) . HC) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
D2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
sub1 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf S) *) \ {{}}
bool X is non empty set
{D2} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf S) *) \ {{}})
inf is Element of bool X
sub2 is Element of bool X
inf \/ sub2 is Element of bool X
{(DD -compound HH)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf S) *) \ {{}})
(S,(abs (ar DD)),HH,HC) \/ {(DD -compound HH)} is non empty functional finite V36() with_non-empty_elements non empty-membered countable set
[((S,(abs (ar DD)),HH,HC) \/ {(DD -compound HH)}),(DD -compound HC)] is non empty V26() (S) (S) set
{[((S,(abs (ar DD)),HH,HC) \/ {(DD -compound HH)}),(DD -compound HC)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (S,{(S)}, {} ) (S,{(S)}) set
U is Element of bool X
[U,sub1] is non empty V26() Element of [:(bool X),(((AllSymbolsOf S) *) \ {{}}):]
[:(bool X),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
{[U,sub1]} is non empty trivial Relation-like non empty-yielding bool X -defined ((AllSymbolsOf S) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() Element of bool [:(bool X),(((AllSymbolsOf S) *) \ {{}}):]
bool [:(bool X),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
{sub1} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf S) *) \ {{}})
X is set
C is set
phi is set
[C,phi] is non empty V26() set
S is V51() V53() eligible Language-like
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
the U1 of S is set
(S) is non empty Relation-like set
AllFormulasOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf S) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf S), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}} : b1 is finite } is set
bool (S) is non empty Element of bool (bool (S))
bool (S) is non empty set
bool (bool (S)) is non empty set
Funcs ((bool (S)),(bool (S))) is non empty functional FUNCTION_DOMAIN of bool (S), bool (S)
bool (Funcs ((bool (S)),(bool (S)))) is non empty set
(S) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total (S) Element of Funcs ((bool (S)),(bool (S)))
(S) is Relation-like bool (S) -defined (S) -valued Element of bool [:(bool (S)),(S):]
[:(bool (S)),(S):] is non empty Relation-like set
bool [:(bool (S)),(S):] is non empty set
(S,(S)) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
{(S)} is non empty trivial functional finite 1 -element with_common_domain countable (S) Element of bool (Funcs ((bool (S)),(bool (S))))
(S) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total (S) Element of Funcs ((bool (S)),(bool (S)))
(S) is Relation-like bool (S) -defined (S) -valued Element of bool [:(bool (S)),(S):]
(S,(S)) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
{(S)} is non empty trivial functional finite 1 -element with_common_domain countable (S) Element of bool (Funcs ((bool (S)),(bool (S))))
(S) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total (S) Element of Funcs ((bool (S)),(bool (S)))
(S) is Relation-like bool (S) -defined (S) -valued Element of bool [:(bool (S)),(S):]
(S,(S)) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
{(S)} is non empty trivial functional finite 1 -element with_common_domain countable (S) Element of bool (Funcs ((bool (S)),(bool (S))))
AllTermsOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf S) *) \ {{}}))
bool (bool (((AllSymbolsOf S) *) \ {{}})) is non empty non trivial non finite non empty-membered set
S -termsOfMaxDepth is Relation-like Function-like set
proj2 (S -termsOfMaxDepth) is set
union (proj2 (S -termsOfMaxDepth)) is set
DD is low-compounding relational ofAtomicFormula Element of AllSymbolsOf S
ar DD is non empty complex ext-real non positive negative finite V40() V41() countable 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 Element of the U1 of S
{ the U3 of S} is non empty trivial finite 1 -element countable 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 non empty-membered set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of S . DD is set
abs (ar DD) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
DD -compound is non empty Relation-like non-empty non empty-yielding (((AllSymbolsOf S) *) \ {{}}) * -defined ((AllSymbolsOf S) *) \ {{}} -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):]
(((AllSymbolsOf S) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf S) *) *)
((AllSymbolsOf S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf S) *
bool (((AllSymbolsOf S) *) *) is non empty non trivial non finite non empty-membered set
[:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf S) *) \ {{}}) *),(((AllSymbolsOf S) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
(DD -compound) . C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(DD -compound) . phi is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
FF is functional Element of bool (Funcs ((bool (S)),(bool (S))))
{(S)} /\ FF is functional finite countable Element of bool (Funcs ((bool (S)),(bool (S))))
{(S)} typed/\ FF is trivial functional finite with_common_domain countable Element of bool {(S)}
bool {(S)} is non empty finite V36() countable set
{(S)} /\ FF is functional finite countable set
{(S)} /\typed FF is functional Element of bool FF
bool FF is non empty set
{(S)} /\ FF is functional finite countable Element of bool (Funcs ((bool (S)),(bool (S))))
{(S)} typed/\ FF is trivial functional finite with_common_domain countable Element of bool {(S)}
bool {(S)} is non empty finite V36() countable set
{(S)} /\ FF is functional finite countable set
{(S)} /\typed FF is functional Element of bool FF
FF /\ {(S)} is functional finite countable Element of bool (Funcs ((bool (S)),(bool (S))))
FF typed/\ {(S)} is functional Element of bool FF
FF /\ {(S)} is functional finite countable set
FF /\typed {(S)} is trivial functional finite with_common_domain countable Element of bool {(S)}
bool {(S)} is non empty finite V36() countable set
(S,FF,X) is Relation-like AllTermsOf S -defined AllTermsOf S -valued 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
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
TheEqSymbOf S is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf S
the U2 of S is Element of the U1 of S
<*(TheEqSymbOf S)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(TheEqSymbOf S)] is non empty V26() set
{[1,(TheEqSymbOf S)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf S -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf S) *) \ {{}} : (<*(TheEqSymbOf S)*> ^ b1) ^ b2 is (S,FF,X) } is set
(abs (ar DD)) -placesOf (S,FF,X) is Relation-like (abs (ar DD)) -tuples_on (AllTermsOf S) -defined (abs (ar DD)) -tuples_on (AllTermsOf S) -valued Element of bool [:((abs (ar DD)) -tuples_on (AllTermsOf S)),((abs (ar DD)) -tuples_on (AllTermsOf S)):]
(abs (ar DD)) -tuples_on (AllTermsOf S) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf S
[:((abs (ar DD)) -tuples_on (AllTermsOf S)),((abs (ar DD)) -tuples_on (AllTermsOf S)):] is non empty Relation-like set
bool [:((abs (ar DD)) -tuples_on (AllTermsOf S)),((abs (ar DD)) -tuples_on (AllTermsOf S)):] is non empty set
(abs (ar DD)) -placesOf (S,FF,X) is Relation-like (abs (ar DD)) -tuples_on (AllTermsOf S) -defined (abs (ar DD)) -tuples_on (AllTermsOf S) -valued Element of bool [:((abs (ar DD)) -tuples_on (AllTermsOf S)),((abs (ar DD)) -tuples_on (AllTermsOf S)):]
Seg (abs (ar DD)) is non empty finite abs (ar DD) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar DD) ) } is set
{ [b1,b2] where b1, b2 is Relation-like NAT -defined AllTermsOf S -valued Function-like finite abs (ar DD) -element FinSequence-like FinSubsequence-like countable V209() Element of (abs (ar DD)) -tuples_on (AllTermsOf S) : for b3 being set holds
( not b3 in Seg (abs (ar DD)) or [(b1 . b3),(b2 . b3)] in (S,FF,X) ) } is set
HH is Relation-like AllTermsOf S -defined AllTermsOf S -valued total quasi_total symmetric Element of bool [:(AllTermsOf S),(AllTermsOf S):]
(abs (ar DD)) -placesOf HH is Relation-like (abs (ar DD)) -tuples_on (AllTermsOf S) -defined (abs (ar DD)) -tuples_on (AllTermsOf S) -valued total quasi_total symmetric Element of bool [:((abs (ar DD)) -tuples_on (AllTermsOf S)),((abs (ar DD)) -tuples_on (AllTermsOf S)):]
(abs (ar DD)) -placesOf HH is Relation-like (abs (ar DD)) -tuples_on (AllTermsOf S) -defined (abs (ar DD)) -tuples_on (AllTermsOf S) -valued total quasi_total Element of bool [:((abs (ar DD)) -tuples_on (AllTermsOf S)),((abs (ar DD)) -tuples_on (AllTermsOf S)):]
{ [b1,b2] where b1, b2 is Relation-like NAT -defined AllTermsOf S -valued Function-like finite abs (ar DD) -element FinSequence-like FinSubsequence-like countable V209() Element of (abs (ar DD)) -tuples_on (AllTermsOf S) : for b3 being set holds
( not b3 in Seg (abs (ar DD)) or [(b1 . b3),(b2 . b3)] in HH ) } is set
[phi,C] is non empty V26() set
HC is Relation-like (abs (ar DD)) -tuples_on (AllTermsOf S) -defined (abs (ar DD)) -tuples_on (AllTermsOf S) -valued total quasi_total symmetric Element of bool [:((abs (ar DD)) -tuples_on (AllTermsOf S)),((abs (ar DD)) -tuples_on (AllTermsOf S)):]
X is non empty set
C is set
chi (C,X) is non empty Relation-like X -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:X,BOOLEAN:]
[:X,BOOLEAN:] is non empty Relation-like set
bool [:X,BOOLEAN:] is non empty set
phi is Element of X
S is Element of X
(chi (C,X)) . phi is boolean Element of BOOLEAN
(chi (C,X)) . S is boolean Element of BOOLEAN
[((chi (C,X)) . phi),((chi (C,X)) . S)] is non empty V26() Element of [:BOOLEAN,BOOLEAN:]
X is set
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
phi is low-compounding relational ofAtomicFormula Element of AllSymbolsOf C
X -freeInterpreter phi is non empty Relation-like (abs (ar phi)) -tuples_on (AllTermsOf C) -defined (AllTermsOf C) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of phi, AllTermsOf C
ar phi is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C . phi is set
abs (ar phi) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar phi)) -tuples_on (AllTermsOf C) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf C
(AllTermsOf C) \/ BOOLEAN is non empty set
S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} /\ S is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} typed/\ S is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
{(C)} /\ S is functional finite countable set
{(C)} /\typed S is functional Element of bool S
bool S is non empty set
{(C)} /\ S is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} typed/\ S is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
{(C)} /\ S is functional finite countable set
{(C)} /\typed S is functional Element of bool S
S /\ {(C)} is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
S typed/\ {(C)} is functional Element of bool S
S /\ {(C)} is functional finite countable set
S /\typed {(C)} is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
(C,S,X) is Relation-like AllTermsOf C -defined AllTermsOf C -valued Element of bool [:(AllTermsOf C),(AllTermsOf C):]
[:(AllTermsOf C),(AllTermsOf C):] is non empty Relation-like set
bool [:(AllTermsOf C),(AllTermsOf C):] is non empty set
TermSymbolsOf C is non empty set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} : (<*(TheEqSymbOf C)*> ^ b1) ^ b2 is (C,S,X) } is set
AtomicFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : b1 is 0wff } is set
chi (X,(AtomicFormulasOf C)) is non empty Relation-like AtomicFormulasOf C -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(AtomicFormulasOf C),BOOLEAN:]
[:(AtomicFormulasOf C),BOOLEAN:] is non empty Relation-like set
bool [:(AtomicFormulasOf C),BOOLEAN:] is non empty set
phi -compound is non empty Relation-like non-empty non empty-yielding (((AllSymbolsOf C) *) \ {{}}) * -defined ((AllSymbolsOf C) *) \ {{}} -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf C) *) \ {{}}) *),(((AllSymbolsOf C) *) \ {{}}):]
(((AllSymbolsOf C) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf C) *) *)
((AllSymbolsOf C) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf C) *
bool (((AllSymbolsOf C) *) *) is non empty non trivial non finite non empty-membered set
[:((((AllSymbolsOf C) *) \ {{}}) *),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf C) *) \ {{}}) *),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
seqt is set
HH is set
[seqt,HH] is non empty V26() set
(abs (ar phi)) -placesOf (C,S,X) is Relation-like (abs (ar phi)) -tuples_on (AllTermsOf C) -defined (abs (ar phi)) -tuples_on (AllTermsOf C) -valued Element of bool [:((abs (ar phi)) -tuples_on (AllTermsOf C)),((abs (ar phi)) -tuples_on (AllTermsOf C)):]
[:((abs (ar phi)) -tuples_on (AllTermsOf C)),((abs (ar phi)) -tuples_on (AllTermsOf C)):] is non empty Relation-like set
bool [:((abs (ar phi)) -tuples_on (AllTermsOf C)),((abs (ar phi)) -tuples_on (AllTermsOf C)):] is non empty set
(abs (ar phi)) -placesOf (C,S,X) is Relation-like (abs (ar phi)) -tuples_on (AllTermsOf C) -defined (abs (ar phi)) -tuples_on (AllTermsOf C) -valued Element of bool [:((abs (ar phi)) -tuples_on (AllTermsOf C)),((abs (ar phi)) -tuples_on (AllTermsOf C)):]
Seg (abs (ar phi)) is non empty finite abs (ar phi) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar phi) ) } is set
{ [b1,b2] where b1, b2 is Relation-like NAT -defined AllTermsOf C -valued Function-like finite abs (ar phi) -element FinSequence-like FinSubsequence-like countable V209() Element of (abs (ar phi)) -tuples_on (AllTermsOf C) : for b3 being set holds
( not b3 in Seg (abs (ar phi)) or [(b1 . b3),(b2 . b3)] in (C,S,X) ) } is set
(((AllSymbolsOf C) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf C) *) \ {{}}
(AllTermsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf C) *) \ {{}}) *)
bool ((((AllSymbolsOf C) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
HC is Relation-like NAT -defined AllTermsOf C -valued Function-like finite abs (ar phi) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf C) *
a is Relation-like NAT -defined AllTermsOf C -valued Function-like finite abs (ar phi) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf C) *
(C,(abs (ar phi)),HC,a) is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf C)
[:(Seg (abs (ar phi))),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg (abs (ar phi))),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
{ ((<*(TheEqSymbOf C)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar phi)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar phi)) -defined ((AllSymbolsOf C) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar phi))),(((AllSymbolsOf C) *) \ {{}}):] : ( b2 = HC & b3 = a ) } is set
AtomicFormulaSymbolsOf C is non empty Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
TheNorSymbOf C is set
{(TheNorSymbOf C)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf C) \ {(TheNorSymbOf C)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) typed\ {(TheNorSymbOf C)} is Element of bool (AllSymbolsOf C)
phi -compound HC is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf C) *) \ {{}}
<*phi*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,phi] is non empty V26() set
{[1,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
C -multiCat is non empty Relation-like ((AllSymbolsOf C) *) * -defined (AllSymbolsOf C) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf C) *) *),((AllSymbolsOf C) *):]
((AllSymbolsOf C) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf C) *
[:(((AllSymbolsOf C) *) *),((AllSymbolsOf C) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf C) *) *),((AllSymbolsOf C) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) -multiCat is non empty Relation-like ((AllSymbolsOf C) *) * -defined (AllSymbolsOf C) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf C) *) *),((AllSymbolsOf C) *):]
K295((AllSymbolsOf C)) is non empty Relation-like [:((AllSymbolsOf C) *),((AllSymbolsOf C) *):] -defined (AllSymbolsOf C) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf C) *),((AllSymbolsOf C) *):],((AllSymbolsOf C) *):]
[:((AllSymbolsOf C) *),((AllSymbolsOf C) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf C) *),((AllSymbolsOf C) *):],((AllSymbolsOf C) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf C) *),((AllSymbolsOf C) *):],((AllSymbolsOf C) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf C)) is non empty Relation-like (((AllSymbolsOf C) *) *) \ {{}} -defined (AllSymbolsOf C) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf C) *) *) \ {{}}),((AllSymbolsOf C) *):]
(((AllSymbolsOf C) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) *)
bool (((AllSymbolsOf C) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf C) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf C) *) *)
[:((((AllSymbolsOf C) *) *) \ {{}}),((AllSymbolsOf C) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf C) *) *) \ {{}}),((AllSymbolsOf C) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf C))) is non empty Relation-like Function-like Function-yielding V156() set
(C -multiCat) . HC is Relation-like NAT -defined AllSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf C) *
<*phi*> ^ ((C -multiCat) . HC) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
phi -compound a is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf C) *) \ {{}}
(C -multiCat) . a is Relation-like NAT -defined AllSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf C) *
<*phi*> ^ ((C -multiCat) . a) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
D2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf C) *) \ {{}}
sub1 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf C) *) \ {{}}
(phi -compound) . seqt is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff Element of AtomicFormulasOf C
(phi -compound) . HH is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff Element of AtomicFormulasOf C
(chi (X,(AtomicFormulasOf C))) . D2 is boolean set
(chi (X,(AtomicFormulasOf C))) . sub1 is boolean set
[((chi (X,(AtomicFormulasOf C))) . D2),((chi (X,(AtomicFormulasOf C))) . sub1)] is non empty V26() set
(X -freeInterpreter phi) . HC is set
(X -freeInterpreter phi) . a is set
(X -freeInterpreter phi) . seqt is set
(X -freeInterpreter phi) . HH is set
[((X -freeInterpreter phi) . seqt),((X -freeInterpreter phi) . HH)] is non empty V26() set
X is non empty set
[:X,X:] is non empty Relation-like set
bool [:X,X:] is non empty set
C is set
[:C,X:] is Relation-like set
bool [:C,X:] is non empty set
phi is set
[phi,phi] is non empty V26() set
{[phi,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
S is Relation-like X -defined X -valued total quasi_total reflexive Element of bool [:X,X:]
DD is Relation-like C -defined X -valued Function-like total quasi_total Element of bool [:C,X:]
D is non empty set
[:D,X:] is non empty Relation-like set
bool [:D,X:] is non empty set
phii is set
psi is set
[phii,psi] is non empty V26() set
FF is Relation-like set
Y is non empty Relation-like D -defined X -valued Function-like total quasi_total Element of bool [:D,X:]
H is Element of D
Y . H is Element of X
m is Element of D
Y . m is Element of X
DD . phii is set
DD . psi is set
[(DD . phii),(DD . psi)] is non empty V26() set
X is non empty set
[:X,X:] is non empty Relation-like set
bool [:X,X:] is non empty set
X \/ BOOLEAN is non empty set
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
phi is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf C
ar phi is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of INT
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C . phi is set
abs (ar phi) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of NAT
(abs (ar phi)) -tuples_on X is non empty functional V36() FinSequence-membered empty-membered FinSequenceSet of X
S is Relation-like X -defined X -valued total quasi_total reflexive Element of bool [:X,X:]
FF is non empty Relation-like (abs (ar phi)) -tuples_on X -defined X \/ BOOLEAN -valued Function-like total quasi_total Interpreter of phi,X
DD is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
DD -tuples_on X is non empty functional V36() FinSequence-membered empty-membered FinSequenceSet of X
[:{{}},X:] is non empty Relation-like set
bool [:{{}},X:] is non empty set
D is non empty Relation-like {{}} -defined X -valued Function-like total quasi_total finite countable V209() Element of bool [:{{}},X:]
DD -placesOf S is Relation-like DD -tuples_on X -defined DD -tuples_on X -valued Element of bool [:(DD -tuples_on X),(DD -tuples_on X):]
[:(DD -tuples_on X),(DD -tuples_on X):] is non empty Relation-like set
bool [:(DD -tuples_on X),(DD -tuples_on X):] is non empty set
DD -placesOf S is non empty Relation-like DD -tuples_on X -defined DD -tuples_on X -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(DD -tuples_on X),(DD -tuples_on X):]
Seg DD is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal DD -element {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= DD ) } is set
{ [b1,b2] where b1, b2 is Relation-like NAT -defined X -valued Function-like finite DD -element FinSequence-like FinSubsequence-like countable V209() Element of DD -tuples_on X : for b3 being set holds
( not b3 in Seg DD or [(b1 . b3),(b2 . b3)] in S ) } is set
X is set
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
phi is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf C
X -freeInterpreter phi is non empty Relation-like (abs (ar phi)) -tuples_on (AllTermsOf C) -defined (AllTermsOf C) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of phi, AllTermsOf C
ar phi is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of INT
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C . phi is set
abs (ar phi) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of NAT
(abs (ar phi)) -tuples_on (AllTermsOf C) is non empty functional V36() FinSequence-membered empty-membered FinSequenceSet of AllTermsOf C
(AllTermsOf C) \/ BOOLEAN is non empty set
S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,S,X) is Relation-like AllTermsOf C -defined AllTermsOf C -valued Element of bool [:(AllTermsOf C),(AllTermsOf C):]
[:(AllTermsOf C),(AllTermsOf C):] is non empty Relation-like set
bool [:(AllTermsOf C),(AllTermsOf C):] is non empty set
TermSymbolsOf C is non empty set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} : (<*(TheEqSymbOf C)*> ^ b1) ^ b2 is (C,S,X) } is set
D is Relation-like AllTermsOf C -defined AllTermsOf C -valued total quasi_total reflexive symmetric transitive Element of bool [:(AllTermsOf C),(AllTermsOf C):]
X is set
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
phi is ofAtomicFormula Element of AllSymbolsOf C
X -freeInterpreter phi is non empty Relation-like (abs (ar phi)) -tuples_on (AllTermsOf C) -defined (AllTermsOf C) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of phi, AllTermsOf C
ar phi is complex ext-real finite V40() V41() countable Element of INT
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C . phi is set
abs (ar phi) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar phi)) -tuples_on (AllTermsOf C) is non empty functional V36() FinSequence-membered FinSequenceSet of AllTermsOf C
(AllTermsOf C) \/ BOOLEAN is non empty set
S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S /\ {(C)} is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
S typed/\ {(C)} is functional Element of bool S
bool S is non empty set
S /\ {(C)} is functional finite countable set
S /\typed {(C)} is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
{(C)} /\ S is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} typed/\ S is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
{(C)} /\ S is functional finite countable set
{(C)} /\typed S is functional Element of bool S
{(C)} /\ S is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} typed/\ S is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
{(C)} /\ S is functional finite countable set
{(C)} /\typed S is functional Element of bool S
S /\ {(C)} is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
S typed/\ {(C)} is functional Element of bool S
S /\ {(C)} is functional finite countable set
S /\typed {(C)} is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
(C,S,X) is Relation-like AllTermsOf C -defined AllTermsOf C -valued Element of bool [:(AllTermsOf C),(AllTermsOf C):]
[:(AllTermsOf C),(AllTermsOf C):] is non empty Relation-like set
bool [:(AllTermsOf C),(AllTermsOf C):] is non empty set
TermSymbolsOf C is non empty set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} : (<*(TheEqSymbOf C)*> ^ b1) ^ b2 is (C,S,X) } is set
AtomicFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : b1 is 0wff } is set
chi (X,(AtomicFormulasOf C)) is non empty Relation-like AtomicFormulasOf C -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(AtomicFormulasOf C),BOOLEAN:]
[:(AtomicFormulasOf C),BOOLEAN:] is non empty Relation-like set
bool [:(AtomicFormulasOf C),BOOLEAN:] is non empty set
phi -compound is non empty Relation-like non-empty non empty-yielding (((AllSymbolsOf C) *) \ {{}}) * -defined ((AllSymbolsOf C) *) \ {{}} -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf C) *) \ {{}}) *),(((AllSymbolsOf C) *) \ {{}}):]
(((AllSymbolsOf C) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf C) *) *)
((AllSymbolsOf C) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf C) *
bool (((AllSymbolsOf C) *) *) is non empty non trivial non finite non empty-membered set
[:((((AllSymbolsOf C) *) \ {{}}) *),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf C) *) \ {{}}) *),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
HH is functional Element of bool S
HC is functional Element of bool S
HH \/ HC is functional Element of bool S
a is non relational termal own ofAtomicFormula Element of AllSymbolsOf C
{(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
D2 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf C
X -freeInterpreter D2 is non empty Relation-like (abs (ar D2)) -tuples_on (AllTermsOf C) -defined (AllTermsOf C) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of D2, AllTermsOf C
ar D2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of INT
the adicity of C . D2 is set
abs (ar D2) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of NAT
(abs (ar D2)) -tuples_on (AllTermsOf C) is non empty functional V36() FinSequence-membered empty-membered FinSequenceSet of AllTermsOf C
a is non relational termal own ofAtomicFormula Element of AllSymbolsOf C
D2 is low-compounding ofAtomicFormula Element of AllSymbolsOf C
X -freeInterpreter D2 is non empty Relation-like (abs (ar D2)) -tuples_on (AllTermsOf C) -defined (AllTermsOf C) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of D2, AllTermsOf C
ar D2 is non empty complex ext-real finite V40() V41() countable Element of INT
the adicity of C . D2 is set
abs (ar D2) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar D2)) -tuples_on (AllTermsOf C) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf C
a is non relational termal own ofAtomicFormula Element of AllSymbolsOf C
a is low-compounding relational ofAtomicFormula Element of AllSymbolsOf C
X -freeInterpreter a is non empty Relation-like (abs (ar a)) -tuples_on (AllTermsOf C) -defined (AllTermsOf C) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of a, AllTermsOf C
ar a is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of C . a is set
abs (ar a) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar a)) -tuples_on (AllTermsOf C) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf C
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X),(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
{(X),(X),(X),(X),(X),(X),(X),(X)} \/ {(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is functional Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X),(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
{(X),(X),(X),(X),(X),(X),(X),(X)} \/ {(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
DD is functional Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is functional (2,X) Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X),(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
{(X),(X),(X),(X),(X),(X),(X),(X)} \/ {(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
the functional (2,X) Element of bool (Funcs ((bool (X)),(bool (X)))) is functional (2,X) Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
the functional (1,X) Element of bool (Funcs ((bool (X)),(bool (X)))) is functional (1,X) Element of bool (Funcs ((bool (X)),(bool (X))))
X is set
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
phi is ofAtomicFormula Element of AllSymbolsOf C
X -freeInterpreter phi is non empty Relation-like (abs (ar phi)) -tuples_on (AllTermsOf C) -defined (AllTermsOf C) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of phi, AllTermsOf C
ar phi is complex ext-real finite V40() V41() countable Element of INT
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C . phi is set
abs (ar phi) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar phi)) -tuples_on (AllTermsOf C) is non empty functional V36() FinSequence-membered FinSequenceSet of AllTermsOf C
(AllTermsOf C) \/ BOOLEAN is non empty set
S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,S,X) is Relation-like AllTermsOf C -defined AllTermsOf C -valued Element of bool [:(AllTermsOf C),(AllTermsOf C):]
[:(AllTermsOf C),(AllTermsOf C):] is non empty Relation-like set
bool [:(AllTermsOf C),(AllTermsOf C):] is non empty set
TermSymbolsOf C is non empty set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} : (<*(TheEqSymbOf C)*> ^ b1) ^ b2 is (C,S,X) } is set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
S /\ {(C)} is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
S typed/\ {(C)} is functional Element of bool S
bool S is non empty set
S /\ {(C)} is functional finite countable set
S /\typed {(C)} is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
S /\ {(C)} is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
S typed/\ {(C)} is functional Element of bool S
S /\ {(C)} is functional finite countable set
S /\typed {(C)} is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
S /\ {(C)} is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
S typed/\ {(C)} is functional Element of bool S
S /\ {(C)} is functional finite countable set
S /\typed {(C)} is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
S /\ {(C)} is functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
S typed/\ {(C)} is functional Element of bool S
S /\ {(C)} is functional finite countable set
S /\typed {(C)} is trivial functional finite with_common_domain countable Element of bool {(C)}
bool {(C)} is non empty finite V36() countable set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional (1,X) Element of bool (Funcs ((bool (X)),(bool (X))))
S is ofAtomicFormula Element of AllSymbolsOf X
ar S is complex ext-real finite V40() V41() countable Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X . S is set
abs (ar S) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
(abs (ar S)) -tuples_on (AllTermsOf X) is non empty functional V36() FinSequence-membered FinSequenceSet of AllTermsOf X
(AllTermsOf X) \/ BOOLEAN is non empty set
phi is (X,C) set
phi -freeInterpreter S is non empty Relation-like (abs (ar S)) -tuples_on (AllTermsOf X) -defined (AllTermsOf X) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of S, AllTermsOf X
(X,C,phi) is Relation-like AllTermsOf X -defined AllTermsOf X -valued Element of bool [:(AllTermsOf X),(AllTermsOf X):]
[:(AllTermsOf X),(AllTermsOf X):] is non empty Relation-like set
bool [:(AllTermsOf X),(AllTermsOf X):] is non empty set
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}} : (<*(TheEqSymbOf X)*> ^ b1) ^ b2 is (X,C,phi) } is set
DD is non empty Relation-like (abs (ar S)) -tuples_on (AllTermsOf X) -defined (AllTermsOf X) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of S, AllTermsOf X
X is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
[:(AllTermsOf C),(AllTermsOf C):] is non empty Relation-like set
bool [:(AllTermsOf C),(AllTermsOf C):] is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(C,phi,X) is Relation-like AllTermsOf C -defined AllTermsOf C -valued Element of bool [:(AllTermsOf C),(AllTermsOf C):]
TermSymbolsOf C is non empty set
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} : (<*(TheEqSymbOf C)*> ^ b1) ^ b2 is (C,phi,X) } is set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
{(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional ( 0 ,X) Element of bool (Funcs ((bool (X)),(bool (X))))
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
[:(AllTermsOf X),(AllTermsOf X):] is non empty Relation-like set
bool [:(AllTermsOf X),(AllTermsOf X):] is non empty set
phi is (X,C) set
(X,C,phi) is Relation-like AllTermsOf X -defined AllTermsOf X -valued Element of bool [:(AllTermsOf X),(AllTermsOf X):]
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}} : (<*(TheEqSymbOf X)*> ^ b1) ^ b2 is (X,C,phi) } is set
S is Relation-like AllTermsOf X -defined AllTermsOf X -valued Element of bool [:(AllTermsOf X),(AllTermsOf X):]
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
the functional (1,X) Element of bool (Funcs ((bool (X)),(bool (X)))) is functional (1,X) Element of bool (Funcs ((bool (X)),(bool (X))))
phi is functional ( 0 ,X) Element of bool (Funcs ((bool (X)),(bool (X))))
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
S is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
DD is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
C is set
X is set
X is V51() V53() eligible Language-like
C is (X) (X) set
{C} is non empty trivial finite 1 -element countable set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
X is V51() V53() eligible Language-like
C is (X) set
phi is (X) set
C \/ phi is set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty set
DD is Relation-like (X) Element of bool (X)
FF is Relation-like (X) Element of bool (X)
DD \/ FF is Relation-like (X) Element of bool (X)
D is set
X is V51() V53() eligible Language-like
C is (X) (X) set
phi is (X) (X) set
{C,phi} is non empty finite countable set
{C} is non empty trivial finite 1 -element countable (X) set
{phi} is non empty trivial finite 1 -element countable (X) set
{C} \/ {phi} is non empty finite countable (X) set
S is set
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
X + C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
phi is set
S is set
{phi,S} is non empty finite countable set
DD is set
FF is V51() V53() eligible Language-like
(FF) is non empty Relation-like set
AllFormulasOf FF is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf FF -prefix FF -prefix Element of bool (((AllSymbolsOf FF) *) \ {{}})
AllSymbolsOf FF is non empty non trivial non finite non empty-membered set
the U1 of FF is set
AllSymbolsOf FF is non empty non trivial non finite non empty-membered set
(AllSymbolsOf FF) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf FF
((AllSymbolsOf FF) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf FF) *)
bool ((AllSymbolsOf FF) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf FF) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf FF) *)
bool (((AllSymbolsOf FF) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf FF) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf FF
((AllSymbolsOf FF) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf FF) *)
bool ((AllSymbolsOf FF) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf FF) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf FF) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf FF) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf FF) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf FF), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf FF) *) \ {{}} : b1 is finite } is set
bool (FF) is non empty Element of bool (bool (FF))
bool (FF) is non empty set
bool (bool (FF)) is non empty set
Funcs ((bool (FF)),(bool (FF))) is non empty functional FUNCTION_DOMAIN of bool (FF), bool (FF)
bool (Funcs ((bool (FF)),(bool (FF)))) is non empty set
D is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
Y is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
D \/ Y is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
phii is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
(D \/ Y) \/ phii is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
psi is (FF) set
H is (FF) set
psi \/ H is (FF) set
(FF,D) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
(FF,Y) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
(FF,phii) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
(FF,(D \/ Y)) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
(FF,((D \/ Y) \/ phii)) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
sub2 is Relation-like (FF) Element of bool (FF)
inf is Relation-like (FF) Element of bool (FF)
sub2 \/ inf is Relation-like (FF) Element of bool (FF)
(FF,D,X) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
iter ((FF,D),X) is Relation-like Function-like set
(FF,D,X) . sub2 is Relation-like (FF) Element of bool (FF)
(FF,Y,X) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
iter ((FF,Y),X) is Relation-like Function-like set
(FF,Y,X) . inf is Relation-like (FF) Element of bool (FF)
sub2 null inf is Relation-like inf \/ (proj1 sub2) -defined inf \/ (proj2 sub2) -valued set
proj1 sub2 is set
inf \/ (proj1 sub2) is set
proj2 sub2 is set
inf \/ (proj2 sub2) is set
sub2 \typed/ inf is Relation-like Element of bool (sub2 \/ inf)
sub2 \/ inf is Relation-like (FF) set
bool (sub2 \/ inf) is non empty set
inf null sub2 is Relation-like sub2 \/ (proj1 inf) -defined sub2 \/ (proj2 inf) -valued set
proj1 inf is set
sub2 \/ (proj1 inf) is set
proj2 inf is set
sub2 \/ (proj2 inf) is set
inf \typed/ sub2 is Relation-like Element of bool (inf \/ sub2)
inf \/ sub2 is Relation-like (FF) set
bool (inf \/ sub2) is non empty set
D null Y is set
D \typed/ Y is functional Element of bool (D \/ Y)
D \/ Y is functional set
bool (D \/ Y) is non empty set
Y null D is set
Y \typed/ D is functional Element of bool (Y \/ D)
Y \/ D is functional set
bool (Y \/ D) is non empty set
(FF,(D \/ Y),X) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
iter ((FF,(D \/ Y)),X) is Relation-like Function-like set
(FF,(D \/ Y),X) . (sub2 \/ inf) is Relation-like (FF) Element of bool (FF)
II1 is (FF) (FF) set
II2 is (FF) (FF) set
{II1,II2} is non empty finite countable (FF) set
(iter ((FF,(D \/ Y)),X)) . (sub2 \/ inf) is set
(FF,phii,C) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
iter ((FF,phii),C) is Relation-like Function-like set
(FF,phii,C) . {phi,S} is (FF) set
{DD} is non empty trivial finite 1 -element countable set
(iter ((FF,phii),C)) . {phi,S} is set
iter ((FF,((D \/ Y) \/ phii)),(X + C)) is Relation-like Function-like set
(iter ((FF,((D \/ Y) \/ phii)),(X + C))) . (sub2 \/ inf) is set
(FF,((D \/ Y) \/ phii),(X + C)) is Relation-like bool (FF) -defined bool (FF) -valued Function-like total quasi_total Element of Funcs ((bool (FF)),(bool (FF)))
(FF,((D \/ Y) \/ phii),(X + C)) . (sub2 \/ inf) is Relation-like (FF) Element of bool (FF)
X is set
C is set
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
S is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
DD is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
FF is set
FF `1 is set
FF `2 is set
{FF} is non empty trivial finite 1 -element countable set
X is set
C is set
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
S is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
S . C is set
{S} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (phi)),(bool (phi))))
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
(phi,{S}) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
iter ((phi,{S}),1) is Relation-like Function-like set
dom S is Element of bool (bool (phi))
bool (bool (phi)) is non empty set
(phi,{S},1) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
phii is Relation-like (phi) Element of bool (phi)
(phi,{S},1) . phii is Relation-like (phi) Element of bool (phi)
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
xnot C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf X)*> ^ C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ C) ^ C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth C),(Depth C)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
Depth C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth C),(Depth C)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
xnot phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ phi) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth phi)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth phi),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot C),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
(<*(TheNorSymbOf X)*> ^ C) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth C),(Depth phi)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth C),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[{(xnot C),(xnot phi)},((<*(TheNorSymbOf X)*> ^ C) ^ phi)] is non empty V26() (X) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
[{(xnot C),(xnot phi)},(xnot C)] is non empty V26() (X) (1,X,{(X)}, {} ) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
[{(xnot C),(xnot phi)},(xnot phi)] is non empty V26() (X) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
{[{(xnot C),(xnot phi)},(xnot C)],[{(xnot C),(xnot phi)},(xnot phi)]} is non empty Relation-like non empty-yielding bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued finite with_non-empty_elements non empty-membered countable (X) Element of bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
{[{(xnot C),(xnot phi)},(xnot C)]} is non empty trivial Relation-like non empty-yielding bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() (X) Element of bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
HH is Relation-like (X) Element of bool (X)
{[{(xnot C),(xnot phi)},(xnot C)]} \ HH is Relation-like bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued finite countable Element of bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
{[{(xnot C),(xnot phi)},(xnot C)]} typed\ HH is trivial Relation-like bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite Function-yielding V156() with_non-empty_elements countable V208() V209() Element of bool {[{(xnot C),(xnot phi)},(xnot C)]}
bool {[{(xnot C),(xnot phi)},(xnot C)]} is non empty finite V36() countable set
{[{(xnot C),(xnot phi)},(xnot C)]} \ HH is trivial Relation-like bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite Function-yielding V156() with_non-empty_elements countable V208() V209() Element of bool {[{(xnot C),(xnot phi)},(xnot C)]}
{[{(xnot C),(xnot phi)},(xnot phi)]} is non empty trivial Relation-like non empty-yielding bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() (X) Element of bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
{[{(xnot C),(xnot phi)},(xnot phi)]} \ HH is Relation-like bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued finite countable Element of bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
{[{(xnot C),(xnot phi)},(xnot phi)]} typed\ HH is trivial Relation-like bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite Function-yielding V156() with_non-empty_elements countable V208() V209() Element of bool {[{(xnot C),(xnot phi)},(xnot phi)]}
bool {[{(xnot C),(xnot phi)},(xnot phi)]} is non empty finite V36() countable set
{[{(xnot C),(xnot phi)},(xnot phi)]} \ HH is trivial Relation-like bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite Function-yielding V156() with_non-empty_elements countable V208() V209() Element of bool {[{(xnot C),(xnot phi)},(xnot phi)]}
[{(xnot C),(xnot phi)},(xnot C)] `1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf X) *) \ {{}})
([{(xnot C),(xnot phi)},(xnot C)] `1) \+\ {(xnot C),(xnot phi)} is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (((AllSymbolsOf X) *) \ {{}})
[{(xnot C),(xnot phi)},(xnot phi)] `1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf X) *) \ {{}})
([{(xnot C),(xnot phi)},(xnot phi)] `1) \+\ {(xnot C),(xnot phi)} is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (((AllSymbolsOf X) *) \ {{}})
[{(xnot C),(xnot phi)},((<*(TheNorSymbOf X)*> ^ C) ^ phi)] `1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf X) *) \ {{}})
([{(xnot C),(xnot phi)},((<*(TheNorSymbOf X)*> ^ C) ^ phi)] `1) \+\ {(xnot C),(xnot phi)} is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (((AllSymbolsOf X) *) \ {{}})
[{(xnot C),(xnot phi)},(xnot C)] `2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
([{(xnot C),(xnot phi)},(xnot C)] `2) \+\ (xnot C) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[{(xnot C),(xnot phi)},(xnot phi)] `2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
([{(xnot C),(xnot phi)},(xnot phi)] `2) \+\ (xnot phi) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[{(xnot C),(xnot phi)},((<*(TheNorSymbOf X)*> ^ C) ^ phi)] `2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
([{(xnot C),(xnot phi)},((<*(TheNorSymbOf X)*> ^ C) ^ phi)] `2) \+\ ((<*(TheNorSymbOf X)*> ^ C) ^ phi) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
seqt is (X) (X) Element of (X)
[HH,seqt] is non empty V26() Element of [:(bool (X)),(X):]
(X) . HH is Relation-like (X) Element of bool (X)
HC is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{C,phi} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[{C,phi},phi] is non empty V26() (X) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
{phi,C} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[{phi,C},phi] is non empty V26() (X) (1,X,{(X)}, {} ) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
S is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
C is (X) set
phi is (X) (X) set
[C,phi] is non empty V26() set
D is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,D) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X,D) . C is set
FF is Relation-like (X) Element of bool (X)
DD is (X) (X) Element of (X)
[FF,DD] is non empty V26() Element of [:(bool (X)),(X):]
(X,D) . FF is Relation-like (X) Element of bool (X)
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
X is set
S is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
C is set
S . C is set
{S} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (phi)),(bool (phi))))
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is set
S is set
{S} is non empty trivial finite 1 -element countable set
S is set
{S} is non empty trivial finite 1 -element countable set
X is set
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
bool X is non empty set
{phi} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
[{phi},phi] is non empty V26() (C) (1,C,{(C)}, {} ) (C) Element of [:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):]
[:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
{[{phi},phi]} is non empty trivial Relation-like non empty-yielding bool (((AllSymbolsOf C) *) \ {{}}) -defined ((AllSymbolsOf C) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() (C) (C,{(C)}, {} ) (C,{(C)}) Element of bool [:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):]
bool [:(bool (((AllSymbolsOf C) *) \ {{}})),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
S is Element of bool X
FF is V51() V53() eligible Language-like
(FF) is non empty Relation-like set
AllFormulasOf FF is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf FF -prefix FF -prefix Element of bool (((AllSymbolsOf FF) *) \ {{}})
AllSymbolsOf FF is non empty non trivial non finite non empty-membered set
the U1 of FF is set
AllSymbolsOf FF is non empty non trivial non finite non empty-membered set
(AllSymbolsOf FF) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf FF
((AllSymbolsOf FF) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf FF) *)
bool ((AllSymbolsOf FF) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf FF) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf FF) *)
bool (((AllSymbolsOf FF) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf FF) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf FF
((AllSymbolsOf FF) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf FF) *)
bool ((AllSymbolsOf FF) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf FF) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf FF) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf FF) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf FF) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf FF), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf FF) *) \ {{}} : b1 is finite } is set
bool (FF) is non empty Element of bool (bool (FF))
bool (FF) is non empty set
bool (bool (FF)) is non empty set
Funcs ((bool (FF)),(bool (FF))) is non empty functional FUNCTION_DOMAIN of bool (FF), bool (FF)
bool (Funcs ((bool (FF)),(bool (FF)))) is non empty set
D is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
Y is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
D \/ Y is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
phii is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
(D \/ Y) \/ phii is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
psi is (FF) set
phi is set
H is (FF) set
S is set
C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{phi,S} is non empty finite countable set
DD is set
X + C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
psi \/ H is (FF) set
FF is V51() V53() eligible Language-like
(FF) is non empty Relation-like set
AllFormulasOf FF is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf FF -prefix FF -prefix Element of bool (((AllSymbolsOf FF) *) \ {{}})
AllSymbolsOf FF is non empty non trivial non finite non empty-membered set
the U1 of FF is set
AllSymbolsOf FF is non empty non trivial non finite non empty-membered set
(AllSymbolsOf FF) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf FF
((AllSymbolsOf FF) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf FF) *)
bool ((AllSymbolsOf FF) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf FF) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf FF) *)
bool (((AllSymbolsOf FF) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf FF) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf FF
((AllSymbolsOf FF) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf FF) *)
bool ((AllSymbolsOf FF) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf FF) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf FF) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf FF) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf FF) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf FF), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf FF) *) \ {{}} : b1 is finite } is set
bool (FF) is non empty Element of bool (bool (FF))
bool (FF) is non empty set
bool (bool (FF)) is non empty set
Funcs ((bool (FF)),(bool (FF))) is non empty functional FUNCTION_DOMAIN of bool (FF), bool (FF)
bool (Funcs ((bool (FF)),(bool (FF)))) is non empty set
D is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
Y is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
D \/ Y is functional Element of bool (Funcs ((bool (FF)),(bool (FF))))
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
S is set
phi is set
C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{phi} is non empty trivial finite 1 -element countable set
DD is set
X + C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
S is V51() V53() eligible Language-like
(S) is non empty Relation-like set
AllFormulasOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
the U1 of S is set
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf S) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf S), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}} : b1 is finite } is set
bool (S) is non empty Element of bool (bool (S))
bool (S) is non empty set
bool (bool (S)) is non empty set
Funcs ((bool (S)),(bool (S))) is non empty functional FUNCTION_DOMAIN of bool (S), bool (S)
bool (Funcs ((bool (S)),(bool (S)))) is non empty set
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
DD is functional Element of bool (Funcs ((bool (S)),(bool (S))))
phi is set
C is set
{C} is non empty trivial finite 1 -element countable set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
S is Relation-like (X) Element of bool (X)
DD is Relation-like (X) Element of bool (X)
Y is set
(X) . S is Relation-like (X) Element of bool (X)
phii is (X) (X) Element of (X)
[S,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
phii `1 is set
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phii `2 is set
psi is set
H is set
psi `1 is set
H `1 is set
psi `2 is set
m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ m) ^ m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth m),(Depth m)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
Depth m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth m),(Depth m)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
H `2 is set
seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ seqt) ^ seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth seqt),(Depth seqt)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
Depth seqt is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth seqt),(Depth seqt)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(<*(TheNorSymbOf X)*> ^ m) ^ seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth m),(Depth seqt)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth m),(Depth seqt)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[DD,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . DD is Relation-like (X) Element of bool (X)
S is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
S is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
DD is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
C is set
X is set
S is V51() V53() eligible Language-like
(S) is non empty Relation-like set
AllFormulasOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
the U1 of S is set
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf S) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf S), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}} : b1 is finite } is set
bool (S) is non empty Element of bool (bool (S))
bool (S) is non empty set
bool (bool (S)) is non empty set
Funcs ((bool (S)),(bool (S))) is non empty functional FUNCTION_DOMAIN of bool (S), bool (S)
bool (Funcs ((bool (S)),(bool (S)))) is non empty set
X is set
C is set
DD is functional Element of bool (Funcs ((bool (S)),(bool (S))))
phi is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
S is Relation-like (X) Element of bool (X)
DD is Relation-like (X) Element of bool (X)
Y is set
(X) . S is Relation-like (X) Element of bool (X)
phii is (X) (X) Element of (X)
[S,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phii `1 is set
phii `2 is set
psi is set
H is set
psi `1 is set
H `1 is set
psi `2 is set
seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
H `2 is set
<*(TheNorSymbOf X)*> ^ seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ seqt) ^ HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth seqt),(Depth HH)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
Depth seqt is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth HH is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth seqt),(Depth HH)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{m} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{m} \/ (phii `1) is non empty set
<*(TheNorSymbOf X)*> ^ m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ m) ^ m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth m),(Depth m)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
Depth m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth m),(Depth m)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[DD,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . DD is Relation-like (X) Element of bool (X)
S is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
S is Relation-like (X) Element of bool (X)
DD is Relation-like (X) Element of bool (X)
Y is set
(X) . S is Relation-like (X) Element of bool (X)
phii is (X) (X) Element of (X)
[S,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
phii `1 is set
phii `2 is set
psi is set
psi `1 is set
psi `2 is set
[DD,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . DD is Relation-like (X) Element of bool (X)
S is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is set
{X} is non empty trivial finite 1 -element countable set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S is (C) set
FF is Relation-like (C) Element of bool (C)
D is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is set
(X,C) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{ ((X,C,b1) . phi) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
D is set
(X,C) [*] is Relation-like bool (X) -defined bool (X) -valued reflexive transitive Element of bool [:(bool (X)),(bool (X)):]
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
{phi} is non empty trivial finite 1 -element countable set
((X,C) [*]) .: {phi} is Element of bool (bool (X))
bool (bool (X)) is non empty set
union (((X,C) [*]) .: {phi}) is Relation-like (X) Element of bool (X)
union { ((X,C,b1) . phi) where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : verum } is set
Y is set
phii is set
psi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(X,C,psi) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
iter ((X,C),psi) is Relation-like Function-like set
(X,C,psi) . phi is (X) set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is set
S is set
{} /\ X is Relation-like functional finite countable (X) set
{} typed/\ X is empty trivial non proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {}
{} /\typed X is Element of bool X
bool X is non empty set
Y is set
Y `1 is set
Y `2 is set
{Y} is non empty trivial finite 1 -element countable set
phii is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X)
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[phii,psi] is non empty V26() Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
D is Relation-like (X) Element of bool (X)
H is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
m is set
[m,S] is non empty V26() set
seqt is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
Y is set
phii is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[Y,S] is non empty V26() set
Y is set
phii is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[Y,S] is non empty V26() set
psi is non empty V26() set
psi `1 is set
psi `2 is set
{psi} is non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable set
psi is non empty V26() set
psi `1 is set
psi `2 is set
{psi} is non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable set
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is set
phi is set
S is V51() V53() eligible Language-like
(S) is non empty Relation-like set
AllFormulasOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
the U1 of S is set
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf S) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf S), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}} : b1 is finite } is set
bool (S) is non empty Element of bool (bool (S))
bool (S) is non empty set
bool (bool (S)) is non empty set
Funcs ((bool (S)),(bool (S))) is non empty functional FUNCTION_DOMAIN of bool (S), bool (S)
bool (Funcs ((bool (S)),(bool (S)))) is non empty set
DD is functional Element of bool (Funcs ((bool (S)),(bool (S))))
FF is functional Element of bool (Funcs ((bool (S)),(bool (S))))
(S,DD,X) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
(S,DD) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
iter ((S,DD),X) is Relation-like Function-like set
(S,FF,X) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
(S,FF) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
iter ((S,FF),X) is Relation-like Function-like set
(S,DD,X) . phi is (S) set
(S,FF,X) . phi is (S) set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
S is Relation-like (X) Element of bool (X)
DD is Relation-like (X) Element of bool (X)
Y is set
(X) . S is Relation-like (X) Element of bool (X)
phii is (X) (X) Element of (X)
[S,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
phii `1 is set
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phii `2 is set
psi is set
psi `1 is set
psi `2 is set
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ H) ^ m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth H),(Depth m)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
Depth H is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth H),(Depth m)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
<*(TheNorSymbOf X)*> ^ m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ m) ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth m),(Depth H)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth m),(Depth H)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[DD,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . DD is Relation-like (X) Element of bool (X)
S is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
S is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
C is set
X is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional (1,X) ( 0 ,X) Element of bool (Funcs ((bool (X)),(bool (X))))
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
phi is (X,C) set
(X,phi) -freeInterpreter is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, AllTermsOf X -interpreter-like Element of (AllTermsOf X) -InterpretersOf X
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllTermsOf X
(AllTermsOf X) \/ BOOLEAN is non empty set
K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) is non empty functional M30((AllTermsOf X) * ,(AllTermsOf X) \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))
(AllTermsOf X) -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) : b1 is X, AllTermsOf X -interpreter-like } is set
(X,C,phi) is Relation-like AllTermsOf X -defined AllTermsOf X -valued total quasi_total reflexive symmetric transitive Element of bool [:(AllTermsOf X),(AllTermsOf X):]
[:(AllTermsOf X),(AllTermsOf X):] is non empty Relation-like set
bool [:(AllTermsOf X),(AllTermsOf X):] is non empty set
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}} : (<*(TheEqSymbOf X)*> ^ b1) ^ b2 is (X,C,phi) } is set
D is own ofAtomicFormula Element of AllSymbolsOf X
ar D is complex ext-real finite V40() V41() countable Element of INT
the adicity of X . D is set
abs (ar D) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar D)) -tuples_on (AllTermsOf X) is non empty functional V36() FinSequence-membered FinSequenceSet of AllTermsOf X
((X,phi) -freeInterpreter) . D is non empty Relation-like (abs (ar D)) -tuples_on (AllTermsOf X) -defined (AllTermsOf X) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of D, AllTermsOf X
phi -freeInterpreter D is non empty Relation-like (abs (ar D)) -tuples_on (AllTermsOf X) -defined (AllTermsOf X) \/ BOOLEAN -valued Function-like total quasi_total (X,C,phi) -respecting Interpreter of D, AllTermsOf X
D is Relation-like Function-like Function-yielding V156() X, AllTermsOf X -interpreter-like set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional ( 0 ,X) Element of bool (Funcs ((bool (X)),(bool (X))))
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
phi is (X,C) set
(X,C,phi) is Relation-like AllTermsOf X -defined AllTermsOf X -valued total quasi_total reflexive symmetric transitive Element of bool [:(AllTermsOf X),(AllTermsOf X):]
[:(AllTermsOf X),(AllTermsOf X):] is non empty Relation-like set
bool [:(AllTermsOf X),(AllTermsOf X):] is non empty set
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}} : (<*(TheEqSymbOf X)*> ^ b1) ^ b2 is (X,C,phi) } is set
(X,phi) -freeInterpreter is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, AllTermsOf X -interpreter-like Element of (AllTermsOf X) -InterpretersOf X
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllTermsOf X
(AllTermsOf X) \/ BOOLEAN is non empty set
K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) is non empty functional M30((AllTermsOf X) * ,(AllTermsOf X) \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))
(AllTermsOf X) -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) : b1 is X, AllTermsOf X -interpreter-like } is set
((X,phi) -freeInterpreter) quotient (X,C,phi) is Relation-like OwnSymbolsOf X -defined Function-like set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional ( 0 ,X) Element of bool (Funcs ((bool (X)),(bool (X))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
phi is (X,C) set
(X,C,phi) is Relation-like Function-like set
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
(X,C,phi) is Relation-like AllTermsOf X -defined AllTermsOf X -valued total quasi_total reflexive symmetric transitive Element of bool [:(AllTermsOf X),(AllTermsOf X):]
[:(AllTermsOf X),(AllTermsOf X):] is non empty Relation-like set
bool [:(AllTermsOf X),(AllTermsOf X):] is non empty set
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}} : (<*(TheEqSymbOf X)*> ^ b1) ^ b2 is (X,C,phi) } is set
(X,phi) -freeInterpreter is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, AllTermsOf X -interpreter-like Element of (AllTermsOf X) -InterpretersOf X
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllTermsOf X
(AllTermsOf X) \/ BOOLEAN is non empty set
K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) is non empty functional M30((AllTermsOf X) * ,(AllTermsOf X) \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))
(AllTermsOf X) -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) : b1 is X, AllTermsOf X -interpreter-like } is set
((X,phi) -freeInterpreter) quotient (X,C,phi) is Relation-like OwnSymbolsOf X -defined Function-like set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional (1,X) ( 0 ,X) Element of bool (Funcs ((bool (X)),(bool (X))))
phi is (X,C) set
(X,C,phi) is Relation-like OwnSymbolsOf X -defined Function-like set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
(X,C,phi) is Relation-like AllTermsOf X -defined AllTermsOf X -valued total quasi_total reflexive symmetric transitive Element of bool [:(AllTermsOf X),(AllTermsOf X):]
[:(AllTermsOf X),(AllTermsOf X):] is non empty Relation-like set
bool [:(AllTermsOf X),(AllTermsOf X):] is non empty set
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}} : (<*(TheEqSymbOf X)*> ^ b1) ^ b2 is (X,C,phi) } is set
(X,phi) -freeInterpreter is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, AllTermsOf X -interpreter-like (X,C,phi) -respecting Element of (AllTermsOf X) -InterpretersOf X
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllTermsOf X
(AllTermsOf X) \/ BOOLEAN is non empty set
K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) is non empty functional M30((AllTermsOf X) * ,(AllTermsOf X) \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))
(AllTermsOf X) -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) : b1 is X, AllTermsOf X -interpreter-like } is set
((X,phi) -freeInterpreter) quotient (X,C,phi) is Relation-like OwnSymbolsOf X -defined Function-like Function-yielding V156() X, Class (X,C,phi) -interpreter-like set
Class (X,C,phi) is non empty with_non-empty_elements non empty-membered a_partition of AllTermsOf X
S is Relation-like Function-like set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional (1,X) ( 0 ,X) Element of bool (Funcs ((bool (X)),(bool (X))))
phi is (X,C) set
(X,C,phi) is Relation-like OwnSymbolsOf X -defined Function-like Function-yielding V156() X, Class (X,C,phi) -interpreter-like set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
(X,C,phi) is Relation-like AllTermsOf X -defined AllTermsOf X -valued total quasi_total reflexive symmetric transitive Element of bool [:(AllTermsOf X),(AllTermsOf X):]
[:(AllTermsOf X),(AllTermsOf X):] is non empty Relation-like set
bool [:(AllTermsOf X),(AllTermsOf X):] is non empty set
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}} : (<*(TheEqSymbOf X)*> ^ b1) ^ b2 is (X,C,phi) } is set
Class (X,C,phi) is non empty with_non-empty_elements non empty-membered a_partition of AllTermsOf X
(X,phi) -freeInterpreter is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, AllTermsOf X -interpreter-like (X,C,phi) -respecting Element of (AllTermsOf X) -InterpretersOf X
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllTermsOf X
(AllTermsOf X) \/ BOOLEAN is non empty set
K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) is non empty functional M30((AllTermsOf X) * ,(AllTermsOf X) \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))
(AllTermsOf X) -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) : b1 is X, AllTermsOf X -interpreter-like } is set
((X,phi) -freeInterpreter) quotient (X,C,phi) is Relation-like OwnSymbolsOf X -defined Function-like Function-yielding V156() X, Class (X,C,phi) -interpreter-like set
(Class (X,C,phi)) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of Class (X,C,phi)
(Class (X,C,phi)) \/ BOOLEAN is non empty set
K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN)) is non empty functional M30((Class (X,C,phi)) * ,(Class (X,C,phi)) \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN))
(Class (X,C,phi)) -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN))) : b1 is X, Class (X,C,phi) -interpreter-like } is set
((X,phi) -freeInterpreter) quotient (X,C,phi) is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, Class (X,C,phi) -interpreter-like Element of (Class (X,C,phi)) -InterpretersOf X
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ C) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth C),(Depth phi)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
Depth C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth C),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
xnot C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ C) ^ C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth C),(Depth C)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth C),(Depth C)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
xnot phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ phi) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth phi)) -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth phi),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot C),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
[{(xnot C),(xnot phi)},((<*(TheNorSymbOf X)*> ^ C) ^ phi)] is non empty V26() (X) (1,X,{(X)},{[{(xnot C),(xnot phi)},(xnot C)],[{(xnot C),(xnot phi)},(xnot phi)]}) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
[{(xnot C),(xnot phi)},(xnot C)] is non empty V26() (X) (1,X,{(X)}, {} ) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
[{(xnot C),(xnot phi)},(xnot phi)] is non empty V26() (X) (1,X,{(X)}, {} ) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
{[{(xnot C),(xnot phi)},(xnot C)],[{(xnot C),(xnot phi)},(xnot phi)]} is non empty Relation-like non empty-yielding bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued finite with_non-empty_elements non empty-membered countable (X) Element of bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
{} /\ X is Relation-like functional finite countable (X) set
{} typed/\ X is empty trivial non proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {}
{} /\typed X is Element of bool X
bool X is non empty set
1 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
({(X)} \/ {(X)}) \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
m is (X) set
m \/ m is (X) set
{[{(xnot C),(xnot phi)},((<*(TheNorSymbOf X)*> ^ C) ^ phi)]} is non empty trivial Relation-like non empty-yielding bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() (X) Element of bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
seqt is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional ( 0 ,X) Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
C is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{C} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
S is set
X is V51() V53() eligible Language-like
C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
C null X is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined X \/ (proj1 C) -defined {{}} -valued X -valued X \/ (proj2 C) -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element len C -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
proj1 C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
X \/ (proj1 C) is set
proj2 C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
X \/ (proj2 C) is set
len C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of NAT
C \typed/ X is Element of bool (C \/ X)
C \/ X is set
bool (C \/ X) is non empty set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
C /\ (AllFormulasOf X) is Relation-like functional finite V36() FinSequence-membered with_non-empty_elements countable AllFormulasOf X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
C typed/\ (AllFormulasOf X) is empty trivial non proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool C
bool C is non empty finite V36() countable set
C /\ (AllFormulasOf X) is Relation-like functional finite countable AllFormulasOf X -prefix set
C /\typed (AllFormulasOf X) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X)
bool (AllFormulasOf X) is non empty set
S is set
X is set
bool X is non empty set
C is V51() V53() eligible Language-like
{} /\ X is Relation-like functional finite countable set
{} typed/\ X is empty trivial non proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {}
{} /\typed X is Element of bool X
{} null C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined C \/ (proj1 {}) -defined C \/ (proj1 {}) -defined {{}} -valued C -valued {{}} -valued C \/ (proj2 {}) -valued C \/ (proj2 {}) -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element len {} -element len {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() C -correct (C) set
C \/ (proj1 {}) is set
C \/ (proj2 {}) is set
{} \typed/ C is Element of bool ({} \/ C)
{} \/ C is set
bool ({} \/ C) is non empty set
phi is Element of bool X
X is V51() V53() eligible Language-like
bool X is non empty set
the finite countable (X) Element of bool X is finite countable (X) Element of bool X
X is V51() V53() eligible Language-like
C is finite countable (X) set
bool C is non empty finite V36() countable set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
DD is finite countable Element of bool C
S is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
bool S is non empty finite V36() countable set
X is V51() V53() eligible Language-like
C is finite countable (X) set
phi is finite countable (X) set
phi null C is set
phi \typed/ C is finite countable Element of bool (phi \/ C)
phi \/ C is finite countable set
bool (phi \/ C) is non empty finite V36() countable set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
X is V51() V53() eligible Language-like
phi is set
C is finite countable (X) set
C null phi is set
C \typed/ phi is Element of bool (C \/ phi)
C \/ phi is set
bool (C \/ phi) is non empty set
X is V51() V53() eligible Language-like
C is finite countable (X) set
phi is finite countable (X) set
C \/ phi is finite countable set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
(X,C,C) is functional finite V36() FinSequence-membered with_non-empty_elements countable (X) Element of bool (AllFormulasOf X)
bool (AllFormulasOf X) is non empty set
C \typed/ C is finite countable Element of bool (C \/ C)
C \/ C is finite countable set
bool (C \/ C) is non empty finite V36() countable set
C null C is finite countable (X) set
(X,phi,phi) is functional finite V36() FinSequence-membered with_non-empty_elements countable (X) Element of bool (AllFormulasOf X)
phi \typed/ phi is finite countable Element of bool (phi \/ phi)
phi \/ phi is finite countable set
bool (phi \/ phi) is non empty finite V36() countable set
phi null phi is finite countable (X) set
(X,C,C) \/ (X,phi,phi) is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
DD is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
C is finite countable (X) set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[C,phi] is non empty V26() set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
DD is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
[DD,phi] is non empty V26() (X) (X) Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
C is finite countable (X) set
phi is finite countable (X) set
C \/ phi is finite countable (X) set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[(C \/ phi),S] is non empty V26() (X) (X) set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
[C,S] is non empty V26() (X) (X) set
{[C,S]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
(X,phi,C) is functional finite V36() FinSequence-membered with_non-empty_elements countable (X) Element of bool (AllFormulasOf X)
C \typed/ phi is finite countable (X) Element of bool (C \/ phi)
bool (C \/ phi) is non empty finite V36() countable set
C null phi is finite countable (X) set
{[C,S]} \ {[C,S]} is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {[C,S]}
bool {[C,S]} is non empty finite V36() countable set
{[C,S]} typed\ {[C,S]} is trivial Relation-like Function-like constant finite with_non-empty_elements countable V209() Element of bool {[C,S]}
[C,S] `1 is set
([C,S] `1) \+\ C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[(C \/ phi),S] `1 is set
([(C \/ phi),S] `1) \+\ (C \/ phi) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[(C \/ phi),S] `2 is set
([(C \/ phi),S] `2) \+\ S is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[C,S] `2 is set
([C,S] `2) \+\ S is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
H is Relation-like (X) Element of bool (X)
psi is (X) (X) Element of (X)
[H,psi] is non empty V26() Element of [:(bool (X)),(X):]
(X) . {[C,S]} is set
m is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
S ^ DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
C is finite countable (X) set
C null (S ^ DD) is finite countable (X) set
C \typed/ (S ^ DD) is finite countable Element of bool (C \/ (S ^ DD))
C \/ (S ^ DD) is non empty finite countable set
bool (C \/ (S ^ DD)) is non empty finite V36() countable set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
xnot phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf X)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ phi) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth phi)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot phi),(xnot phi)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth phi),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(xnot phi),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
[(C null (S ^ DD)),(xnot phi)] is non empty V26() (X) (X) set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{phi} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
C \/ {phi} is non empty finite countable (X) set
[(C \/ {phi}),S] is non empty V26() (X) (1,X,{(X)},{[C,S]}) (X) set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
[C,S] is non empty V26() (X) (X) set
{[C,S]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
<*(TheNorSymbOf X)*> ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ S) ^ DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth S),(Depth DD)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot S),(xnot DD)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth S is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth DD is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth S),(Depth DD)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
xnot S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ S) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth S),(Depth S)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot S),(xnot S)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth S),(Depth S)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot S),(xnot S)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
xnot DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ DD) ^ DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth DD),(Depth DD)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot DD),(xnot DD)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth DD),(Depth DD)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot DD),(xnot DD)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
{(xnot S),(xnot DD)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)] is non empty V26() (X) (1,X,{(X)},{[C,((<*(TheNorSymbOf X)*> ^ S) ^ DD)]}) (X) set
[C,((<*(TheNorSymbOf X)*> ^ S) ^ DD)] is non empty V26() (X) (X) set
{[C,((<*(TheNorSymbOf X)*> ^ S) ^ DD)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
{[(C \/ {phi}),S],[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)]} is non empty Relation-like finite with_non-empty_elements non empty-membered countable (X) set
[C,(xnot phi)] is non empty V26() (X) (X) set
{[(C \/ {phi}),S]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
{[(C \/ {phi}),S]} \ {[(C \/ {phi}),S],[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)]} is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {[(C \/ {phi}),S]}
bool {[(C \/ {phi}),S]} is non empty finite V36() countable set
{[(C \/ {phi}),S]} typed\ {[(C \/ {phi}),S],[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)]} is trivial Relation-like Function-like constant finite with_non-empty_elements countable V209() Element of bool {[(C \/ {phi}),S]}
{[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
{[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)]} \ {[(C \/ {phi}),S],[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)]} is trivial Relation-like Function-like constant finite with_non-empty_elements countable V209() Element of bool {[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)]}
bool {[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)]} is non empty finite V36() countable set
{[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)]} typed\ {[(C \/ {phi}),S],[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)]} is trivial Relation-like Function-like constant finite with_non-empty_elements countable V209() Element of bool {[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)]}
[(C \/ {phi}),S] `1 is set
([(C \/ {phi}),S] `1) \+\ (C \/ {phi}) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)] `1 is set
([(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)] `1) \+\ (C \/ {phi}) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[(C \/ {phi}),S] `2 is set
([(C \/ {phi}),S] `2) \+\ S is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)] `2 is set
([(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)] `2) \+\ ((<*(TheNorSymbOf X)*> ^ S) ^ DD) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[C,(xnot phi)] `1 is set
([C,(xnot phi)] `1) \+\ C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[C,(xnot phi)] `2 is set
([C,(xnot phi)] `2) \+\ (xnot phi) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
HC is Relation-like (X) Element of bool (X)
HH is (X) (X) Element of (X)
[HC,HH] is non empty V26() Element of [:(bool (X)),(X):]
(X) . {[(C \/ {phi}),S],[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ S) ^ DD)]} is set
a is set
X is V51() V53() eligible Language-like
{} null X is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined X \/ (proj1 {}) -defined X \/ (proj1 {}) -defined {{}} -valued X -valued {{}} -valued X \/ (proj2 {}) -valued X \/ (proj2 {}) -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element len {} -element len {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() X -correct (X) set
X \/ (proj1 {}) is set
X \/ (proj2 {}) is set
{} \typed/ X is Element of bool ({} \/ X)
{} \/ X is set
bool ({} \/ X) is non empty set
{} /\ X is Relation-like functional finite countable (X) set
{} typed/\ X is empty trivial non proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {}
{} /\typed X is Element of bool X
bool X is non empty set
C is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
C is finite countable (X) set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{phi} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
C \/ {phi} is non empty finite countable (X) set
[(C \/ {phi}),phi] is non empty V26() (X) (1,X,{(X)},{[C,phi]}) (X) set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
[C,phi] is non empty V26() (X) (X) set
{[C,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{} null X is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined X \/ (proj1 {}) -defined X \/ (proj1 {}) -defined {{}} -valued X -valued {{}} -valued X \/ (proj2 {}) -valued X \/ (proj2 {}) -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element len {} -element len {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() X -correct (X) (X) set
X \/ (proj1 {}) is set
X \/ (proj2 {}) is set
{} \typed/ X is Element of bool ({} \/ X)
{} \/ X is set
bool ({} \/ X) is non empty set
[(C \/ {phi}),phi] `2 is set
([(C \/ {phi}),phi] `2) \+\ phi is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[(C \/ {phi}),phi] `1 is set
([(C \/ {phi}),phi] `1) \+\ (C \/ {phi}) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(X,C,{phi}) is functional finite V36() FinSequence-membered with_non-empty_elements countable (X) Element of bool (AllFormulasOf X)
{phi} \typed/ C is finite countable (X) Element of bool ({phi} \/ C)
{phi} \/ C is non empty finite countable (X) set
bool ({phi} \/ C) is non empty finite V36() countable set
{phi} null C is finite countable (X) set
(X,C,{phi}) \ (C \/ {phi}) is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf X)
(X,C,{phi}) typed\ (C \/ {phi}) is functional finite V36() FinSequence-membered with_non-empty_elements countable (X) Element of bool (X,C,{phi})
bool (X,C,{phi}) is non empty finite V36() countable set
(X,C,{phi}) \ (C \/ {phi}) is functional finite V36() FinSequence-membered with_non-empty_elements countable (X) Element of bool (X,C,{phi})
phii is Relation-like (X) Element of bool (X)
Y is (X) (X) Element of (X)
[phii,Y] is non empty V26() Element of [:(bool (X)),(X):]
(X) . ({} null X) is set
psi is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
C is finite countable (X) set
C null S is finite countable (X) set
C \typed/ S is finite countable Element of bool (C \/ S)
C \/ S is non empty finite countable set
bool (C \/ S) is non empty finite V36() countable set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
xnot phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf X)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ phi) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth phi)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot phi),(xnot phi)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth phi),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(xnot phi),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
[(C null S),(xnot phi)] is non empty V26() (X) (X) set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
({(X)} \/ {(X)}) \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
(<*(TheNorSymbOf X)*> ^ phi) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth S)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot phi),(xnot S)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth S is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth phi),(Depth S)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
xnot S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ S) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth S),(Depth S)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot S),(xnot S)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth S),(Depth S)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot S),(xnot S)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
{(xnot phi),(xnot S)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)] is non empty V26() (X) (X) set
{[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
{phi} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
C \/ {phi} is non empty finite countable (X) set
[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ phi) ^ S)] is non empty V26() (X) (1,X,{(X)},{[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]}) (X) set
[(C \/ {phi}),phi] is non empty V26() (X) (1,X,{(X)}, {} ) (1,X,{(X)},{[C,phi]}) (X) set
[C,phi] is non empty V26() (X) (X) set
{[C,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
{} null X is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined X \/ (proj1 {}) -defined X \/ (proj1 {}) -defined {{}} -valued X -valued {{}} -valued X \/ (proj2 {}) -valued X \/ (proj2 {}) -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element len {} -element len {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() X -correct (X) (X) set
X \/ (proj1 {}) is set
X \/ (proj2 {}) is set
{} \typed/ X is Element of bool ({} \/ X)
{} \/ X is set
bool ({} \/ X) is non empty set
phi ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
C null (phi ^ S) is finite countable (X) set
C \typed/ (phi ^ S) is finite countable Element of bool (C \/ (phi ^ S))
C \/ (phi ^ S) is non empty finite countable set
bool (C \/ (phi ^ S)) is non empty finite V36() countable set
[(C null (phi ^ S)),(xnot phi)] is non empty V26() (X) (1,X,{(X)},{[(C \/ {phi}),phi],[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ phi) ^ S)]}) (X) set
{[(C \/ {phi}),phi],[(C \/ {phi}),((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} is non empty Relation-like finite with_non-empty_elements non empty-membered countable (X) set
1 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
({} null X) \/ {[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} is non empty Relation-like finite countable (X) set
seqt is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
C is finite countable (X) set
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ S) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth S),(Depth phi)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot S),(xnot phi)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth S is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth S),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
xnot S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ S) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth S),(Depth S)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot S),(xnot S)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth S),(Depth S)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot S),(xnot S)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
xnot phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ phi) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth phi)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot phi),(xnot phi)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth phi),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot phi),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
{(xnot S),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)] is non empty V26() (X) (X) set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
(<*(TheNorSymbOf X)*> ^ phi) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth S)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot phi),(xnot S)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth phi),(Depth S)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot phi),(xnot S)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)] is non empty V26() (X) (X) set
{[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
{[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} \ {[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]}
bool {[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} is non empty finite V36() countable set
{[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} typed\ {[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} is trivial Relation-like Function-like constant finite with_non-empty_elements countable V209() Element of bool {[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]}
[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)] `1 is set
([C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)] `1) \+\ C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)] `1 is set
([C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)] `1) \+\ C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)] `2 is set
([C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)] `2) \+\ ((<*(TheNorSymbOf X)*> ^ phi) ^ S) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)] `2 is set
([C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)] `2) \+\ ((<*(TheNorSymbOf X)*> ^ S) ^ phi) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
seqt is Relation-like (X) Element of bool (X)
m is (X) (X) Element of (X)
[seqt,m] is non empty V26() Element of [:(bool (X)),(X):]
(X) . {[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} is set
HH is set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
C is finite countable (X) set
C null phi is finite countable (X) set
C \typed/ phi is finite countable Element of bool (C \/ phi)
C \/ phi is non empty finite countable set
bool (C \/ phi) is non empty finite V36() countable set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
xnot S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf X)*> ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ S) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth S),(Depth S)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot S),(xnot S)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth S is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth S),(Depth S)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(xnot S),(xnot S)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
[(C null phi),(xnot S)] is non empty V26() (X) (2,X,({(X)} \/ {(X)}) \/ {(X)},{[C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)]}) (X) set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
({(X)} \/ {(X)}) \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
(<*(TheNorSymbOf X)*> ^ S) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth S),(Depth phi)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot S),(xnot phi)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth S),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
xnot phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ phi) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth phi)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot phi),(xnot phi)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth phi),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot phi),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
{(xnot S),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)] is non empty V26() (X) (1,X,{(X)},{[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]}) (X) set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
(<*(TheNorSymbOf X)*> ^ phi) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth S)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot phi),(xnot S)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth phi),(Depth S)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot phi),(xnot S)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)] is non empty V26() (X) (1,X,{(X)},{[C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)]}) (X) set
{[C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
{[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
(({(X)} \/ {(X)}) \/ {(X)}) \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
({(X)} \/ {(X)}) \/ (({(X)} \/ {(X)}) \/ {(X)}) is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{[C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)],[C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)]} is non empty Relation-like finite with_non-empty_elements non empty-membered countable (X) set
{[C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)]} \/ {[C,((<*(TheNorSymbOf X)*> ^ S) ^ phi)]} is non empty Relation-like finite with_non-empty_elements non empty-membered countable (X) set
1 + 2 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
{[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} \/ {[C,((<*(TheNorSymbOf X)*> ^ phi) ^ S)]} is non empty Relation-like finite with_non-empty_elements non empty-membered countable (X) set
HH is set
X is V51() V53() eligible Language-like
C is (X) (X) set
C `1 is set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
(X) is non empty Relation-like set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
DD is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X)
FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[DD,FF] is non empty V26() Element of [:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (AllFormulasOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
D is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is set
phi is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi null C is set
phi \typed/ C is Element of bool (phi \/ C)
phi \/ C is set
bool (phi \/ C) is non empty set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
DD is finite countable (X) set
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{C} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
DD \/ {C} is non empty finite countable (X) set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{phi} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
(DD \/ {C}) \/ {phi} is non empty finite countable (X) set
FF is literal non operational non relational termal own ofAtomicFormula non (DD \/ {C}) \/ {phi} -occurring Element of AllSymbolsOf X
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
<*S*> is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,S] is non empty V26() set
{[1,S]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*S*> ^ C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff 1 + (Depth C) -wff non Depth C -wff wff exal Element of ((AllSymbolsOf X) *) \ {{}}
Depth C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
1 + (Depth C) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
{(<*S*> ^ C)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
DD \/ {(<*S*> ^ C)} is non empty finite countable (X) set
(DD \/ {(<*S*> ^ C)}) null FF is finite countable (X) set
(DD \/ {(<*S*> ^ C)}) \typed/ FF is Element of bool ((DD \/ {(<*S*> ^ C)}) \/ FF)
(DD \/ {(<*S*> ^ C)}) \/ FF is non empty set
bool ((DD \/ {(<*S*> ^ C)}) \/ FF) is non empty set
[((DD \/ {(<*S*> ^ C)}) null FF),phi] is non empty V26() (X) (X) set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(S,FF) -SymbolSubstIn C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
C +~ (S,FF) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((S,FF) -SymbolSubstIn C)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
DD \/ {((S,FF) -SymbolSubstIn C)} is non empty finite countable (X) set
[(DD \/ {((S,FF) -SymbolSubstIn C)}),phi] is non empty V26() (X) (1,X,{(X)},{[DD,phi]}) (X) set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
[DD,phi] is non empty V26() (X) (X) set
{[DD,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
{[(DD \/ {((S,FF) -SymbolSubstIn C)}),phi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{D} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
DD \/ {D} is non empty finite countable (X) set
[(DD \/ {D}),phi] is non empty V26() (X) (1,X,{(X)},{[DD,phi]}) (X) set
[(DD \/ {(<*S*> ^ C)}),phi] is non empty V26() (X) (1,X,{(X)},{[DD,phi]}) (X) set
{[(DD \/ {D}),phi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
S SubstWith FF is non empty Relation-like (AllSymbolsOf X) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
sub2 is (X) (X) Element of (X)
sub2 `1 is finite countable (X) set
(sub2 `1) \+\ (DD \/ {(<*S*> ^ C)}) is finite countable set
sub2 `2 is set
(sub2 `2) \+\ phi is set
sub1 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(S SubstWith FF) . sub1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((S SubstWith FF) . sub1)} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
DD \/ {((S SubstWith FF) . sub1)} is non empty finite countable set
[(DD \/ {((S SubstWith FF) . sub1)}),(sub2 `2)] is non empty V26() set
inf is Relation-like (X) Element of bool (X)
[inf,sub2] is non empty V26() Element of [:(bool (X)),(X):]
(X) . inf is Relation-like (X) Element of bool (X)
U is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
X is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
phi is finite countable (C) set
S is finite countable (C) set
phi \/ S is finite countable (C) set
(phi \/ S) null X is finite countable (C) set
(phi \/ S) \typed/ X is finite countable Element of bool ((phi \/ S) \/ X)
(phi \/ S) \/ X is non empty finite countable set
bool ((phi \/ S) \/ X) is non empty finite V36() countable set
DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
[((phi \/ S) null X),DD] is non empty V26() (C) (C) set
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
[phi,DD] is non empty V26() (C) (C) set
{[phi,DD]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[(phi \/ S),DD] is non empty V26() (C) (1,C,{(C)},{[phi,DD]}) (C) set
phii is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
phii + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
{[(phi \/ S),DD]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
(phi \/ S) \/ (phi \/ S) is finite countable (C) set
[((phi \/ S) \/ (phi \/ S)),DD] is non empty V26() (C) (1,C,{(C)},{[(phi \/ S),DD]}) (C) set
0 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
psi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
psi + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(psi + 1) + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
psi is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
X is set
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
xnot phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ phi) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth phi)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot phi),(xnot phi)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth phi),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot phi),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheNorSymbOf C)*> ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ FF) ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth FF),(Depth D)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot FF),(xnot D)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth FF is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth D is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth FF),(Depth D)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
xnot FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ FF) ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth FF),(Depth FF)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot FF),(xnot FF)}) Element of ((AllSymbolsOf C) *) \ {{}}
max ((Depth FF),(Depth FF)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot FF),(xnot FF)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
xnot D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheNorSymbOf C)*> ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ D) ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth D),(Depth D)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot D),(xnot D)}) Element of ((AllSymbolsOf C) *) \ {{}}
max ((Depth D),(Depth D)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot D),(xnot D)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
{(xnot FF),(xnot D)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
phii is set
psi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[phii,FF] is non empty V26() set
Y is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
H is set
m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[H,Y] is non empty V26() set
bool X is non empty set
HC is (C) (C) set
HC `1 is finite countable (C) set
a is (C) (C) set
a `1 is finite countable (C) set
D2 is finite countable (C) set
sub1 is finite countable (C) set
D2 \/ sub1 is finite countable (C) set
{phi} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
(D2 \/ sub1) \/ {phi} is non empty finite countable (C) set
inf is non empty functional (C) Element of bool (Funcs ((bool (C)),(bool (C))))
U is Relation-like Function-like Element of inf
{U} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool inf
bool inf is non empty set
inf \/ {U} is non empty functional set
inf null {U} is set
inf \typed/ {U} is functional Element of bool (inf \/ {U})
bool (inf \/ {U}) is non empty set
(C,U,inf) is functional Element of bool (Funcs ((bool (C)),(bool (C))))
inf \typed/ U is Element of bool (inf \/ U)
inf \/ U is non empty set
bool (inf \/ U) is non empty set
inf null U is set
II1 is Relation-like Function-like Element of inf
{II1} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool inf
inf \/ {II1} is non empty functional set
inf null {II1} is set
inf \typed/ {II1} is functional Element of bool (inf \/ {II1})
bool (inf \/ {II1}) is non empty set
(C,II1,inf) is functional Element of bool (Funcs ((bool (C)),(bool (C))))
inf \typed/ II1 is Element of bool (inf \/ II1)
inf \/ II1 is non empty set
bool (inf \/ II1) is non empty set
inf null II1 is set
S \/ S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(S \/ S) \/ {(C)} is non empty functional Element of bool (Funcs ((bool (C)),(bool (C))))
seqt is Element of bool X
HH is Element of bool X
seqt \/ HH is Element of bool X
m + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
sub2 is finite countable (C) set
[sub2,FF] is non empty V26() (C) (C) set
{[sub2,FF]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
sub2 \/ sub2 is finite countable (C) set
(sub2 \/ sub2) null (m + 1) is finite countable (C) set
(sub2 \/ sub2) \typed/ (m + 1) is finite countable Element of bool ((sub2 \/ sub2) \/ (m + 1))
(sub2 \/ sub2) \/ (m + 1) is non empty finite countable set
bool ((sub2 \/ sub2) \/ (m + 1)) is non empty finite V36() countable set
[((sub2 \/ sub2) null (m + 1)),FF] is non empty V26() (C) (m + 1,C,{(C)},{[sub2,FF]}) (C) set
psi + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
[sub2,Y] is non empty V26() (C) (C) set
{[sub2,Y]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
(sub2 \/ sub2) null (psi + 1) is finite countable (C) set
(sub2 \/ sub2) \typed/ (psi + 1) is finite countable Element of bool ((sub2 \/ sub2) \/ (psi + 1))
(sub2 \/ sub2) \/ (psi + 1) is non empty finite countable set
bool ((sub2 \/ sub2) \/ (psi + 1)) is non empty finite V36() countable set
[((sub2 \/ sub2) null (psi + 1)),Y] is non empty V26() (C) (psi + 1,C,{(C)},{[sub2,Y]}) (C) set
S \/ {(C)} is non empty functional Element of bool (Funcs ((bool (C)),(bool (C))))
sub1 \/ {phi} is non empty finite countable (C) set
D2 \/ (sub1 \/ {phi}) is non empty finite countable (C) set
[(D2 \/ (sub1 \/ {phi})),FF] is non empty V26() (C) (1,C,{(C)},{[D2,FF]}) (C) set
[D2,FF] is non empty V26() (C) (C) set
{[D2,FF]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
(psi + 1) + (m + 1) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
D2 \/ {phi} is non empty finite countable (C) set
sub1 \/ (D2 \/ {phi}) is non empty finite countable (C) set
[(sub1 \/ (D2 \/ {phi})),Y] is non empty V26() (C) (1,C,{(C)},{[sub1,Y]}) (C) set
[sub1,Y] is non empty V26() (C) (C) set
{[sub1,Y]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
(m + 1) + (psi + 1) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
{[sub2,FF],[sub2,Y]} is non empty Relation-like finite with_non-empty_elements non empty-membered countable (C) set
FF ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
sub1 \/ D2 is finite countable (C) set
(sub1 \/ D2) null (FF ^ D) is finite countable (C) set
(sub1 \/ D2) \typed/ (FF ^ D) is finite countable Element of bool ((sub1 \/ D2) \/ (FF ^ D))
(sub1 \/ D2) \/ (FF ^ D) is non empty finite countable set
bool ((sub1 \/ D2) \/ (FF ^ D)) is non empty finite V36() countable set
[((sub1 \/ D2) null (FF ^ D)),(xnot phi)] is non empty V26() (C) (1,C,{(C)},{[((sub1 \/ D2) \/ {phi}),FF],[((sub1 \/ D2) \/ {phi}),((<*(TheNorSymbOf C)*> ^ FF) ^ D)]}) (C) set
(sub1 \/ D2) \/ {phi} is non empty finite countable (C) set
[((sub1 \/ D2) \/ {phi}),FF] is non empty V26() (C) (1,C,{(C)},{[(sub1 \/ D2),FF]}) (C) set
[(sub1 \/ D2),FF] is non empty V26() (C) (1,C,{(C)},{[sub1,FF]}) (C) set
[sub1,FF] is non empty V26() (C) (C) set
{[sub1,FF]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[(sub1 \/ D2),FF]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[((sub1 \/ D2) \/ {phi}),((<*(TheNorSymbOf C)*> ^ FF) ^ D)] is non empty V26() (C) (1,C,{(C)},{[(sub1 \/ D2),((<*(TheNorSymbOf C)*> ^ FF) ^ D)]}) (1,C,{(C)},{[((sub1 \/ D2) \/ {phi}),((<*(TheNorSymbOf C)*> ^ D) ^ FF)]}) (C) set
[(sub1 \/ D2),((<*(TheNorSymbOf C)*> ^ FF) ^ D)] is non empty V26() (C) (1,C,{(C)},{[sub1,((<*(TheNorSymbOf C)*> ^ FF) ^ D)]}) (1,C,{(C)},{[(sub1 \/ D2),((<*(TheNorSymbOf C)*> ^ D) ^ FF)]}) (C) set
[sub1,((<*(TheNorSymbOf C)*> ^ FF) ^ D)] is non empty V26() (C) (1,C,{(C)},{[sub1,((<*(TheNorSymbOf C)*> ^ D) ^ FF)]}) (C) set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(<*(TheNorSymbOf C)*> ^ D) ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth D),(Depth FF)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot D),(xnot FF)}) Element of ((AllSymbolsOf C) *) \ {{}}
max ((Depth D),(Depth FF)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot D),(xnot FF)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
[sub1,((<*(TheNorSymbOf C)*> ^ D) ^ FF)] is non empty V26() (C) (1,C,{(C)},{[sub1,((<*(TheNorSymbOf C)*> ^ FF) ^ D)]}) (C) set
{[sub1,((<*(TheNorSymbOf C)*> ^ FF) ^ D)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[sub1,((<*(TheNorSymbOf C)*> ^ D) ^ FF)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[(sub1 \/ D2),((<*(TheNorSymbOf C)*> ^ D) ^ FF)] is non empty V26() (C) (1,C,{(C)},{[sub1,((<*(TheNorSymbOf C)*> ^ D) ^ FF)]}) (1,C,{(C)},{[(sub1 \/ D2),((<*(TheNorSymbOf C)*> ^ FF) ^ D)]}) (C) set
{[(sub1 \/ D2),((<*(TheNorSymbOf C)*> ^ FF) ^ D)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[(sub1 \/ D2),((<*(TheNorSymbOf C)*> ^ D) ^ FF)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[((sub1 \/ D2) \/ {phi}),((<*(TheNorSymbOf C)*> ^ D) ^ FF)] is non empty V26() (C) (1,C,{(C)},{[(sub1 \/ D2),((<*(TheNorSymbOf C)*> ^ D) ^ FF)]}) (1,C,{(C)},{[((sub1 \/ D2) \/ {phi}),((<*(TheNorSymbOf C)*> ^ FF) ^ D)]}) (C) set
{[((sub1 \/ D2) \/ {phi}),((<*(TheNorSymbOf C)*> ^ FF) ^ D)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[((sub1 \/ D2) \/ {phi}),((<*(TheNorSymbOf C)*> ^ D) ^ FF)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[((sub1 \/ D2) \/ {phi}),FF],[((sub1 \/ D2) \/ {phi}),((<*(TheNorSymbOf C)*> ^ FF) ^ D)]} is non empty Relation-like finite with_non-empty_elements non empty-membered countable (C) set
psi + m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(psi + m) + 2 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
((psi + m) + 2) + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
{} null C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined C \/ (proj1 {}) -defined C \/ (proj1 {}) -defined {{}} -valued C -valued {{}} -valued C \/ (proj2 {}) -valued C \/ (proj2 {}) -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element len {} -element len {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() C -correct (C) (C) set
C \/ (proj1 {}) is set
C \/ (proj2 {}) is set
{} \typed/ C is Element of bool ({} \/ C)
{} \/ C is set
bool ({} \/ C) is non empty set
({} null C) \/ ({} null C) is Relation-like empty-yielding NAT -defined {{}} -valued functional finite V36() countable (C) (C) set
[(sub1 \/ D2),(xnot phi)] is non empty V26() (C) (1,C,{(C)},{[sub1,(xnot phi)]}) (C) set
[sub1,(xnot phi)] is non empty V26() (C) (C) set
{[sub1,(xnot phi)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
S is Relation-like (X) Element of bool (X)
DD is Relation-like (X) Element of bool (X)
Y is set
(X) . S is Relation-like (X) Element of bool (X)
phii is (X) (X) Element of (X)
[S,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
phii `1 is finite countable (X) set
phii `2 is set
{(phii `2)} is non empty trivial finite 1 -element countable set
m is set
psi is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
<*psi*> is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,psi] is non empty V26() set
{[1,psi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
seqt is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
<*psi*> ^ seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{(<*psi*> ^ seqt)} is non empty trivial functional finite V36() 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
m \/ {(<*psi*> ^ seqt)} is non empty set
{seqt} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
m \/ {seqt} is non empty set
(m \/ {seqt}) \/ {(phii `2)} is non empty set
H is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
psi SubstWith H is non empty Relation-like (AllSymbolsOf X) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(psi SubstWith H) . seqt is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((psi SubstWith H) . seqt)} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
m \/ {((psi SubstWith H) . seqt)} is non empty set
[(m \/ {((psi SubstWith H) . seqt)}),(phii `2)] is non empty V26() set
[DD,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . DD is Relation-like (X) Element of bool (X)
S is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
C is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
phi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(C,phi) SubstIn S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
Funcs ((AllFormulasOf X),(AllFormulasOf X)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf X, AllFormulasOf X
C Subst1 phi is Relation-like AllFormulasOf X -defined AllFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of Funcs ((AllFormulasOf X),(AllFormulasOf X))
id (AllFormulasOf X) is non empty Relation-like non-empty non empty-yielding AllFormulasOf X -defined AllFormulasOf X -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(AllFormulasOf X),(AllFormulasOf X):]
[:(AllFormulasOf X),(AllFormulasOf X):] is non empty Relation-like set
bool [:(AllFormulasOf X),(AllFormulasOf X):] is non empty set
C AtomicSubst phi is non empty Relation-like non-empty non empty-yielding AtomicFormulasOf X -defined AtomicFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(AtomicFormulasOf X),(AtomicFormulasOf X):]
AtomicFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : b1 is 0wff } is set
[:(AtomicFormulasOf X),(AtomicFormulasOf X):] is non empty Relation-like set
bool [:(AtomicFormulasOf X),(AtomicFormulasOf X):] is non empty set
(id (AllFormulasOf X)) +* (C AtomicSubst phi) is non empty Relation-like non-empty Function-like Function-yielding V156() set
(C,phi) Subst4 (C Subst1 phi) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf X),(AllFormulasOf X)) -valued Function-like total quasi_total Function-yielding V156() Element of bool [:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):]
[:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):] is non empty non trivial non finite non empty-membered set
Depth S is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
((C,phi) Subst4 (C Subst1 phi)) . (Depth S) is Relation-like Function-like Function-yielding V156() V208() Element of Funcs ((AllFormulasOf X),(AllFormulasOf X))
(((C,phi) Subst4 (C Subst1 phi)) . (Depth S)) . S is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((C,phi) SubstIn S)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
<*C*> is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
[1,C] is non empty V26() set
{[1,C]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*C*> ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff 1 + (Depth S) -wff non Depth S -wff wff exal Element of ((AllSymbolsOf X) *) \ {{}}
1 + (Depth S) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
[{((C,phi) SubstIn S)},(<*C*> ^ S)] is non empty V26() (X) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
(X) is non empty Relation-like set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
{} null X is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined X \/ (proj1 {}) -defined X \/ (proj1 {}) -defined {{}} -valued X -valued {{}} -valued X \/ (proj2 {}) -valued X \/ (proj2 {}) -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element len {} -element len {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() X -correct (X) (X) set
X \/ (proj1 {}) is set
X \/ (proj2 {}) is set
{} \typed/ X is Element of bool ({} \/ X)
{} \/ X is set
bool ({} \/ X) is non empty set
D is (X) (X) set
Y is (X) set
phii is (X) (X) Element of (X)
phii `1 is finite countable (X) set
(phii `1) \+\ {((C,phi) SubstIn S)} is finite countable set
phii `2 is set
(phii `2) \+\ (<*C*> ^ S) is set
psi is Relation-like (X) Element of bool (X)
[psi,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . Y is set
H is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
S is Relation-like (X) Element of bool (X)
DD is Relation-like (X) Element of bool (X)
Y is set
(X) . S is Relation-like (X) Element of bool (X)
phii is (X) (X) Element of (X)
[S,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
phii `1 is finite countable (X) set
phii `2 is set
psi is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
m is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(psi,m) SubstIn H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
Funcs ((AllFormulasOf X),(AllFormulasOf X)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf X, AllFormulasOf X
psi Subst1 m is Relation-like AllFormulasOf X -defined AllFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of Funcs ((AllFormulasOf X),(AllFormulasOf X))
id (AllFormulasOf X) is non empty Relation-like non-empty non empty-yielding AllFormulasOf X -defined AllFormulasOf X -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(AllFormulasOf X),(AllFormulasOf X):]
[:(AllFormulasOf X),(AllFormulasOf X):] is non empty Relation-like set
bool [:(AllFormulasOf X),(AllFormulasOf X):] is non empty set
psi AtomicSubst m is non empty Relation-like non-empty non empty-yielding AtomicFormulasOf X -defined AtomicFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(AtomicFormulasOf X),(AtomicFormulasOf X):]
AtomicFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : b1 is 0wff } is set
[:(AtomicFormulasOf X),(AtomicFormulasOf X):] is non empty Relation-like set
bool [:(AtomicFormulasOf X),(AtomicFormulasOf X):] is non empty set
(id (AllFormulasOf X)) +* (psi AtomicSubst m) is non empty Relation-like non-empty Function-like Function-yielding V156() set
(psi,m) Subst4 (psi Subst1 m) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf X),(AllFormulasOf X)) -valued Function-like total quasi_total Function-yielding V156() Element of bool [:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):]
[:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):] is non empty non trivial non finite non empty-membered set
Depth H is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
((psi,m) Subst4 (psi Subst1 m)) . (Depth H) is Relation-like Function-like Function-yielding V156() V208() Element of Funcs ((AllFormulasOf X),(AllFormulasOf X))
(((psi,m) Subst4 (psi Subst1 m)) . (Depth H)) . H is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((psi,m) SubstIn H)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
<*psi*> is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
[1,psi] is non empty V26() set
{[1,psi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*psi*> ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff 1 + (Depth H) -wff non Depth H -wff wff exal Element of ((AllSymbolsOf X) *) \ {{}}
1 + (Depth H) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
[DD,phii] is non empty V26() Element of [:(bool (X)),(X):]
(X) . DD is Relation-like (X) Element of bool (X)
S is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
TheNorSymbOf X is set
the U3 of X is Element of the U1 of X
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
C is non empty functional (1,X) ( 0 ,X) Element of bool (Funcs ((bool (X)),(bool (X))))
phi is (X,C) set
(X,C,phi) is Relation-like AllTermsOf X -defined AllTermsOf X -valued total quasi_total reflexive symmetric transitive Element of bool [:(AllTermsOf X),(AllTermsOf X):]
[:(AllTermsOf X),(AllTermsOf X):] is non empty Relation-like set
bool [:(AllTermsOf X),(AllTermsOf X):] is non empty set
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}} : (<*(TheEqSymbOf X)*> ^ b1) ^ b2 is (X,C,phi) } is set
Class (X,C,phi) is non empty with_non-empty_elements non empty-membered a_partition of AllTermsOf X
(X,C,phi) is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, Class (X,C,phi) -interpreter-like Element of (Class (X,C,phi)) -InterpretersOf X
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
(Class (X,C,phi)) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of Class (X,C,phi)
(Class (X,C,phi)) \/ BOOLEAN is non empty set
K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN)) is non empty functional M30((Class (X,C,phi)) * ,(Class (X,C,phi)) \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN))
(Class (X,C,phi)) -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491(((Class (X,C,phi)) *),((Class (X,C,phi)) \/ BOOLEAN))) : b1 is X, Class (X,C,phi) -interpreter-like } is set
(X,phi) -freeInterpreter is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, AllTermsOf X -interpreter-like (X,C,phi) -respecting Element of (AllTermsOf X) -InterpretersOf X
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllTermsOf X
(AllTermsOf X) \/ BOOLEAN is non empty set
K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) is non empty functional M30((AllTermsOf X) * ,(AllTermsOf X) \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))
(AllTermsOf X) -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) : b1 is X, AllTermsOf X -interpreter-like } is set
((X,phi) -freeInterpreter) quotient (X,C,phi) is Relation-like OwnSymbolsOf X -defined Function-like Function-yielding V156() X, Class (X,C,phi) -interpreter-like set
S is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
(X,C,phi) -AtomicEval S is boolean Element of BOOLEAN
(X,C,phi) === is Relation-like Function-like Function-yielding V156() X, Class (X,C,phi) -interpreter-like (X,C,phi) -extension set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
(Class (X,C,phi)) -deltaInterpreter is non empty Relation-like 2 -tuples_on (Class (X,C,phi)) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on (Class (X,C,phi))),BOOLEAN:]
2 -tuples_on (Class (X,C,phi)) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of Class (X,C,phi)
[:(2 -tuples_on (Class (X,C,phi))),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on (Class (X,C,phi))),BOOLEAN:] is non empty set
[:((Class (X,C,phi)) *),((Class (X,C,phi)) *):] is non empty non trivial Relation-like non finite non empty-membered set
K295((Class (X,C,phi))) is non empty Relation-like [:((Class (X,C,phi)) *),((Class (X,C,phi)) *):] -defined (Class (X,C,phi)) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((Class (X,C,phi)) *),((Class (X,C,phi)) *):],((Class (X,C,phi)) *):]
[:[:((Class (X,C,phi)) *),((Class (X,C,phi)) *):],((Class (X,C,phi)) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((Class (X,C,phi)) *),((Class (X,C,phi)) *):],((Class (X,C,phi)) *):] is non empty non trivial non finite non empty-membered set
1 -tuples_on (Class (X,C,phi)) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of Class (X,C,phi)
id (1 -tuples_on (Class (X,C,phi))) is non empty Relation-like non-empty non empty-yielding 1 -tuples_on (Class (X,C,phi)) -defined 1 -tuples_on (Class (X,C,phi)) -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(1 -tuples_on (Class (X,C,phi))),(1 -tuples_on (Class (X,C,phi))):]
[:(1 -tuples_on (Class (X,C,phi))),(1 -tuples_on (Class (X,C,phi))):] is non empty Relation-like set
bool [:(1 -tuples_on (Class (X,C,phi))),(1 -tuples_on (Class (X,C,phi))):] is non empty set
K295((Class (X,C,phi))) .: (id (1 -tuples_on (Class (X,C,phi)))) is functional V36() FinSequence-membered Element of bool ((Class (X,C,phi)) *)
bool ((Class (X,C,phi)) *) is non empty non trivial non finite non empty-membered set
chi ((K295((Class (X,C,phi))) .: (id (1 -tuples_on (Class (X,C,phi))))),(2 -tuples_on (Class (X,C,phi)))) is non empty Relation-like 2 -tuples_on (Class (X,C,phi)) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on (Class (X,C,phi))),BOOLEAN:]
(TheEqSymbOf X) .--> ((Class (X,C,phi)) -deltaInterpreter) is non empty trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on (Class (X,C,phi))),BOOLEAN:] -valued Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element countable set
{(TheEqSymbOf X)} --> ((Class (X,C,phi)) -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on (Class (X,C,phi))),BOOLEAN:] -valued {((Class (X,C,phi)) -deltaInterpreter)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{(TheEqSymbOf X)},{((Class (X,C,phi)) -deltaInterpreter)}:]
{((Class (X,C,phi)) -deltaInterpreter)} is non empty trivial functional finite 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{(TheEqSymbOf X)},{((Class (X,C,phi)) -deltaInterpreter)}:] is non empty Relation-like finite countable set
bool [:{(TheEqSymbOf X)},{((Class (X,C,phi)) -deltaInterpreter)}:] is non empty finite V36() countable set
(X,C,phi) +* ((TheEqSymbOf X) .--> ((Class (X,C,phi)) -deltaInterpreter)) is non empty Relation-like Function-like Function-yielding V156() set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X -firstChar) . S is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
((X,C,phi) ===) . ((X -firstChar) . S) is non empty Relation-like (abs (ar ((X -firstChar) . S))) -tuples_on (Class (X,C,phi)) -defined (Class (X,C,phi)) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . S, Class (X,C,phi)
ar ((X -firstChar) . S) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . S) is set
abs (ar ((X -firstChar) . S)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar ((X -firstChar) . S))) -tuples_on (Class (X,C,phi)) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of Class (X,C,phi)
SubTerms S is Relation-like NAT -defined (proj2 S) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . S)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 S is non empty finite countable set
(proj2 S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 S
(TermSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V36() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(X,C,phi) -TermEval is non empty Relation-like non-empty non empty-yielding AllTermsOf X -defined Class (X,C,phi) -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),(Class (X,C,phi)):]
[:(AllTermsOf X),(Class (X,C,phi)):] is non empty Relation-like set
bool [:(AllTermsOf X),(Class (X,C,phi)):] is non empty set
(SubTerms S) * ((X,C,phi) -TermEval) is Relation-like non-empty NAT -defined Class (X,C,phi) -valued Function-like finite countable V209() set
(((X,C,phi) ===) . ((X -firstChar) . S)) . ((SubTerms S) * ((X,C,phi) -TermEval)) is set
(X,C,phi) -TruthEval S is boolean Element of BOOLEAN
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
AtomicFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : b1 is 0wff } is set
ar (TheEqSymbOf X) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . (TheEqSymbOf X) is set
abs (ar (TheEqSymbOf X)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar (TheEqSymbOf X))) - 2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
a is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, Class (X,C,phi) -interpreter-like Element of (Class (X,C,phi)) -InterpretersOf X
a -TermEval is non empty Relation-like non-empty non empty-yielding AllTermsOf X -defined Class (X,C,phi) -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),(Class (X,C,phi)):]
a -AtomicEval S is boolean Element of BOOLEAN
a === is Relation-like Function-like Function-yielding V156() X, Class (X,C,phi) -interpreter-like a -extension set
a +* ((TheEqSymbOf X) .--> ((Class (X,C,phi)) -deltaInterpreter)) is non empty Relation-like Function-like Function-yielding V156() set
(a ===) . ((X -firstChar) . S) is non empty Relation-like (abs (ar ((X -firstChar) . S))) -tuples_on (Class (X,C,phi)) -defined (Class (X,C,phi)) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . S, Class (X,C,phi)
(SubTerms S) * (a -TermEval) is Relation-like non-empty NAT -defined Class (X,C,phi) -valued Function-like finite countable V209() set
((a ===) . ((X -firstChar) . S)) . ((SubTerms S) * (a -TermEval)) is set
a -TruthEval S is boolean Element of BOOLEAN
((X,phi) -freeInterpreter) -TermEval is non empty Relation-like non-empty non empty-yielding AllTermsOf X -defined AllTermsOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(AllTermsOf X),(AllTermsOf X):]
((X,phi) -freeInterpreter) -AtomicEval S is boolean Element of BOOLEAN
((X,phi) -freeInterpreter) === is Relation-like Function-like Function-yielding V156() X, AllTermsOf X -interpreter-like (X,phi) -freeInterpreter -extension set
(AllTermsOf X) -deltaInterpreter is non empty Relation-like 2 -tuples_on (AllTermsOf X) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on (AllTermsOf X)),BOOLEAN:]
2 -tuples_on (AllTermsOf X) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf X
[:(2 -tuples_on (AllTermsOf X)),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on (AllTermsOf X)),BOOLEAN:] is non empty set
[:((AllTermsOf X) *),((AllTermsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
K295((AllTermsOf X)) is non empty Relation-like [:((AllTermsOf X) *),((AllTermsOf X) *):] -defined (AllTermsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllTermsOf X) *),((AllTermsOf X) *):],((AllTermsOf X) *):]
[:[:((AllTermsOf X) *),((AllTermsOf X) *):],((AllTermsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllTermsOf X) *),((AllTermsOf X) *):],((AllTermsOf X) *):] is non empty non trivial non finite non empty-membered set
1 -tuples_on (AllTermsOf X) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf X
id (1 -tuples_on (AllTermsOf X)) is non empty Relation-like non-empty non empty-yielding 1 -tuples_on (AllTermsOf X) -defined 1 -tuples_on (AllTermsOf X) -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(1 -tuples_on (AllTermsOf X)),(1 -tuples_on (AllTermsOf X)):]
[:(1 -tuples_on (AllTermsOf X)),(1 -tuples_on (AllTermsOf X)):] is non empty Relation-like set
bool [:(1 -tuples_on (AllTermsOf X)),(1 -tuples_on (AllTermsOf X)):] is non empty set
K295((AllTermsOf X)) .: (id (1 -tuples_on (AllTermsOf X))) is functional V36() FinSequence-membered Element of bool ((AllTermsOf X) *)
bool ((AllTermsOf X) *) is non empty non trivial non finite non empty-membered set
chi ((K295((AllTermsOf X)) .: (id (1 -tuples_on (AllTermsOf X)))),(2 -tuples_on (AllTermsOf X))) is non empty Relation-like 2 -tuples_on (AllTermsOf X) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on (AllTermsOf X)),BOOLEAN:]
(TheEqSymbOf X) .--> ((AllTermsOf X) -deltaInterpreter) is non empty trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on (AllTermsOf X)),BOOLEAN:] -valued Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{(TheEqSymbOf X)} --> ((AllTermsOf X) -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on (AllTermsOf X)),BOOLEAN:] -valued {((AllTermsOf X) -deltaInterpreter)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{(TheEqSymbOf X)},{((AllTermsOf X) -deltaInterpreter)}:]
{((AllTermsOf X) -deltaInterpreter)} is non empty trivial functional finite 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{(TheEqSymbOf X)},{((AllTermsOf X) -deltaInterpreter)}:] is non empty Relation-like finite countable set
bool [:{(TheEqSymbOf X)},{((AllTermsOf X) -deltaInterpreter)}:] is non empty finite V36() countable set
((X,phi) -freeInterpreter) +* ((TheEqSymbOf X) .--> ((AllTermsOf X) -deltaInterpreter)) is non empty Relation-like Function-like Function-yielding V156() set
(((X,phi) -freeInterpreter) ===) . ((X -firstChar) . S) is non empty Relation-like (abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X) -defined (AllTermsOf X) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . S, AllTermsOf X
(abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf X
(SubTerms S) * (((X,phi) -freeInterpreter) -TermEval) is Relation-like non-empty NAT -defined AllTermsOf X -valued Function-like finite Function-yielding V156() countable V208() V209() set
((((X,phi) -freeInterpreter) ===) . ((X -firstChar) . S)) . ((SubTerms S) * (((X,phi) -freeInterpreter) -TermEval)) is set
((X,phi) -freeInterpreter) -TruthEval S is boolean Element of BOOLEAN
a . ((X -firstChar) . S) is Relation-like Function-like set
((X,phi) -freeInterpreter) . ((X -firstChar) . S) is Relation-like Function-like set
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
I1 is non empty Relation-like non empty-yielding NAT -defined AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . S)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X)
Seg (abs (ar ((X -firstChar) . S))) is non empty finite abs (ar ((X -firstChar) . S)) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar ((X -firstChar) . S)) ) } is set
Funcs ((Seg (abs (ar ((X -firstChar) . S)))),(AllTermsOf X)) is non empty functional FUNCTION_DOMAIN of Seg (abs (ar ((X -firstChar) . S))), AllTermsOf X
[:(Seg (abs (ar ((X -firstChar) . S)))),(AllTermsOf X):] is non empty Relation-like set
bool [:(Seg (abs (ar ((X -firstChar) . S)))),(AllTermsOf X):] is non empty set
2 -tuples_on (((AllSymbolsOf X) *) \ {{}}) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
{ <*b1,b2*> where b1, b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : verum } is set
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
<*((X -firstChar) . S)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,((X -firstChar) . S)] is non empty V26() set
{[1,((X -firstChar) . S)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
(X -multiCat) . (SubTerms S) is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*((X -firstChar) . S)*> ^ ((X -multiCat) . (SubTerms S)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(X,C,phi) -class is non empty Relation-like non-empty non empty-yielding AllTermsOf X -defined Class (X,C,phi) -valued Function-like total quasi_total onto Element of bool [:(AllTermsOf X),(Class (X,C,phi)):]
((X,C,phi) -class) * (((X,phi) -freeInterpreter) -TermEval) is non empty Relation-like non-empty non empty-yielding AllTermsOf X -defined Class (X,C,phi) -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),(Class (X,C,phi)):]
id (AllTermsOf X) is non empty Relation-like non-empty non empty-yielding AllTermsOf X -defined AllTermsOf X -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(AllTermsOf X),(AllTermsOf X):]
[:((abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X)),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
((X -firstChar) . S) -compound is non empty Relation-like non-empty non empty-yielding (((AllSymbolsOf X) *) \ {{}}) * -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) \ {{}}) *),(((AllSymbolsOf X) *) \ {{}}):]
[:((((AllSymbolsOf X) *) \ {{}}) *),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) \ {{}}) *),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
(((X -firstChar) . S) -compound) | ((abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X)) is Relation-like (abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X) -defined (((AllSymbolsOf X) *) \ {{}}) * -defined (abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X) -defined (((AllSymbolsOf X) *) \ {{}}) * -defined ((AllSymbolsOf X) *) \ {{}} -valued ((AllSymbolsOf X) *) \ {{}} -valued AtomicFormulasOf X -valued Function-like Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) \ {{}}) *),(((AllSymbolsOf X) *) \ {{}}):]
0 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(0 + 1) + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
X1 is Relation-like NAT -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (((AllSymbolsOf X) *) \ {{}}) *
U is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*U,I*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V209() set
<*U*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,U] is non empty V26() set
{[1,U]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*I*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,I] is non empty V26() set
{[1,I]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*U*> ^ <*I*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element 1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
1 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
1 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(X -multiCat) . <*U,I*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
U ^ I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(1 + 1) + 0 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
X22 is non empty Relation-like non empty-yielding NAT -defined AllTermsOf X -valued Function-like finite (0 + 1) + 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
X22 . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{(X22 . (0 + 1))} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
{(X22 . (0 + 1))} \ (AllTermsOf X) is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {(X22 . (0 + 1))}
bool {(X22 . (0 + 1))} is non empty finite V36() countable set
{(X22 . (0 + 1))} typed\ (AllTermsOf X) is trivial functional finite V36() with_common_domain countable Element of bool {(X22 . (0 + 1))}
phi is non empty Relation-like non empty-yielding NAT -defined AllTermsOf X -valued Function-like finite (1 + 1) + 0 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
phi . (1 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{(phi . (1 + 1))} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
{(phi . (1 + 1))} \ (AllTermsOf X) is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {(phi . (1 + 1))}
bool {(phi . (1 + 1))} is non empty finite V36() countable set
{(phi . (1 + 1))} typed\ (AllTermsOf X) is trivial functional finite V36() with_common_domain countable Element of bool {(phi . (1 + 1))}
(SubTerms S) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(SubTerms S) . 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
l22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
F2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
((X,C,phi) -class) . l22 is non empty Element of Class (X,C,phi)
EqClass ((X,C,phi),l22) is non empty Element of Class (X,C,phi)
bool (AllTermsOf X) is non empty set
{l22} is non empty trivial functional finite V36() 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
(X,C,phi) .: {l22} is set
((X,C,phi) -class) . F2 is non empty Element of Class (X,C,phi)
EqClass ((X,C,phi),F2) is non empty Element of Class (X,C,phi)
{F2} is non empty trivial functional finite V36() 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
(X,C,phi) .: {F2} is set
(id (AllTermsOf X)) . l22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
{((id (AllTermsOf X)) . l22)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (AllTermsOf X)
{l22} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (AllTermsOf X)
{((id (AllTermsOf X)) . l22)} \ {l22} is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (AllTermsOf X)
{((id (AllTermsOf X)) . l22)} typed\ {l22} is trivial functional finite V36() FinSequence-membered with_non-empty_elements with_common_domain countable Element of bool {((id (AllTermsOf X)) . l22)}
bool {((id (AllTermsOf X)) . l22)} is non empty finite V36() countable set
{((id (AllTermsOf X)) . l22)} \ {l22} is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {((id (AllTermsOf X)) . l22)}
(id (AllTermsOf X)) . F2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
{((id (AllTermsOf X)) . F2)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (AllTermsOf X)
{F2} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable Element of bool (AllTermsOf X)
{((id (AllTermsOf X)) . F2)} \ {F2} is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (AllTermsOf X)
{((id (AllTermsOf X)) . F2)} typed\ {F2} is trivial functional finite V36() FinSequence-membered with_non-empty_elements with_common_domain countable Element of bool {((id (AllTermsOf X)) . F2)}
bool {((id (AllTermsOf X)) . F2)} is non empty finite V36() countable set
{((id (AllTermsOf X)) . F2)} \ {F2} is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool {((id (AllTermsOf X)) . F2)}
(((X,C,phi) -class) * (((X,phi) -freeInterpreter) -TermEval)) . l22 is non empty Element of Class (X,C,phi)
(((X,phi) -freeInterpreter) -TermEval) . l22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
((X,C,phi) -class) . ((((X,phi) -freeInterpreter) -TermEval) . l22) is non empty Element of Class (X,C,phi)
((((X,C,phi) -class) * (((X,phi) -freeInterpreter) -TermEval)) . l22) \+\ (((X,C,phi) -class) . ((((X,phi) -freeInterpreter) -TermEval) . l22)) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(((X,C,phi) -class) * (((X,phi) -freeInterpreter) -TermEval)) . F2 is non empty Element of Class (X,C,phi)
(((X,phi) -freeInterpreter) -TermEval) . F2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
((X,C,phi) -class) . ((((X,phi) -freeInterpreter) -TermEval) . F2) is non empty Element of Class (X,C,phi)
((((X,C,phi) -class) * (((X,phi) -freeInterpreter) -TermEval)) . F2) \+\ (((X,C,phi) -class) . ((((X,phi) -freeInterpreter) -TermEval) . F2)) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[l22,F2] is non empty V26() Element of [:(AllTermsOf X),(AllTermsOf X):]
F1 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ F1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
F5 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ F1) ^ F5 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
seqt2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
z is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
[seqt2,z] is non empty V26() Element of [:(((AllSymbolsOf X) *) \ {{}}),(((AllSymbolsOf X) *) \ {{}}):]
[:(((AllSymbolsOf X) *) \ {{}}),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
<*(TheEqSymbOf X)*> ^ seqt2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ seqt2) ^ z is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
seqt2 ^ z is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ (seqt2 ^ z) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
{S} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
bool phi is non empty set
{S} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
[{S},S] is non empty V26() (X) (1,X,{(X)}, {} ) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
{[{S},S]} is non empty trivial Relation-like non empty-yielding bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() (X) (X,{(X)}, {} ) (X,{(X)}) Element of bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
seqt2 is Element of bool phi
X22 is own ofAtomicFormula Element of OwnSymbolsOf X
((X,phi) -freeInterpreter) . X22 is non empty Relation-like (abs (ar X22)) -tuples_on (AllTermsOf X) -defined (AllTermsOf X) \/ BOOLEAN -valued Function-like total quasi_total (X,C,phi) -respecting Interpreter of X22, AllTermsOf X
ar X22 is complex ext-real finite V40() V41() countable Element of INT
the adicity of X . X22 is set
abs (ar X22) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar X22)) -tuples_on (AllTermsOf X) is non empty functional V36() FinSequence-membered FinSequenceSet of AllTermsOf X
(((X,phi) -freeInterpreter) . X22) . ((SubTerms S) * (((X,phi) -freeInterpreter) -TermEval)) is set
I2 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar ((X -firstChar) . S))) -defined AllTermsOf X -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar ((X -firstChar) . S)))),(AllTermsOf X):]
(id (AllTermsOf X)) * I2 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar ((X -firstChar) . S))) -defined AllTermsOf X -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar ((X -firstChar) . S)))),(AllTermsOf X):]
(((X,phi) -freeInterpreter) . X22) . ((id (AllTermsOf X)) * I2) is set
(((X,phi) -freeInterpreter) . X22) . I2 is set
phi -freeInterpreter X22 is non empty Relation-like (abs (ar X22)) -tuples_on (AllTermsOf X) -defined (AllTermsOf X) \/ BOOLEAN -valued Function-like total quasi_total (X,C,phi) -respecting Interpreter of X22, AllTermsOf X
(phi -freeInterpreter X22) . (SubTerms S) is set
X22 -compound is non empty Relation-like non-empty non empty-yielding (((AllSymbolsOf X) *) \ {{}}) * -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) \ {{}}) *),(((AllSymbolsOf X) *) \ {{}}):]
(X22 -compound) | ((abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X)) is Relation-like (abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X) -defined (((AllSymbolsOf X) *) \ {{}}) * -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) \ {{}}) *),(((AllSymbolsOf X) *) \ {{}}):]
chi (phi,(AtomicFormulasOf X)) is non empty Relation-like AtomicFormulasOf X -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(AtomicFormulasOf X),BOOLEAN:]
[:(AtomicFormulasOf X),BOOLEAN:] is non empty Relation-like set
bool [:(AtomicFormulasOf X),BOOLEAN:] is non empty set
(chi (phi,(AtomicFormulasOf X))) * ((X22 -compound) | ((abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X))) is Relation-like (abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X) -defined (((AllSymbolsOf X) *) \ {{}}) * -defined BOOLEAN -valued Function-like Element of bool [:((((AllSymbolsOf X) *) \ {{}}) *),BOOLEAN:]
[:((((AllSymbolsOf X) *) \ {{}}) *),BOOLEAN:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) \ {{}}) *),BOOLEAN:] is non empty non trivial non finite non empty-membered set
((chi (phi,(AtomicFormulasOf X))) * ((X22 -compound) | ((abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X)))) . I1 is set
X2 is non empty Relation-like non-empty non empty-yielding (abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((abs (ar ((X -firstChar) . S))) -tuples_on (AllTermsOf X)),(((AllSymbolsOf X) *) \ {{}}):]
X2 . I1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(chi (phi,(AtomicFormulasOf X))) . (X2 . I1) is boolean set
(X22 -compound) . I1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(chi (phi,(AtomicFormulasOf X))) . ((X22 -compound) . I1) is boolean set
X1 is Relation-like NAT -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (((AllSymbolsOf X) *) \ {{}}) *
X22 -compound X1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*X22*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,X22] is non empty V26() set
{[1,X22]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
(X -multiCat) . X1 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*X22*> ^ ((X -multiCat) . X1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(chi (phi,(AtomicFormulasOf X))) . (X22 -compound X1) is boolean set
(chi (phi,(AtomicFormulasOf X))) . S is boolean set
(chi (phi,(AtomicFormulasOf X))) " {1} is set
phi /\ (AtomicFormulasOf X) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf X) *) \ {{}})
phi typed/\ (AtomicFormulasOf X) is Element of bool phi
bool phi is non empty set
phi /\ (AtomicFormulasOf X) is functional set
phi /\typed (AtomicFormulasOf X) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AtomicFormulasOf X)
bool (AtomicFormulasOf X) is non empty set
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty functional (1,X) ( 0 ,X) Element of bool (Funcs ((bool (X)),(bool (X))))
S is (X,phi) set
(X,phi,S) is Relation-like AllTermsOf X -defined AllTermsOf X -valued total quasi_total reflexive symmetric transitive Element of bool [:(AllTermsOf X),(AllTermsOf X):]
[:(AllTermsOf X),(AllTermsOf X):] is non empty Relation-like set
bool [:(AllTermsOf X),(AllTermsOf X):] is non empty set
TermSymbolsOf X is non empty set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}} : (<*(TheEqSymbOf X)*> ^ b1) ^ b2 is (X,phi,S) } is set
Class (X,phi,S) is non empty with_non-empty_elements non empty-membered a_partition of AllTermsOf X
(X,phi,S) is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, Class (X,phi,S) -interpreter-like Element of (Class (X,phi,S)) -InterpretersOf X
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
(Class (X,phi,S)) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of Class (X,phi,S)
(Class (X,phi,S)) \/ BOOLEAN is non empty set
K491(((Class (X,phi,S)) *),((Class (X,phi,S)) \/ BOOLEAN)) is non empty functional M30((Class (X,phi,S)) * ,(Class (X,phi,S)) \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491(((Class (X,phi,S)) *),((Class (X,phi,S)) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491(((Class (X,phi,S)) *),((Class (X,phi,S)) \/ BOOLEAN))
(Class (X,phi,S)) -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491(((Class (X,phi,S)) *),((Class (X,phi,S)) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491(((Class (X,phi,S)) *),((Class (X,phi,S)) \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491(((Class (X,phi,S)) *),((Class (X,phi,S)) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491(((Class (X,phi,S)) *),((Class (X,phi,S)) \/ BOOLEAN))) : b1 is X, Class (X,phi,S) -interpreter-like } is set
(X,S) -freeInterpreter is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, AllTermsOf X -interpreter-like (X,phi,S) -respecting Element of (AllTermsOf X) -InterpretersOf X
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllTermsOf X
(AllTermsOf X) \/ BOOLEAN is non empty set
K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) is non empty functional M30((AllTermsOf X) * ,(AllTermsOf X) \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))
(AllTermsOf X) -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) : b1 is X, AllTermsOf X -interpreter-like } is set
((X,S) -freeInterpreter) quotient (X,phi,S) is Relation-like OwnSymbolsOf X -defined Function-like Function-yielding V156() X, Class (X,phi,S) -interpreter-like set
(X,phi,S) -TruthEval C is boolean Element of BOOLEAN
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
LettersOf X is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
{0} is non empty trivial functional finite V36() 1 -element empty-membered with_common_domain countable Element of bool NAT
0 * is non empty functional V36() FinSequence-membered FinSequenceSet of 0
{0} is non empty trivial functional finite V36() 1 -element empty-membered with_common_domain countable set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
AtomicFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : b1 is 0wff } is set
(Class (X,phi,S)) -deltaInterpreter is non empty Relation-like 2 -tuples_on (Class (X,phi,S)) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on (Class (X,phi,S))),BOOLEAN:]
2 -tuples_on (Class (X,phi,S)) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of Class (X,phi,S)
[:(2 -tuples_on (Class (X,phi,S))),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on (Class (X,phi,S))),BOOLEAN:] is non empty set
[:((Class (X,phi,S)) *),((Class (X,phi,S)) *):] is non empty non trivial Relation-like non finite non empty-membered set
K295((Class (X,phi,S))) is non empty Relation-like [:((Class (X,phi,S)) *),((Class (X,phi,S)) *):] -defined (Class (X,phi,S)) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((Class (X,phi,S)) *),((Class (X,phi,S)) *):],((Class (X,phi,S)) *):]
[:[:((Class (X,phi,S)) *),((Class (X,phi,S)) *):],((Class (X,phi,S)) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((Class (X,phi,S)) *),((Class (X,phi,S)) *):],((Class (X,phi,S)) *):] is non empty non trivial non finite non empty-membered set
1 -tuples_on (Class (X,phi,S)) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of Class (X,phi,S)
id (1 -tuples_on (Class (X,phi,S))) is non empty Relation-like non-empty non empty-yielding 1 -tuples_on (Class (X,phi,S)) -defined 1 -tuples_on (Class (X,phi,S)) -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(1 -tuples_on (Class (X,phi,S))),(1 -tuples_on (Class (X,phi,S))):]
[:(1 -tuples_on (Class (X,phi,S))),(1 -tuples_on (Class (X,phi,S))):] is non empty Relation-like set
bool [:(1 -tuples_on (Class (X,phi,S))),(1 -tuples_on (Class (X,phi,S))):] is non empty set
K295((Class (X,phi,S))) .: (id (1 -tuples_on (Class (X,phi,S)))) is functional V36() FinSequence-membered Element of bool ((Class (X,phi,S)) *)
bool ((Class (X,phi,S)) *) is non empty non trivial non finite non empty-membered set
chi ((K295((Class (X,phi,S))) .: (id (1 -tuples_on (Class (X,phi,S))))),(2 -tuples_on (Class (X,phi,S)))) is non empty Relation-like 2 -tuples_on (Class (X,phi,S)) -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on (Class (X,phi,S))),BOOLEAN:]
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool phi is non empty set
X22 is functional Element of bool (Funcs ((bool (X)),(bool (X))))
U is functional Element of bool (Funcs ((bool (X)),(bool (X))))
I is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is functional Element of bool (Funcs ((bool (X)),(bool (X))))
l22 is functional Element of bool (Funcs ((bool (X)),(bool (X))))
F2 is functional Element of bool (Funcs ((bool (X)),(bool (X))))
F1 is functional Element of bool (Funcs ((bool (X)),(bool (X))))
F5 is functional Element of bool phi
seqt2 is functional Element of bool phi
F5 \/ seqt2 is functional Element of bool phi
F8 is functional Element of bool phi
(F5 \/ seqt2) \/ F8 is functional Element of bool phi
F5 \/ ((F5 \/ seqt2) \/ F8) is functional Element of bool phi
F6 is functional Element of bool phi
F5 \/ F6 is functional Element of bool phi
F7 is functional Element of bool phi
((F5 \/ seqt2) \/ F8) \/ F7 is functional Element of bool phi
F5 \/ (((F5 \/ seqt2) \/ F8) \/ F7) is functional Element of bool phi
I is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, Class (X,phi,S) -interpreter-like Element of (Class (X,phi,S)) -InterpretersOf X
I -TermEval is non empty Relation-like non-empty non empty-yielding AllTermsOf X -defined Class (X,phi,S) -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),(Class (X,phi,S)):]
[:(AllTermsOf X),(Class (X,phi,S)):] is non empty Relation-like set
bool [:(AllTermsOf X),(Class (X,phi,S)):] is non empty set
((X,S) -freeInterpreter) -TermEval is non empty Relation-like non-empty non empty-yielding AllTermsOf X -defined AllTermsOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(AllTermsOf X),(AllTermsOf X):]
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
n is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
I -TruthEval n is boolean Element of BOOLEAN
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
Vn is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
I -AtomicEval Vn is boolean Element of BOOLEAN
I === is Relation-like Function-like Function-yielding V156() X, Class (X,phi,S) -interpreter-like I -extension set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
(TheEqSymbOf X) .--> ((Class (X,phi,S)) -deltaInterpreter) is non empty trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on (Class (X,phi,S))),BOOLEAN:] -valued Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element countable set
{(TheEqSymbOf X)} --> ((Class (X,phi,S)) -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on (Class (X,phi,S))),BOOLEAN:] -valued {((Class (X,phi,S)) -deltaInterpreter)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{(TheEqSymbOf X)},{((Class (X,phi,S)) -deltaInterpreter)}:]
{((Class (X,phi,S)) -deltaInterpreter)} is non empty trivial functional finite 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{(TheEqSymbOf X)},{((Class (X,phi,S)) -deltaInterpreter)}:] is non empty Relation-like finite countable set
bool [:{(TheEqSymbOf X)},{((Class (X,phi,S)) -deltaInterpreter)}:] is non empty finite V36() countable set
I +* ((TheEqSymbOf X) .--> ((Class (X,phi,S)) -deltaInterpreter)) is non empty Relation-like Function-like Function-yielding V156() set
(X -firstChar) . Vn is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(I ===) . ((X -firstChar) . Vn) is non empty Relation-like (abs (ar ((X -firstChar) . Vn))) -tuples_on (Class (X,phi,S)) -defined (Class (X,phi,S)) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . Vn, Class (X,phi,S)
ar ((X -firstChar) . Vn) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . Vn) is set
abs (ar ((X -firstChar) . Vn)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar ((X -firstChar) . Vn))) -tuples_on (Class (X,phi,S)) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of Class (X,phi,S)
SubTerms Vn is Relation-like NAT -defined (proj2 Vn) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . Vn)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 Vn is non empty finite countable set
(proj2 Vn) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 Vn
(TermSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V36() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf X) *) *)
(SubTerms Vn) * (I -TermEval) is Relation-like non-empty NAT -defined Class (X,phi,S) -valued Function-like finite countable V209() set
((I ===) . ((X -firstChar) . Vn)) . ((SubTerms Vn) * (I -TermEval)) is set
I -TruthEval Vn is boolean Element of BOOLEAN
n is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
n + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(I,n) -TruthEval is Relation-like ((AllSymbolsOf X) *) \ {{}} -defined BOOLEAN -valued Function-like M31(((AllSymbolsOf X) *) \ {{}}, BOOLEAN ,K491((((AllSymbolsOf X) *) \ {{}}),BOOLEAN))
K491((((AllSymbolsOf X) *) \ {{}}),BOOLEAN) is non empty functional M30(((AllSymbolsOf X) *) \ {{}}, BOOLEAN )
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
I -TruthEval phi is boolean Element of BOOLEAN
(X -firstChar) . phi is Element of AllSymbolsOf X
phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff n + 1 -wff wff exal Element of ((AllSymbolsOf X) *) \ {{}}
head phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() n -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
SubWffsOf phii is set
(SubWffsOf phii) `1 is set
(X -firstChar) . phii is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
phi2 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
<*phi2*> is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
[1,phi2] is non empty V26() set
{[1,phi2]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phi1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() n -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
<*phi2*> ^ phi1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff n + 1 -wff 1 + (Depth phi1) -wff non Depth phi1 -wff wff exal Element of ((AllSymbolsOf X) *) \ {{}}
n + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
Depth phi1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
1 + (Depth phi1) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
tail phii is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued AllSymbolsOf X -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of (AllSymbolsOf X) *
(SubWffsOf phii) `2 is set
(<*phi2*> ^ phi1) ^ (tail phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(<*phi2*> ^ phi1) null (tail phii) is Relation-like NAT -defined (tail phii) \/ (proj1 (<*phi2*> ^ phi1)) -defined (tail phii) \/ (proj2 (<*phi2*> ^ phi1)) -valued Function-like finite len (<*phi2*> ^ phi1) -element FinSequence-like FinSubsequence-like countable V209() set
proj1 (<*phi2*> ^ phi1) is non empty finite countable set
(tail phii) \/ (proj1 (<*phi2*> ^ phi1)) is non empty finite countable set
proj2 (<*phi2*> ^ phi1) is non empty finite countable set
(tail phii) \/ (proj2 (<*phi2*> ^ phi1)) is non empty finite countable set
len (<*phi2*> ^ phi1) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(<*phi2*> ^ phi1) \typed/ (tail phii) is Relation-like NAT -defined finite countable Element of bool ((<*phi2*> ^ phi1) \/ (tail phii))
(<*phi2*> ^ phi1) \/ (tail phii) is non empty Relation-like NAT -defined finite countable set
bool ((<*phi2*> ^ phi1) \/ (tail phii)) is non empty finite V36() countable set
(tail phii) ^ (<*phi2*> ^ phi1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
bool (AllTermsOf X) is non empty set
H is non empty Element of Class (X,phi,S)
(phi2,H) ReassignIn I is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, Class (X,phi,S) -interpreter-like Element of (Class (X,phi,S)) -InterpretersOf X
{} .--> H is non empty trivial Relation-like non empty-yielding {{}} -defined Class (X,phi,S) -valued Function-like one-to-one constant finite 1 -element countable V209() set
{{}} --> H is non empty Relation-like non-empty non empty-yielding {{}} -defined Class (X,phi,S) -valued {H} -valued Function-like constant total quasi_total finite countable V209() Element of bool [:{{}},{H}:]
{H} is non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable set
[:{{}},{H}:] is non empty Relation-like finite countable set
bool [:{{}},{H}:] is non empty finite V36() countable set
phi2 .--> ({} .--> H) is non empty trivial Relation-like AllSymbolsOf X -defined {phi2} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{phi2} is non empty trivial finite 1 -element countable set
{phi2} --> ({} .--> H) is non empty Relation-like non-empty non empty-yielding {phi2} -defined {({} .--> H)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{phi2},{({} .--> H)}:]
{({} .--> H)} is non empty trivial functional finite V36() 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{phi2},{({} .--> H)}:] is non empty Relation-like finite countable set
bool [:{phi2},{({} .--> H)}:] is non empty finite V36() countable set
I +* (phi2 .--> ({} .--> H)) is non empty Relation-like Function-like Function-yielding V156() set
((phi2,H) ReassignIn I) -TruthEval phi1 is boolean Element of BOOLEAN
psi1 is set
Class ((X,phi,S),psi1) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllTermsOf X)
{psi1} is non empty trivial finite 1 -element countable set
(X,phi,S) .: {psi1} is set
u is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
(phi2,u) SubstIn phi1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() n -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
Funcs ((AllFormulasOf X),(AllFormulasOf X)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf X, AllFormulasOf X
phi2 Subst1 u is Relation-like AllFormulasOf X -defined AllFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of Funcs ((AllFormulasOf X),(AllFormulasOf X))
id (AllFormulasOf X) is non empty Relation-like non-empty non empty-yielding AllFormulasOf X -defined AllFormulasOf X -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(AllFormulasOf X),(AllFormulasOf X):]
[:(AllFormulasOf X),(AllFormulasOf X):] is non empty Relation-like set
bool [:(AllFormulasOf X),(AllFormulasOf X):] is non empty set
phi2 AtomicSubst u is non empty Relation-like non-empty non empty-yielding AtomicFormulasOf X -defined AtomicFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(AtomicFormulasOf X),(AtomicFormulasOf X):]
[:(AtomicFormulasOf X),(AtomicFormulasOf X):] is non empty Relation-like set
bool [:(AtomicFormulasOf X),(AtomicFormulasOf X):] is non empty set
(id (AllFormulasOf X)) +* (phi2 AtomicSubst u) is non empty Relation-like non-empty Function-like Function-yielding V156() set
(phi2,u) Subst4 (phi2 Subst1 u) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf X),(AllFormulasOf X)) -valued Function-like total quasi_total Function-yielding V156() Element of bool [:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):]
[:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):] is non empty non trivial non finite non empty-membered set
((phi2,u) Subst4 (phi2 Subst1 u)) . (Depth phi1) is Relation-like Function-like Function-yielding V156() V208() Element of Funcs ((AllFormulasOf X),(AllFormulasOf X))
(((phi2,u) Subst4 (phi2 Subst1 u)) . (Depth phi1)) . phi1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
id (AllTermsOf X) is non empty Relation-like non-empty non empty-yielding AllTermsOf X -defined AllTermsOf X -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(AllTermsOf X),(AllTermsOf X):]
(id (AllTermsOf X)) . u is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
((id (AllTermsOf X)) . u) \+\ u is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(X,phi,S) -class is non empty Relation-like non-empty non empty-yielding AllTermsOf X -defined Class (X,phi,S) -valued Function-like total quasi_total onto Element of bool [:(AllTermsOf X),(Class (X,phi,S)):]
((X,phi,S) -class) * (((X,S) -freeInterpreter) -TermEval) is non empty Relation-like non-empty non empty-yielding AllTermsOf X -defined Class (X,phi,S) -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),(Class (X,phi,S)):]
(((X,phi,S) -class) * (((X,S) -freeInterpreter) -TermEval)) . u is non empty Element of Class (X,phi,S)
(((X,S) -freeInterpreter) -TermEval) . u is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
((X,phi,S) -class) . ((((X,S) -freeInterpreter) -TermEval) . u) is non empty Element of Class (X,phi,S)
((((X,phi,S) -class) * (((X,S) -freeInterpreter) -TermEval)) . u) \+\ (((X,phi,S) -class) . ((((X,S) -freeInterpreter) -TermEval) . u)) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(I -TermEval) . u is non empty Element of Class (X,phi,S)
I2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() n -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
I -TruthEval I2 is boolean Element of BOOLEAN
{I2} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
{((phi2,u) SubstIn phi1)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
[{((phi2,u) SubstIn phi1)},(<*phi2*> ^ phi1)] is non empty V26() (X) (1,X,{(X)}, {} ) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
ST is functional Element of bool phi
proj2 phi1 is non empty finite countable set
H is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(phi2,H) -SymbolSubstIn phi1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() n -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
phi1 +~ (phi2,H) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
I . H is non empty Relation-like (abs (ar H)) -tuples_on (Class (X,phi,S)) -defined (Class (X,phi,S)) \/ BOOLEAN -valued Function-like total quasi_total Interpreter of H, Class (X,phi,S)
ar H is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of INT
the adicity of X . H is set
abs (ar H) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of NAT
(abs (ar H)) -tuples_on (Class (X,phi,S)) is non empty functional V36() FinSequence-membered empty-membered FinSequenceSet of Class (X,phi,S)
(I . H) . {} is set
u is non empty Element of Class (X,phi,S)
(H,u) ReassignIn I is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, Class (X,phi,S) -interpreter-like Element of (Class (X,phi,S)) -InterpretersOf X
{} .--> u is non empty trivial Relation-like non empty-yielding {{}} -defined Class (X,phi,S) -valued Function-like one-to-one constant finite 1 -element countable V209() set
{{}} --> u is non empty Relation-like non-empty non empty-yielding {{}} -defined Class (X,phi,S) -valued {u} -valued Function-like constant total quasi_total finite countable V209() Element of bool [:{{}},{u}:]
{u} is non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable set
[:{{}},{u}:] is non empty Relation-like finite countable set
bool [:{{}},{u}:] is non empty finite V36() countable set
H .--> ({} .--> u) is non empty trivial Relation-like AllSymbolsOf X -defined {H} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{H} is non empty trivial finite 1 -element countable set
{H} --> ({} .--> u) is non empty Relation-like non-empty non empty-yielding {H} -defined {({} .--> u)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{H},{({} .--> u)}:]
{({} .--> u)} is non empty trivial functional finite V36() 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{H},{({} .--> u)}:] is non empty Relation-like finite countable set
bool [:{H},{({} .--> u)}:] is non empty finite V36() countable set
I +* (H .--> ({} .--> u)) is non empty Relation-like Function-like Function-yielding V156() set
(phi2,u) ReassignIn I is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, Class (X,phi,S) -interpreter-like Element of (Class (X,phi,S)) -InterpretersOf X
phi2 .--> ({} .--> u) is non empty trivial Relation-like AllSymbolsOf X -defined {phi2} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{phi2} --> ({} .--> u) is non empty Relation-like non-empty non empty-yielding {phi2} -defined {({} .--> u)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{phi2},{({} .--> u)}:]
[:{phi2},{({} .--> u)}:] is non empty Relation-like finite countable set
bool [:{phi2},{({} .--> u)}:] is non empty finite V36() countable set
I +* (phi2 .--> ({} .--> u)) is non empty Relation-like Function-like Function-yielding V156() set
I2 is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, Class (X,phi,S) -interpreter-like Element of (Class (X,phi,S)) -InterpretersOf X
psi1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() n -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
I2 -TruthEval psi1 is boolean Element of BOOLEAN
I1 is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, Class (X,phi,S) -interpreter-like Element of (Class (X,phi,S)) -InterpretersOf X
I1 -TruthEval phi1 is boolean Element of BOOLEAN
phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff n + 1 -wff wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
head phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() n -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
SubWffsOf phii is set
(SubWffsOf phii) `1 is set
tail phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() n -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
(SubWffsOf phii) `2 is set
(X -firstChar) . phii is non relational Element of AllSymbolsOf X
((X -firstChar) . phii) \+\ (TheNorSymbOf X) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf X)*> ^ (head phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ (head phii)) ^ (tail phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth (head phii)),(Depth (tail phii))) -wff n + 1 -wff wff non exal (X,{(X)} \/ {(X)},{(xnot (head phii)),(xnot (tail phii))}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth (head phii) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth (tail phii) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth (head phii)),(Depth (tail phii))) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
n + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
xnot (head phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() n + 1 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ (head phii)) ^ (head phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth (head phii)),(Depth (head phii))) -wff n + 1 -wff wff non exal (X,{(X)} \/ {(X)},{(xnot (head phii)),(xnot (head phii))}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth (head phii)),(Depth (head phii))) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot (head phii)),(xnot (head phii))} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
xnot (tail phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() n + 1 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ (tail phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ (tail phii)) ^ (tail phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth (tail phii)),(Depth (tail phii))) -wff n + 1 -wff wff non exal (X,{(X)} \/ {(X)},{(xnot (tail phii)),(xnot (tail phii))}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth (tail phii)),(Depth (tail phii))) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot (tail phii)),(xnot (tail phii))} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
{(xnot (head phii)),(xnot (tail phii))} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
I -TruthEval (head phii) is boolean Element of BOOLEAN
I -TruthEval (tail phii) is boolean Element of BOOLEAN
bool S is non empty set
H is Element of bool S
S null H is set
S \typed/ H is Element of bool (S \/ H)
S \/ H is set
bool (S \/ H) is non empty set
{phi} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
H is finite countable (X) set
[{phi},phi] is non empty V26() (X) (1,X,{(X)}, {} ) (X) Element of [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
X22 \/ U is functional Element of bool (Funcs ((bool (X)),(bool (X))))
(X22 \/ U) \/ F1 is functional Element of bool (Funcs ((bool (X)),(bool (X))))
{[{phi},phi]} is non empty trivial Relation-like non empty-yielding bool (((AllSymbolsOf X) *) \ {{}}) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() (X) (X,{(X)}, {} ) (X,{(X)}) Element of bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):]
bool [:(bool (((AllSymbolsOf X) *) \ {{}})),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
H null (tail phii) is finite countable (X) set
H \typed/ (tail phii) is finite countable Element of bool (H \/ (tail phii))
H \/ (tail phii) is non empty finite countable set
bool (H \/ (tail phii)) is non empty finite V36() countable set
[(H null (tail phii)),(xnot (head phii))] is non empty V26() (X) (2,X,({(X)} \/ {(X)}) \/ {(X)},{[H,((<*(TheNorSymbOf X)*> ^ (head phii)) ^ (tail phii))]}) (3,X,(({(X)} \/ {(X)}) \/ {(X)}) \/ {(X)},{[H,((<*(TheNorSymbOf X)*> ^ (tail phii)) ^ (head phii))]}) (X) set
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
({(X)} \/ {(X)}) \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
[H,((<*(TheNorSymbOf X)*> ^ (head phii)) ^ (tail phii))] is non empty V26() (X) (1,X,{(X)},{[H,((<*(TheNorSymbOf X)*> ^ (tail phii)) ^ (head phii))]}) (X) set
(<*(TheNorSymbOf X)*> ^ (tail phii)) ^ (head phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth (tail phii)),(Depth (head phii))) -wff n + 1 -wff wff non exal (X,{(X)} \/ {(X)},{(xnot (tail phii)),(xnot (head phii))}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth (tail phii)),(Depth (head phii))) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot (tail phii)),(xnot (head phii))} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[H,((<*(TheNorSymbOf X)*> ^ (tail phii)) ^ (head phii))] is non empty V26() (X) (1,X,{(X)},{[H,((<*(TheNorSymbOf X)*> ^ (head phii)) ^ (tail phii))]}) (X) set
{[H,((<*(TheNorSymbOf X)*> ^ (head phii)) ^ (tail phii))]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
{[H,((<*(TheNorSymbOf X)*> ^ (tail phii)) ^ (head phii))]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
(({(X)} \/ {(X)}) \/ {(X)}) \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
((X22 \/ U) \/ F1) \/ F2 is functional Element of bool (Funcs ((bool (X)),(bool (X))))
[H,phi] is non empty V26() (X) (X) set
{[H,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
H null (head phii) is finite countable (X) set
H \typed/ (head phii) is finite countable Element of bool (H \/ (head phii))
H \/ (head phii) is non empty finite countable set
bool (H \/ (head phii)) is non empty finite V36() countable set
[(H null (head phii)),(xnot (tail phii))] is non empty V26() (X) (2,X,({(X)} \/ {(X)}) \/ {(X)},{[H,((<*(TheNorSymbOf X)*> ^ (tail phii)) ^ (head phii))]}) (3,X,(({(X)} \/ {(X)}) \/ {(X)}) \/ {(X)},{[H,((<*(TheNorSymbOf X)*> ^ (head phii)) ^ (tail phii))]}) (X) set
1 + 2 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
X22 \/ ((X22 \/ U) \/ F1) is functional Element of bool (Funcs ((bool (X)),(bool (X))))
[H,(xnot (head phii))] is non empty V26() (X) (X) set
1 + 3 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
X22 \/ (((X22 \/ U) \/ F1) \/ F2) is functional Element of bool (Funcs ((bool (X)),(bool (X))))
[H,(xnot (tail phii))] is non empty V26() (X) (X) set
4 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
Depth C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
X is set
bool X is non empty set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S is Element of bool X
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheNorSymbOf C)*> ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ FF) ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth FF),(Depth D)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot FF),(xnot D)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth FF is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth D is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth FF),(Depth D)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
xnot FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ FF) ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth FF),(Depth FF)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot FF),(xnot FF)}) Element of ((AllSymbolsOf C) *) \ {{}}
max ((Depth FF),(Depth FF)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot FF),(xnot FF)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
xnot D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheNorSymbOf C)*> ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ D) ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth D),(Depth D)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot D),(xnot D)}) Element of ((AllSymbolsOf C) *) \ {{}}
max ((Depth D),(Depth D)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot D),(xnot D)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
{(xnot FF),(xnot D)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
ExFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is functional set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf X
{S} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (ExFormulasOf X)
bool (ExFormulasOf X) is non empty set
phi \/ {S} is non empty functional set
LettersOf X is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
{0} is non empty trivial functional finite V36() 1 -element empty-membered with_common_domain countable Element of bool NAT
0 * is non empty functional V36() FinSequence-membered FinSequenceSet of 0
{0} is non empty trivial functional finite V36() 1 -element empty-membered with_common_domain countable set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
head S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
SubWffsOf S is set
(SubWffsOf S) `1 is set
{(head S)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
phi \/ {(head S)} is non empty functional set
(((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(((AllSymbolsOf X) *) \ {{}}) typed/\ (phi \/ {(head S)}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf X) *) \ {{}})
(((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) is functional set
(((AllSymbolsOf X) *) \ {{}}) /\typed (phi \/ {(head S)}) is functional Element of bool (phi \/ {(head S)})
bool (phi \/ {(head S)}) is non empty set
SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) is set
((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) \/ {{}} : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) \/ {{}} : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
(LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of bool (AllSymbolsOf X)
(LettersOf X) typed\ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of bool (LettersOf X)
bool (LettersOf X) is non empty non trivial non finite non empty-membered set
(LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of bool (LettersOf X)
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X -firstChar) . S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))
(((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(head S) +~ (((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
phi \/ {((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))} is non empty functional set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
ExFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
phi is functional set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf X
(X,C,phi,S) is set
phi \ (X,C,phi,S) is functional Element of bool phi
bool phi is non empty set
phi typed\ (X,C,phi,S) is functional Element of bool phi
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
LettersOf X is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(X -firstChar) . S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
head S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
SubWffsOf S is set
(SubWffsOf S) `1 is set
{(head S)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
phi \/ {(head S)} is non empty functional set
(((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(((AllSymbolsOf X) *) \ {{}}) typed/\ (phi \/ {(head S)}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf X) *) \ {{}})
(((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) is functional set
(((AllSymbolsOf X) *) \ {{}}) /\typed (phi \/ {(head S)}) is functional Element of bool (phi \/ {(head S)})
bool (phi \/ {(head S)}) is non empty set
SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) is set
((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) \/ {{}} : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) \/ {{}} : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
(LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of bool (AllSymbolsOf X)
(LettersOf X) typed\ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of bool (LettersOf X)
bool (LettersOf X) is non empty non trivial non finite non empty-membered set
(LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of bool (LettersOf X)
the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))
(((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(head S) +~ (((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
{S} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (ExFormulasOf X)
bool (ExFormulasOf X) is non empty set
phi \/ {S} is non empty functional set
phi null {((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))} is set
phi \typed/ {((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))} is functional Element of bool (phi \/ {((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))})
phi \/ {((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))} is non empty functional set
bool (phi \/ {((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))}) is non empty set
HC is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
ExFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is functional set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf X
(X,C,phi,S) is set
(X,C,phi,S) \ phi is Element of bool (X,C,phi,S)
bool (X,C,phi,S) is non empty set
(X,C,phi,S) typed\ phi is Element of bool (X,C,phi,S)
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
LettersOf X is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(X -firstChar) . S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
head S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
SubWffsOf S is set
(SubWffsOf S) `1 is set
{(head S)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
phi \/ {(head S)} is non empty functional set
(((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(((AllSymbolsOf X) *) \ {{}}) typed/\ (phi \/ {(head S)}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf X) *) \ {{}})
(((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) is functional set
(((AllSymbolsOf X) *) \ {{}}) /\typed (phi \/ {(head S)}) is functional Element of bool (phi \/ {(head S)})
bool (phi \/ {(head S)}) is non empty set
SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) is set
((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) \/ {{}} : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) \/ {{}} : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
(LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of bool (AllSymbolsOf X)
(LettersOf X) typed\ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of bool (LettersOf X)
bool (LettersOf X) is non empty non trivial non finite non empty-membered set
(LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of bool (LettersOf X)
the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))
(((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(head S) +~ (((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
{S} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (ExFormulasOf X)
bool (ExFormulasOf X) is non empty set
phi \/ {S} is non empty functional set
phi \/ {((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))} is non empty functional set
{((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))} \ phi is trivial functional finite V36() with_common_domain countable Element of bool {((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))}
bool {((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))} is non empty finite V36() countable set
{((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))} typed\ phi is trivial functional finite V36() with_common_domain countable Element of bool {((((X -firstChar) . S), the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))) -SymbolSubstIn (head S))}
HC is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
ExFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is functional set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf X
(X,C,phi,S) is set
phi \/ (AllFormulasOf X) is non empty functional set
bool (phi \/ (AllFormulasOf X)) is non empty set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
LettersOf X is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(X -firstChar) . S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
head S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
SubWffsOf S is set
(SubWffsOf S) `1 is set
{(head S)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
phi \/ {(head S)} is non empty functional set
(((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
(((AllSymbolsOf X) *) \ {{}}) typed/\ (phi \/ {(head S)}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf X) *) \ {{}})
(((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) is functional set
(((AllSymbolsOf X) *) \ {{}}) /\typed (phi \/ {(head S)}) is functional Element of bool (phi \/ {(head S)})
bool (phi \/ {(head S)}) is non empty set
SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) is set
((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) \/ {{}} : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})) \/ {{}} : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) : b1 in (((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}) } is set
(LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of bool (AllSymbolsOf X)
(LettersOf X) typed\ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of bool (LettersOf X)
bool (LettersOf X) is non empty non trivial non finite non empty-membered set
(LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of bool (LettersOf X)
the Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)}))) is Element of (LettersOf X) \ (SymbolsOf ((((AllSymbolsOf X) *) \ {{}}) /\ (phi \/ {(head S)})))
{S} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (ExFormulasOf X)
bool (ExFormulasOf X) is non empty set
phi \/ {S} is non empty functional set
HC is non empty set
a is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(((X -firstChar) . S),a) -SymbolSubstIn (head S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(head S) +~ (((X -firstChar) . S),a) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf X
{sub1} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (AllFormulasOf X)
phi \/ {sub1} is non empty functional set
phi null (AllFormulasOf X) is set
phi \typed/ (AllFormulasOf X) is functional Element of bool (phi \/ (AllFormulasOf X))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
X is set
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
{phi} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
X \/ {phi} is non empty set
xnot phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ phi) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth phi)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot phi),(xnot phi)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth phi),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot phi),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
bool S is non empty set
seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheNorSymbOf C)*> ^ seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ seqt) ^ HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth seqt),(Depth HH)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot seqt),(xnot HH)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth seqt is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth HH is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth seqt),(Depth HH)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
xnot seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ seqt) ^ seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth seqt),(Depth seqt)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot seqt),(xnot seqt)}) Element of ((AllSymbolsOf C) *) \ {{}}
max ((Depth seqt),(Depth seqt)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot seqt),(xnot seqt)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
xnot HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheNorSymbOf C)*> ^ HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ HH) ^ HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth HH),(Depth HH)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot HH),(xnot HH)}) Element of ((AllSymbolsOf C) *) \ {{}}
max ((Depth HH),(Depth HH)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot HH),(xnot HH)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
{(xnot seqt),(xnot HH)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
a is set
D2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[a,seqt] is non empty V26() set
sub1 is set
sub2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[sub1,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() set
inf is (C) (C) set
inf `1 is finite countable (C) set
(inf `1) \+\ a is set
U is (C) (C) set
U `1 is finite countable (C) set
(U `1) \+\ sub1 is set
bool (X \/ {phi}) is non empty set
bool X is non empty set
II1 is finite countable (C) Element of bool (X \/ {phi})
II1 \ {phi} is finite countable Element of bool (X \/ {phi})
II1 typed\ {phi} is finite countable (C) Element of bool II1
bool II1 is non empty finite V36() countable set
II1 \ {phi} is finite countable (C) Element of bool II1
II2 is finite countable (C) Element of bool (X \/ {phi})
II2 \ {phi} is finite countable Element of bool (X \/ {phi})
II2 typed\ {phi} is finite countable (C) Element of bool II2
bool II2 is non empty finite V36() countable set
II2 \ {phi} is finite countable (C) Element of bool II2
I2 is finite countable (C) Element of bool X
II1 \ I2 is finite countable Element of bool (X \/ {phi})
II1 typed\ I2 is finite countable (C) Element of bool II1
II1 \ I2 is finite countable (C) Element of bool II1
II1 /\ {phi} is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (((AllSymbolsOf C) *) \ {{}})
II1 typed/\ {phi} is finite countable (C) Element of bool II1
II1 /\ {phi} is functional finite countable set
II1 /\typed {phi} is trivial functional finite V36() FinSequence-membered with_non-empty_elements with_common_domain countable (C) Element of bool {phi}
bool {phi} is non empty finite V36() countable set
I1 is finite countable (C) Element of bool X
II2 \ I1 is finite countable Element of bool (X \/ {phi})
II2 typed\ I1 is finite countable (C) Element of bool II2
II2 \ I1 is finite countable (C) Element of bool II2
II2 /\ {phi} is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (((AllSymbolsOf C) *) \ {{}})
II2 typed/\ {phi} is finite countable (C) Element of bool II2
II2 /\ {phi} is functional finite countable set
II2 /\typed {phi} is trivial functional finite V36() FinSequence-membered with_non-empty_elements with_common_domain countable (C) Element of bool {phi}
II1 \/ II2 is finite countable (C) Element of bool (X \/ {phi})
I1 is finite countable (C) Element of bool (X \/ {phi})
I1 \ {phi} is finite countable Element of bool (X \/ {phi})
I1 typed\ {phi} is finite countable (C) Element of bool I1
bool I1 is non empty finite V36() countable set
I1 \ {phi} is finite countable (C) Element of bool I1
I1 /\ {phi} is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (((AllSymbolsOf C) *) \ {{}})
I1 typed/\ {phi} is finite countable (C) Element of bool I1
I1 /\ {phi} is functional finite countable set
I1 /\typed {phi} is trivial functional finite V36() FinSequence-membered with_non-empty_elements with_common_domain countable (C) Element of bool {phi}
D2 + sub2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(D2 + sub2) + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
I2 is finite countable (C) Element of bool X
I2 \/ {phi} is non empty finite countable (C) set
{} null C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined C \/ (proj1 {}) -defined C \/ (proj1 {}) -defined {{}} -valued C -valued {{}} -valued C \/ (proj2 {}) -valued C \/ (proj2 {}) -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element len {} -element len {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() C -correct (C) (C) set
C \/ (proj1 {}) is set
C \/ (proj2 {}) is set
{} \typed/ C is Element of bool ({} \/ C)
{} \/ C is set
bool ({} \/ C) is non empty set
U is finite countable (C) set
[U,seqt] is non empty V26() (C) (C) set
[U,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() (C) (1,C,{(C)},{[U,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (C) set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(<*(TheNorSymbOf C)*> ^ HH) ^ seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth HH),(Depth seqt)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot HH),(xnot seqt)}) Element of ((AllSymbolsOf C) *) \ {{}}
max ((Depth HH),(Depth seqt)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot HH),(xnot seqt)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
[U,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)] is non empty V26() (C) (1,C,{(C)},{[U,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (C) set
{[U,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[U,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
sub2 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
[II1,seqt] is non empty V26() (C) (C) Element of [:(bool (X \/ {phi})),(((AllSymbolsOf C) *) \ {{}}):]
[:(bool (X \/ {phi})),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
{[II1,seqt]} is non empty trivial Relation-like non empty-yielding bool (X \/ {phi}) -defined ((AllSymbolsOf C) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() (C) Element of bool [:(bool (X \/ {phi})),(((AllSymbolsOf C) *) \ {{}}):]
bool [:(bool (X \/ {phi})),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
X2 is finite countable (C) set
II2 \/ X2 is finite countable (C) set
II1 \/ (II2 \/ X2) is finite countable (C) set
(II1 \/ (II2 \/ X2)) null (sub2 + 1) is finite countable (C) set
(II1 \/ (II2 \/ X2)) \typed/ (sub2 + 1) is finite countable Element of bool ((II1 \/ (II2 \/ X2)) \/ (sub2 + 1))
(II1 \/ (II2 \/ X2)) \/ (sub2 + 1) is non empty finite countable set
bool ((II1 \/ (II2 \/ X2)) \/ (sub2 + 1)) is non empty finite V36() countable set
[((II1 \/ (II2 \/ X2)) null (sub2 + 1)),seqt] is non empty V26() (C) (sub2 + 1,C,{(C)},{[II1,seqt]}) (C) set
[II1,seqt] is non empty V26() (C) (C) set
{[II1,seqt]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
D2 + (sub2 + 1) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
S \/ {(C)} is non empty functional Element of bool (Funcs ((bool (C)),(bool (C))))
II2 \/ {phi} is non empty finite countable (C) set
II1 \/ (II2 \/ {phi}) is non empty finite countable (C) set
[(II1 \/ (II2 \/ {phi})),seqt] is non empty V26() (C) (1,C,{(C)},{[II1,seqt]}) (C) set
H is functional Element of bool S
(C,H,S) is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S \typed/ H is functional Element of bool (S \/ H)
S \/ H is functional set
S null H is set
bool (S \/ H) is non empty set
I1 \/ {phi} is non empty finite countable (C) set
[(I1 \/ {phi}),seqt] is non empty V26() (C) (1,C,{(C)},{[I1,seqt]}) (C) set
[I1,seqt] is non empty V26() (C) (C) set
{[I1,seqt]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
X1 is trivial functional finite V36() FinSequence-membered with_non-empty_elements with_common_domain countable (C) Element of bool {phi}
I2 \/ X1 is finite countable (C) set
(I2 \/ X1) \/ {phi} is non empty finite countable (C) set
[((I2 \/ X1) \/ {phi}),seqt] is non empty V26() (C) (1,C,{(C)},{[(I2 \/ X1),seqt]}) (C) set
[(I2 \/ X1),seqt] is non empty V26() (C) (1,C,{(C)},{[I2,seqt]}) (C) set
[I2,seqt] is non empty V26() (C) (C) set
{[I2,seqt]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[(I2 \/ X1),seqt]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
(C,X1,{phi}) is functional finite V36() FinSequence-membered with_non-empty_elements countable (C) Element of bool (AllFormulasOf C)
{phi} \typed/ X1 is functional finite V36() with_non-empty_elements countable (C) Element of bool ({phi} \/ X1)
{phi} \/ X1 is non empty functional finite V36() with_non-empty_elements non empty-membered countable (C) set
{phi} null X1 is finite countable (C) set
bool ({phi} \/ X1) is non empty finite V36() countable set
I2 \/ (C,X1,{phi}) is finite countable (C) set
[(I2 \/ (C,X1,{phi})),seqt] is non empty V26() (C) (1,C,{(C)},{[I2,seqt]}) (C) set
D2 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
[II2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() (C) (1,C,{(C)},{[II2,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (C) Element of [:(bool (X \/ {phi})),(((AllSymbolsOf C) *) \ {{}}):]
[II2,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)] is non empty V26() (C) (1,C,{(C)},{[II2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (C) set
[II2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() (C) (1,C,{(C)},{[II2,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (C) set
{[II2,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[II2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[II2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty trivial Relation-like non empty-yielding bool (X \/ {phi}) -defined ((AllSymbolsOf C) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() (C) Element of bool [:(bool (X \/ {phi})),(((AllSymbolsOf C) *) \ {{}}):]
II1 \/ {phi} is non empty finite countable (C) set
II2 \/ (II1 \/ {phi}) is non empty finite countable (C) set
(II2 \/ (II1 \/ {phi})) null (D2 + 1) is finite countable (C) set
(II2 \/ (II1 \/ {phi})) \typed/ (D2 + 1) is finite countable Element of bool ((II2 \/ (II1 \/ {phi})) \/ (D2 + 1))
(II2 \/ (II1 \/ {phi})) \/ (D2 + 1) is non empty finite countable set
bool ((II2 \/ (II1 \/ {phi})) \/ (D2 + 1)) is non empty finite V36() countable set
[((II2 \/ (II1 \/ {phi})) null (D2 + 1)),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() (C) (1,C,{(C)},{[((II2 \/ (II1 \/ {phi})) null (D2 + 1)),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (D2 + 1,C,{(C)},{[II2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (C) set
[((II2 \/ (II1 \/ {phi})) null (D2 + 1)),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)] is non empty V26() (C) (1,C,{(C)},{[((II2 \/ (II1 \/ {phi})) null (D2 + 1)),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (D2 + 1,C,{(C)},{[II2,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (C) set
{[((II2 \/ (II1 \/ {phi})) null (D2 + 1)),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[((II2 \/ (II1 \/ {phi})) null (D2 + 1)),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
sub2 + (D2 + 1) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
[(II2 \/ (II1 \/ {phi})),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() (C) (1,C,{(C)},{[II2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (1,C,{(C)},{[(II2 \/ (II1 \/ {phi})),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (C) set
[(II2 \/ (II1 \/ {phi})),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)] is non empty V26() (C) (1,C,{(C)},{[II2,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (1,C,{(C)},{[(II2 \/ (II1 \/ {phi})),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (C) set
{[(II2 \/ (II1 \/ {phi})),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[(II2 \/ (II1 \/ {phi})),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[(I1 \/ {phi}),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() (C) (1,C,{(C)},{[I1,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (1,C,{(C)},{[(I1 \/ {phi}),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (C) set
[I1,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() (C) (1,C,{(C)},{[I1,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (C) set
[I1,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)] is non empty V26() (C) (1,C,{(C)},{[I1,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (C) set
{[I1,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[I1,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[(I1 \/ {phi}),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)] is non empty V26() (C) (1,C,{(C)},{[I1,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (1,C,{(C)},{[(I1 \/ {phi}),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (C) set
{[(I1 \/ {phi}),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[(I1 \/ {phi}),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[((I2 \/ X1) \/ {phi}),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() (C) (1,C,{(C)},{[(I2 \/ X1),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (1,C,{(C)},{[((I2 \/ X1) \/ {phi}),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (C) set
[(I2 \/ X1),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() (C) (1,C,{(C)},{[I2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (1,C,{(C)},{[(I2 \/ X1),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (C) set
[I2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() (C) (1,C,{(C)},{[I2,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (C) set
[I2,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)] is non empty V26() (C) (1,C,{(C)},{[I2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (C) set
{[I2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[I2,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[(I2 \/ X1),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)] is non empty V26() (C) (1,C,{(C)},{[I2,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (1,C,{(C)},{[(I2 \/ X1),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (C) set
{[(I2 \/ X1),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[(I2 \/ X1),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[((I2 \/ X1) \/ {phi}),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)] is non empty V26() (C) (1,C,{(C)},{[(I2 \/ X1),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (1,C,{(C)},{[((I2 \/ X1) \/ {phi}),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (C) set
{[((I2 \/ X1) \/ {phi}),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[((I2 \/ X1) \/ {phi}),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[(I2 \/ (C,X1,{phi})),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() (C) (1,C,{(C)},{[I2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (1,C,{(C)},{[(I2 \/ (C,X1,{phi})),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (C) set
[(I2 \/ (C,X1,{phi})),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)] is non empty V26() (C) (1,C,{(C)},{[I2,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (1,C,{(C)},{[(I2 \/ (C,X1,{phi})),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (C) set
{[(I2 \/ (C,X1,{phi})),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[(I2 \/ (C,X1,{phi})),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[(I2 \/ {phi}),seqt] is non empty V26() (C) (1,C,{(C)},{[I2,seqt]}) (C) set
[(I2 \/ {phi}),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)] is non empty V26() (C) (1,C,{(C)},{[I2,((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (1,C,{(C)},{[(I2 \/ {phi}),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (C) set
[(I2 \/ {phi}),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)] is non empty V26() (C) (1,C,{(C)},{[I2,((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]}) (1,C,{(C)},{[(I2 \/ {phi}),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (C) set
{[(I2 \/ {phi}),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[(I2 \/ {phi}),((<*(TheNorSymbOf C)*> ^ HH) ^ seqt)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[(I2 \/ {phi}),seqt],[(I2 \/ {phi}),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]} is non empty Relation-like finite with_non-empty_elements non empty-membered countable (C) set
seqt ^ HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
I2 null (seqt ^ HH) is finite countable (C) set
I2 \typed/ (seqt ^ HH) is finite countable Element of bool (I2 \/ (seqt ^ HH))
I2 \/ (seqt ^ HH) is non empty finite countable set
bool (I2 \/ (seqt ^ HH)) is non empty finite V36() countable set
[(I2 null (seqt ^ HH)),(xnot phi)] is non empty V26() (C) (1,C,{(C)},{[(I2 \/ {phi}),seqt],[(I2 \/ {phi}),((<*(TheNorSymbOf C)*> ^ seqt) ^ HH)]}) (C) set
((D2 + sub2) + 1) + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
S \/ S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
(S \/ S) \/ {(C)} is non empty functional Element of bool (Funcs ((bool (C)),(bool (C))))
I is (C) set
I \/ I is (C) set
[I2,(xnot phi)] is non empty V26() (C) (C) Element of [:(bool X),(((AllSymbolsOf C) *) \ {{}}):]
[:(bool X),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
m is functional Element of bool S
(C,m,S) is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S \typed/ m is functional Element of bool (S \/ m)
S \/ m is functional set
S null m is set
bool (S \/ m) is non empty set
X is set
bool X is non empty set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
DD is finite countable Element of bool X
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheNorSymbOf C)*> ^ DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ DD) ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth DD),(Depth FF)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot DD),(xnot FF)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth DD is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth FF is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth DD),(Depth FF)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
xnot DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ DD) ^ DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth DD),(Depth DD)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot DD),(xnot DD)}) Element of ((AllSymbolsOf C) *) \ {{}}
max ((Depth DD),(Depth DD)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot DD),(xnot DD)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
xnot FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheNorSymbOf C)*> ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ FF) ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth FF),(Depth FF)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot FF),(xnot FF)}) Element of ((AllSymbolsOf C) *) \ {{}}
max ((Depth FF),(Depth FF)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot FF),(xnot FF)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
{(xnot DD),(xnot FF)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
Y is set
phii is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[Y,DD] is non empty V26() set
D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
psi is set
H is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[psi,D] is non empty V26() set
m is (C) (C) set
m `1 is finite countable (C) set
(m `1) \+\ Y is set
seqt is (C) (C) set
seqt `1 is finite countable (C) set
(seqt `1) \+\ psi is set
Y null psi is set
Y \typed/ psi is Element of bool (Y \/ psi)
Y \/ psi is set
bool (Y \/ psi) is non empty set
psi null Y is set
psi \typed/ Y is Element of bool (psi \/ Y)
psi \/ Y is set
bool (psi \/ Y) is non empty set
HH is finite countable (C) Element of bool X
HC is finite countable (C) Element of bool X
HH \/ HC is finite countable (C) Element of bool X
X is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
xnot FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ FF) ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth FF),(Depth FF)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot FF),(xnot FF)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth FF is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth FF),(Depth FF)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot FF),(xnot FF)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
xnot FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ FF) ^ FF is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth FF),(Depth FF)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot FF),(xnot FF)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth FF is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth FF),(Depth FF)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot FF),(xnot FF)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
xnot D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheNorSymbOf C)*> ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ D) ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth D),(Depth D)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot D),(xnot D)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth D is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth D),(Depth D)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot D),(xnot D)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
FF is set
D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
xnot D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ D) ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth D),(Depth D)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot D),(xnot D)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth D is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth D),(Depth D)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot D),(xnot D)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
X is set
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
{phi} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
X \/ {phi} is non empty set
S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
xnot phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ phi) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth phi)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot phi),(xnot phi)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth phi),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot phi),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
X is non empty set
X * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of X
X \/ BOOLEAN is non empty set
K491((X *),(X \/ BOOLEAN)) is non empty functional M30(X * ,X \/ BOOLEAN)
C is set
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
OwnSymbolsOf phi is non empty Element of bool (AllSymbolsOf phi)
bool (AllSymbolsOf phi) is non empty non trivial non finite non empty-membered set
the U2 of phi is Element of the U1 of phi
the U3 of phi is Element of the U1 of phi
{ the U2 of phi, the U3 of phi} is non empty finite countable set
the U1 of phi \ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
bool the U1 of phi is non empty set
the U1 of phi typed\ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
Funcs ((OwnSymbolsOf phi),K491((X *),(X \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf phi,K491((X *),(X \/ BOOLEAN))
X -InterpretersOf phi is non empty functional Element of bool (Funcs ((OwnSymbolsOf phi),K491((X *),(X \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf phi),K491((X *),(X \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf phi -defined K491((X *),(X \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf phi),K491((X *),(X \/ BOOLEAN))) : b1 is phi,X -interpreter-like } is set
S is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
TheNorSymbOf phi is non literal non low-compounding non relational non own Element of AllSymbolsOf phi
FF is Relation-like OwnSymbolsOf phi -defined Function-like total Function-yielding V156() phi,X -interpreter-like Element of X -InterpretersOf phi
<*(TheNorSymbOf phi)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}}
[1,(TheNorSymbOf phi)] is non empty V26() set
{[1,(TheNorSymbOf phi)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}}
<*(TheNorSymbOf phi)*> ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf phi) *) \ {{}}
Y is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}}
(<*(TheNorSymbOf phi)*> ^ D) ^ Y is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth D),(Depth Y)) -wff wff non exal (phi,{(phi)} \/ {(phi)},{(xnot D),(xnot Y)}) Element of ((AllSymbolsOf phi) *) \ {{}}
Depth D is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth Y is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth D),(Depth Y)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(phi) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total (phi) Element of Funcs ((bool (phi)),(bool (phi)))
(phi) is Relation-like bool (phi) -defined (phi) -valued Element of bool [:(bool (phi)),(phi):]
[:(bool (phi)),(phi):] is non empty Relation-like set
bool [:(bool (phi)),(phi):] is non empty set
(phi,(phi)) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
{(phi)} is non empty trivial functional finite 1 -element with_common_domain countable (phi) Element of bool (Funcs ((bool (phi)),(bool (phi))))
(phi) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total (phi) Element of Funcs ((bool (phi)),(bool (phi)))
(phi) is Relation-like bool (phi) -defined (phi) -valued Element of bool [:(bool (phi)),(phi):]
(phi,(phi)) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
{(phi)} is non empty trivial functional finite 1 -element with_common_domain countable (phi) Element of bool (Funcs ((bool (phi)),(bool (phi))))
{(phi)} \/ {(phi)} is non empty functional finite countable (phi) Element of bool (Funcs ((bool (phi)),(bool (phi))))
xnot D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}}
(<*(TheNorSymbOf phi)*> ^ D) ^ D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth D),(Depth D)) -wff wff non exal (phi,{(phi)} \/ {(phi)},{(xnot D),(xnot D)}) Element of ((AllSymbolsOf phi) *) \ {{}}
max ((Depth D),(Depth D)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot D),(xnot D)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf phi) *) \ {{}})
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
xnot Y is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}}
<*(TheNorSymbOf phi)*> ^ Y is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf phi) *) \ {{}}
(<*(TheNorSymbOf phi)*> ^ Y) ^ Y is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth Y),(Depth Y)) -wff wff non exal (phi,{(phi)} \/ {(phi)},{(xnot Y),(xnot Y)}) Element of ((AllSymbolsOf phi) *) \ {{}}
max ((Depth Y),(Depth Y)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot Y),(xnot Y)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf phi) *) \ {{}})
{(xnot D),(xnot Y)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf phi) *) \ {{}})
FF -TruthEval D is boolean Element of BOOLEAN
FF -TruthEval ((<*(TheNorSymbOf phi)*> ^ D) ^ Y) is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
TermSymbolsOf X is non empty set
the U1 of X is set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
C is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ C is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ C) ^ phi is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
SubTerms ((<*(TheEqSymbOf X)*> ^ C) ^ phi) is Relation-like NAT -defined (proj2 ((<*(TheEqSymbOf X)*> ^ C) ^ phi)) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ C) ^ phi))) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(X -firstChar) . ((<*(TheEqSymbOf X)*> ^ C) ^ phi) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ C) ^ phi)) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ C) ^ phi)) is set
abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ C) ^ phi))) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
proj2 ((<*(TheEqSymbOf X)*> ^ C) ^ phi) is non empty finite countable set
(proj2 ((<*(TheEqSymbOf X)*> ^ C) ^ phi)) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 ((<*(TheEqSymbOf X)*> ^ C) ^ phi)
(TermSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V36() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
<*C,phi*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V209() set
<*C*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,C] is non empty V26() set
{[1,C]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*phi*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,phi] is non empty V26() set
{[1,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*C*> ^ <*phi*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element 1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
1 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
1 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(SubTerms ((<*(TheEqSymbOf X)*> ^ C) ^ phi)) \+\ <*C,phi*> is Relation-like finite countable set
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
DD is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
SubTerms DD is Relation-like NAT -defined (proj2 DD) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . DD)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
(X -firstChar) . DD is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
ar ((X -firstChar) . DD) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . DD) is set
abs (ar ((X -firstChar) . DD)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
proj2 DD is non empty finite countable set
(proj2 DD) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 DD
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
2 -tuples_on (AllTermsOf X) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of AllTermsOf X
{ <*b1,b2*> where b1, b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X : verum } is set
C ^ phi is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ (C ^ phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ (C ^ phi)) . 1 is set
((<*(TheEqSymbOf X)*> ^ (C ^ phi)) . 1) \+\ (TheEqSymbOf X) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
DD . 1 is set
(X -multiCat) . (SubTerms DD) is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*(TheEqSymbOf X)*> ^ ((X -multiCat) . (SubTerms DD)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
ar (TheEqSymbOf X) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . (TheEqSymbOf X) is set
abs (ar (TheEqSymbOf X)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar (TheEqSymbOf X))) - 2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
((abs (ar (TheEqSymbOf X))) - 2) + 2 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
0 + 2 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
<*seqt,HH*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V209() set
<*seqt*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,seqt] is non empty V26() set
{[1,seqt]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*HH*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,HH] is non empty V26() set
{[1,HH]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*seqt*> ^ <*HH*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element 1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
HC is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() set
a is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() set
<*HC,a*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V209() set
<*HC*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,HC] is non empty V26() set
{[1,HC]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*a*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,a] is non empty V26() set
{[1,a]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*HC*> ^ <*a*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element 1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
(X -multiCat) . <*HC,a*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
HC ^ a is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() set
((X -multiCat) . <*HC,a*>) \+\ (HC ^ a) is Relation-like finite countable set
D2 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() set
sub1 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() set
D2 ^ sub1 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() set
sub2 is set
X is non empty set
C is V51() V53() eligible Language-like
TermSymbolsOf C is non empty set
the U1 of C is set
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U2 of C is Element of the U1 of C
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
phi is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheEqSymbOf C)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
S is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ phi) ^ S is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf C) *) \ {{}}
AtomicFormulaSymbolsOf C is non empty Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
TheNorSymbOf C is set
{(TheNorSymbOf C)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf C) \ {(TheNorSymbOf C)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) typed\ {(TheNorSymbOf C)} is Element of bool (AllSymbolsOf C)
SubTerms ((<*(TheEqSymbOf C)*> ^ phi) ^ S) is Relation-like NAT -defined (proj2 ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) * -valued (TermSymbolsOf C) * -valued AllTermsOf C -valued Function-like finite abs (ar ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S))) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf C) *
C -firstChar is non empty Relation-like ((AllSymbolsOf C) *) \ {{}} -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):]
[:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) -firstChar is non empty Relation-like ((AllSymbolsOf C) *) \ {{}} -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):]
(AllSymbolsOf C) -pr1 is non empty Relation-like [:(AllSymbolsOf C),(AllSymbolsOf C):] -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):]
[:(AllSymbolsOf C),(AllSymbolsOf C):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf C),(AllSymbolsOf C)) is non empty Relation-like [:(AllSymbolsOf C),(AllSymbolsOf C):] -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):]
MultPlace ((AllSymbolsOf C) -pr1) is non empty Relation-like ((AllSymbolsOf C) *) \ {{}} -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):]
(C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf C
ar ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of C . ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) is set
abs (ar ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S))) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
proj2 ((<*(TheEqSymbOf C)*> ^ phi) ^ S) is non empty finite countable set
(proj2 ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 ((<*(TheEqSymbOf C)*> ^ phi) ^ S)
(TermSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of TermSymbolsOf C
AllTermsOf C is non empty functional V36() FinSequence-membered AllSymbolsOf C -prefix C -prefix Element of bool ((AllSymbolsOf C) *)
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
((AllSymbolsOf C) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf C) *
(AllTermsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf C) *) *)
bool (((AllSymbolsOf C) *) *) is non empty non trivial non finite non empty-membered set
phi ^ S is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheEqSymbOf C)*> ^ (phi ^ S) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ (phi ^ S)) . 1 is set
((<*(TheEqSymbOf C)*> ^ (phi ^ S)) . 1) \+\ (TheEqSymbOf C) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
((<*(TheEqSymbOf C)*> ^ phi) ^ S) . 1 is set
<*phi,S*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V209() set
<*phi*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,phi] is non empty V26() set
{[1,phi]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*S*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,S] is non empty V26() set
{[1,S]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*phi*> ^ <*S*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element 1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
(SubTerms ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) \+\ <*phi,S*> is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(SubTerms ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(SubTerms ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) . 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
phii is Relation-like Function-like Function-yielding V156() C,X -interpreter-like set
phii -AtomicEval ((<*(TheEqSymbOf C)*> ^ phi) ^ S) is boolean Element of BOOLEAN
phii === is Relation-like Function-like Function-yielding V156() C,X -interpreter-like phii -extension set
TheEqSymbOf C is Element of AtomicFormulaSymbolsOf C
X -deltaInterpreter is non empty Relation-like 2 -tuples_on X -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on X),BOOLEAN:]
2 -tuples_on X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of X
[:(2 -tuples_on X),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on X),BOOLEAN:] is non empty set
X * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of X
[:(X *),(X *):] is non empty non trivial Relation-like non finite non empty-membered set
K295(X) is non empty Relation-like [:(X *),(X *):] -defined X * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:(X *),(X *):],(X *):]
[:[:(X *),(X *):],(X *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(X *),(X *):],(X *):] is non empty non trivial non finite non empty-membered set
1 -tuples_on X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of X
id (1 -tuples_on X) is non empty Relation-like non-empty non empty-yielding 1 -tuples_on X -defined 1 -tuples_on X -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(1 -tuples_on X),(1 -tuples_on X):]
[:(1 -tuples_on X),(1 -tuples_on X):] is non empty Relation-like set
bool [:(1 -tuples_on X),(1 -tuples_on X):] is non empty set
K295(X) .: (id (1 -tuples_on X)) is functional V36() FinSequence-membered Element of bool (X *)
bool (X *) is non empty non trivial non finite non empty-membered set
chi ((K295(X) .: (id (1 -tuples_on X))),(2 -tuples_on X)) is non empty Relation-like 2 -tuples_on X -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on X),BOOLEAN:]
(TheEqSymbOf C) .--> (X -deltaInterpreter) is non empty trivial Relation-like AtomicFormulaSymbolsOf C -defined {(TheEqSymbOf C)} -defined bool [:(2 -tuples_on X),BOOLEAN:] -valued Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{(TheEqSymbOf C)} is non empty trivial finite 1 -element countable set
{(TheEqSymbOf C)} --> (X -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf C)} -defined bool [:(2 -tuples_on X),BOOLEAN:] -valued {(X -deltaInterpreter)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{(TheEqSymbOf C)},{(X -deltaInterpreter)}:]
{(X -deltaInterpreter)} is non empty trivial functional finite 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{(TheEqSymbOf C)},{(X -deltaInterpreter)}:] is non empty Relation-like finite countable set
bool [:{(TheEqSymbOf C)},{(X -deltaInterpreter)}:] is non empty finite V36() countable set
phii +* ((TheEqSymbOf C) .--> (X -deltaInterpreter)) is non empty Relation-like Function-like Function-yielding V156() set
(phii ===) . ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) is non empty Relation-like (abs (ar ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S)))) -tuples_on X -defined X \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S),X
(abs (ar ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S)))) -tuples_on X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of X
X \/ BOOLEAN is non empty set
phii -TermEval is non empty Relation-like AllTermsOf C -defined X -valued Function-like total quasi_total Element of bool [:(AllTermsOf C),X:]
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
[:(AllTermsOf C),X:] is non empty Relation-like set
bool [:(AllTermsOf C),X:] is non empty set
(SubTerms ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) * (phii -TermEval) is Relation-like NAT -defined X -valued Function-like finite countable V209() set
((phii ===) . ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S))) . ((SubTerms ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) * (phii -TermEval)) is set
(phii -TermEval) . phi is set
(phii -TermEval) . S is set
psi is Relation-like Function-like Function-yielding V156() C,X -interpreter-like set
psi -TermEval is non empty Relation-like AllTermsOf C -defined X -valued Function-like total quasi_total Element of bool [:(AllTermsOf C),X:]
(psi -TermEval) . phi is set
(psi -TermEval) . S is set
psi -AtomicEval ((<*(TheEqSymbOf C)*> ^ phi) ^ S) is boolean Element of BOOLEAN
psi === is Relation-like Function-like Function-yielding V156() C,X -interpreter-like psi -extension set
psi +* ((TheEqSymbOf C) .--> (X -deltaInterpreter)) is non empty Relation-like Function-like Function-yielding V156() set
(psi ===) . ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) is non empty Relation-like (abs (ar ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S)))) -tuples_on X -defined X \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S),X
(SubTerms ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) * (psi -TermEval) is Relation-like NAT -defined X -valued Function-like finite countable V209() set
((psi ===) . ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ phi) ^ S))) . ((SubTerms ((<*(TheEqSymbOf C)*> ^ phi) ^ S)) * (psi -TermEval)) is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
X is V51() V53() eligible Language-like
C is set
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
DD is set
FF is non empty set
FF -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((FF *),(FF \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
FF * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of FF
FF \/ BOOLEAN is non empty set
K491((FF *),(FF \/ BOOLEAN)) is non empty functional M30(FF * ,FF \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((FF *),(FF \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((FF *),(FF \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((FF *),(FF \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((FF *),(FF \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((FF *),(FF \/ BOOLEAN))) : b1 is X,FF -interpreter-like } is set
Y is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,FF -interpreter-like Element of FF -InterpretersOf X
phii is Y -satisfied set
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[phii,psi] is non empty V26() set
dom (X) is Element of bool (bool (X))
bool (bool (X)) is non empty set
[phii,psi] `1 is set
[phii,psi] `2 is set
(X) . DD is set
[DD,[phii,psi]] is non empty V26() set
m is Relation-like (X) Element of bool (X)
seqt is (X) (X) Element of (X)
Y -TruthEval psi is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
m is set
seqt is non empty set
seqt -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
seqt * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of seqt
seqt \/ BOOLEAN is non empty set
K491((seqt *),(seqt \/ BOOLEAN)) is non empty functional M30(seqt * ,seqt \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((seqt *),(seqt \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((seqt *),(seqt \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) : b1 is X,seqt -interpreter-like } is set
HC is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,seqt -interpreter-like Element of seqt -InterpretersOf X
a is HC -satisfied set
D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[a,D2] is non empty V26() set
HC -TermEval is non empty Relation-like AllTermsOf X -defined seqt -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),seqt:]
[:(AllTermsOf X),seqt:] is non empty Relation-like set
bool [:(AllTermsOf X),seqt:] is non empty set
seqt -deltaInterpreter is non empty Relation-like 2 -tuples_on seqt -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on seqt),BOOLEAN:]
2 -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
[:(2 -tuples_on seqt),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on seqt),BOOLEAN:] is non empty set
[:(seqt *),(seqt *):] is non empty non trivial Relation-like non finite non empty-membered set
K295(seqt) is non empty Relation-like [:(seqt *),(seqt *):] -defined seqt * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:(seqt *),(seqt *):],(seqt *):]
[:[:(seqt *),(seqt *):],(seqt *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(seqt *),(seqt *):],(seqt *):] is non empty non trivial non finite non empty-membered set
1 -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
id (1 -tuples_on seqt) is non empty Relation-like non-empty non empty-yielding 1 -tuples_on seqt -defined 1 -tuples_on seqt -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(1 -tuples_on seqt),(1 -tuples_on seqt):]
[:(1 -tuples_on seqt),(1 -tuples_on seqt):] is non empty Relation-like set
bool [:(1 -tuples_on seqt),(1 -tuples_on seqt):] is non empty set
K295(seqt) .: (id (1 -tuples_on seqt)) is functional V36() FinSequence-membered Element of bool (seqt *)
bool (seqt *) is non empty non trivial non finite non empty-membered set
chi ((K295(seqt) .: (id (1 -tuples_on seqt))),(2 -tuples_on seqt)) is non empty Relation-like 2 -tuples_on seqt -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on seqt),BOOLEAN:]
[a,D2] `1 is set
([a,D2] `1) \+\ a is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[a,D2] `2 is set
([a,D2] `2) \+\ D2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
dom (X) is Element of bool (bool (X))
bool (bool (X)) is non empty set
(X) . m is set
[m,[a,D2]] is non empty V26() set
U is Relation-like X -correct (X) Element of bool (X)
II1 is (X) (X) Element of (X)
II1 `1 is finite countable (X) set
II1 `2 is set
II2 is set
II2 `1 is set
II2 `2 is set
bool a is non empty set
I2 is HC -satisfied Element of bool a
[I2,D2] is non empty V26() Element of [:(bool a),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool a),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
HC -TruthEval D2 is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
m is set
seqt is non empty set
seqt -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
seqt * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of seqt
seqt \/ BOOLEAN is non empty set
K491((seqt *),(seqt \/ BOOLEAN)) is non empty functional M30(seqt * ,seqt \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((seqt *),(seqt \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((seqt *),(seqt \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) : b1 is X,seqt -interpreter-like } is set
HC is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,seqt -interpreter-like Element of seqt -InterpretersOf X
a is HC -satisfied set
D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[a,D2] is non empty V26() set
HC -TermEval is non empty Relation-like AllTermsOf X -defined seqt -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),seqt:]
[:(AllTermsOf X),seqt:] is non empty Relation-like set
bool [:(AllTermsOf X),seqt:] is non empty set
seqt -deltaInterpreter is non empty Relation-like 2 -tuples_on seqt -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on seqt),BOOLEAN:]
2 -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
[:(2 -tuples_on seqt),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on seqt),BOOLEAN:] is non empty set
[:(seqt *),(seqt *):] is non empty non trivial Relation-like non finite non empty-membered set
K295(seqt) is non empty Relation-like [:(seqt *),(seqt *):] -defined seqt * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:(seqt *),(seqt *):],(seqt *):]
[:[:(seqt *),(seqt *):],(seqt *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(seqt *),(seqt *):],(seqt *):] is non empty non trivial non finite non empty-membered set
1 -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
id (1 -tuples_on seqt) is non empty Relation-like non-empty non empty-yielding 1 -tuples_on seqt -defined 1 -tuples_on seqt -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(1 -tuples_on seqt),(1 -tuples_on seqt):]
[:(1 -tuples_on seqt),(1 -tuples_on seqt):] is non empty Relation-like set
bool [:(1 -tuples_on seqt),(1 -tuples_on seqt):] is non empty set
K295(seqt) .: (id (1 -tuples_on seqt)) is functional V36() FinSequence-membered Element of bool (seqt *)
bool (seqt *) is non empty non trivial non finite non empty-membered set
chi ((K295(seqt) .: (id (1 -tuples_on seqt))),(2 -tuples_on seqt)) is non empty Relation-like 2 -tuples_on seqt -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on seqt),BOOLEAN:]
[a,D2] `1 is set
([a,D2] `1) \+\ a is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[a,D2] `2 is set
([a,D2] `2) \+\ D2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(X) . m is set
[m,[a,D2]] is non empty V26() set
dom (X) is Element of bool (bool (X))
bool (bool (X)) is non empty set
U is Relation-like X -correct (X) Element of bool (X)
II1 is (X) (X) Element of (X)
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
II1 `2 is set
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
II2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ II2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ II2) ^ II2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
(HC -TermEval) . II2 is set
HC -AtomicEval ((<*(TheEqSymbOf X)*> ^ II2) ^ II2) is boolean Element of BOOLEAN
HC === is Relation-like Function-like Function-yielding V156() X,seqt -interpreter-like HC -extension set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
(TheEqSymbOf X) .--> (seqt -deltaInterpreter) is non empty trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on seqt),BOOLEAN:] -valued Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element countable set
{(TheEqSymbOf X)} --> (seqt -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on seqt),BOOLEAN:] -valued {(seqt -deltaInterpreter)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:]
{(seqt -deltaInterpreter)} is non empty trivial functional finite 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:] is non empty Relation-like finite countable set
bool [:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:] is non empty finite V36() countable set
HC +* ((TheEqSymbOf X) .--> (seqt -deltaInterpreter)) is non empty Relation-like Function-like Function-yielding V156() set
(X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ II2) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(HC ===) . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ II2)) is non empty Relation-like (abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ II2)))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ II2),seqt
ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ II2)) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ II2)) is set
abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ II2))) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ II2)))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
SubTerms ((<*(TheEqSymbOf X)*> ^ II2) ^ II2) is Relation-like NAT -defined (proj2 ((<*(TheEqSymbOf X)*> ^ II2) ^ II2)) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ II2))) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 ((<*(TheEqSymbOf X)*> ^ II2) ^ II2) is non empty finite countable set
(proj2 ((<*(TheEqSymbOf X)*> ^ II2) ^ II2)) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 ((<*(TheEqSymbOf X)*> ^ II2) ^ II2)
(TermSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V36() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf X) *) *)
(SubTerms ((<*(TheEqSymbOf X)*> ^ II2) ^ II2)) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite countable V209() set
((HC ===) . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ II2))) . ((SubTerms ((<*(TheEqSymbOf X)*> ^ II2) ^ II2)) * (HC -TermEval)) is set
HC -TruthEval ((<*(TheEqSymbOf X)*> ^ II2) ^ II2) is boolean Element of BOOLEAN
HC -TruthEval D2 is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
m is set
seqt is non empty set
seqt -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
seqt * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of seqt
seqt \/ BOOLEAN is non empty set
K491((seqt *),(seqt \/ BOOLEAN)) is non empty functional M30(seqt * ,seqt \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((seqt *),(seqt \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((seqt *),(seqt \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) : b1 is X,seqt -interpreter-like } is set
HC is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,seqt -interpreter-like Element of seqt -InterpretersOf X
a is HC -satisfied set
D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[a,D2] is non empty V26() set
HC -TermEval is non empty Relation-like AllTermsOf X -defined seqt -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),seqt:]
[:(AllTermsOf X),seqt:] is non empty Relation-like set
bool [:(AllTermsOf X),seqt:] is non empty set
seqt -deltaInterpreter is non empty Relation-like 2 -tuples_on seqt -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on seqt),BOOLEAN:]
2 -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
[:(2 -tuples_on seqt),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on seqt),BOOLEAN:] is non empty set
[:(seqt *),(seqt *):] is non empty non trivial Relation-like non finite non empty-membered set
K295(seqt) is non empty Relation-like [:(seqt *),(seqt *):] -defined seqt * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:(seqt *),(seqt *):],(seqt *):]
[:[:(seqt *),(seqt *):],(seqt *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(seqt *),(seqt *):],(seqt *):] is non empty non trivial non finite non empty-membered set
1 -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
id (1 -tuples_on seqt) is non empty Relation-like non-empty non empty-yielding 1 -tuples_on seqt -defined 1 -tuples_on seqt -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(1 -tuples_on seqt),(1 -tuples_on seqt):]
[:(1 -tuples_on seqt),(1 -tuples_on seqt):] is non empty Relation-like set
bool [:(1 -tuples_on seqt),(1 -tuples_on seqt):] is non empty set
K295(seqt) .: (id (1 -tuples_on seqt)) is functional V36() FinSequence-membered Element of bool (seqt *)
bool (seqt *) is non empty non trivial non finite non empty-membered set
chi ((K295(seqt) .: (id (1 -tuples_on seqt))),(2 -tuples_on seqt)) is non empty Relation-like 2 -tuples_on seqt -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on seqt),BOOLEAN:]
[a,D2] `1 is set
([a,D2] `1) \+\ a is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[a,D2] `2 is set
([a,D2] `2) \+\ D2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(X) . m is set
[m,[a,D2]] is non empty V26() set
dom (X) is Element of bool (bool (X))
bool (bool (X)) is non empty set
U is Relation-like X -correct (X) Element of bool (X)
II1 is (X) (X) Element of (X)
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
II1 `1 is finite countable (X) set
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
II1 `2 is set
c26 is set
c26 `1 is set
I2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ I2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
I1 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ I2) ^ I1 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
{((<*(TheEqSymbOf X)*> ^ I2) ^ I1)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
(c26 `1) \/ {((<*(TheEqSymbOf X)*> ^ I2) ^ I1)} is non empty set
c26 `2 is set
II2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ II2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ II2) ^ I2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ II2) ^ I1 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
bool a is non empty set
I2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
{I2} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
(c26 `1) null {I2} is set
(c26 `1) \typed/ {I2} is Element of bool ((c26 `1) \/ {I2})
(c26 `1) \/ {I2} is non empty set
bool ((c26 `1) \/ {I2}) is non empty set
{I2} null (c26 `1) is finite countable (X) set
{I2} \typed/ (c26 `1) is Element of bool ({I2} \/ (c26 `1))
{I2} \/ (c26 `1) is non empty set
bool ({I2} \/ (c26 `1)) is non empty set
X1 is HC -satisfied Element of bool a
I02 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
[X1,I02] is non empty V26() Element of [:(bool a),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool a),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
HC -TruthEval I02 is boolean Element of BOOLEAN
HC -AtomicEval I02 is boolean Element of BOOLEAN
HC === is Relation-like Function-like Function-yielding V156() X,seqt -interpreter-like HC -extension set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
(TheEqSymbOf X) .--> (seqt -deltaInterpreter) is non empty trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on seqt),BOOLEAN:] -valued Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element countable set
{(TheEqSymbOf X)} --> (seqt -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on seqt),BOOLEAN:] -valued {(seqt -deltaInterpreter)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:]
{(seqt -deltaInterpreter)} is non empty trivial functional finite 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:] is non empty Relation-like finite countable set
bool [:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:] is non empty finite V36() countable set
HC +* ((TheEqSymbOf X) .--> (seqt -deltaInterpreter)) is non empty Relation-like Function-like Function-yielding V156() set
(X -firstChar) . I02 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(HC ===) . ((X -firstChar) . I02) is non empty Relation-like (abs (ar ((X -firstChar) . I02))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . I02,seqt
ar ((X -firstChar) . I02) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . I02) is set
abs (ar ((X -firstChar) . I02)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar ((X -firstChar) . I02))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
SubTerms I02 is Relation-like NAT -defined (proj2 I02) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . I02)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 I02 is non empty finite countable set
(proj2 I02) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 I02
(TermSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V36() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf X) *) *)
(SubTerms I02) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite countable V209() set
((HC ===) . ((X -firstChar) . I02)) . ((SubTerms I02) * (HC -TermEval)) is set
I1 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
(HC -TermEval) . II2 is set
(HC -TermEval) . I2 is set
X2 is HC -satisfied Element of bool a
HC -TruthEval I2 is boolean Element of BOOLEAN
HC -AtomicEval I2 is boolean Element of BOOLEAN
(X -firstChar) . I2 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(HC ===) . ((X -firstChar) . I2) is non empty Relation-like (abs (ar ((X -firstChar) . I2))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . I2,seqt
ar ((X -firstChar) . I2) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . I2) is set
abs (ar ((X -firstChar) . I2)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar ((X -firstChar) . I2))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
SubTerms I2 is Relation-like NAT -defined (proj2 I2) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . I2)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 I2 is non empty finite countable set
(proj2 I2) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 I2
(SubTerms I2) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite countable V209() set
((HC ===) . ((X -firstChar) . I2)) . ((SubTerms I2) * (HC -TermEval)) is set
(HC -TermEval) . I1 is set
HC -AtomicEval I1 is boolean Element of BOOLEAN
(X -firstChar) . I1 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(HC ===) . ((X -firstChar) . I1) is non empty Relation-like (abs (ar ((X -firstChar) . I1))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . I1,seqt
ar ((X -firstChar) . I1) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . I1) is set
abs (ar ((X -firstChar) . I1)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar ((X -firstChar) . I1))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
SubTerms I1 is Relation-like NAT -defined (proj2 I1) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . I1)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 I1 is non empty finite countable set
(proj2 I1) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 I1
(SubTerms I1) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite countable V209() set
((HC ===) . ((X -firstChar) . I1)) . ((SubTerms I1) * (HC -TermEval)) is set
HC -TruthEval I1 is boolean Element of BOOLEAN
HC -TruthEval D2 is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
m is set
seqt is non empty set
seqt -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
seqt * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of seqt
seqt \/ BOOLEAN is non empty set
K491((seqt *),(seqt \/ BOOLEAN)) is non empty functional M30(seqt * ,seqt \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((seqt *),(seqt \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((seqt *),(seqt \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) : b1 is X,seqt -interpreter-like } is set
HC is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,seqt -interpreter-like Element of seqt -InterpretersOf X
a is HC -satisfied set
D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[a,D2] is non empty V26() set
HC -TermEval is non empty Relation-like AllTermsOf X -defined seqt -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),seqt:]
[:(AllTermsOf X),seqt:] is non empty Relation-like set
bool [:(AllTermsOf X),seqt:] is non empty set
seqt -deltaInterpreter is non empty Relation-like 2 -tuples_on seqt -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on seqt),BOOLEAN:]
2 -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
[:(2 -tuples_on seqt),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on seqt),BOOLEAN:] is non empty set
[:(seqt *),(seqt *):] is non empty non trivial Relation-like non finite non empty-membered set
K295(seqt) is non empty Relation-like [:(seqt *),(seqt *):] -defined seqt * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:(seqt *),(seqt *):],(seqt *):]
[:[:(seqt *),(seqt *):],(seqt *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(seqt *),(seqt *):],(seqt *):] is non empty non trivial non finite non empty-membered set
1 -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
id (1 -tuples_on seqt) is non empty Relation-like non-empty non empty-yielding 1 -tuples_on seqt -defined 1 -tuples_on seqt -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(1 -tuples_on seqt),(1 -tuples_on seqt):]
[:(1 -tuples_on seqt),(1 -tuples_on seqt):] is non empty Relation-like set
bool [:(1 -tuples_on seqt),(1 -tuples_on seqt):] is non empty set
K295(seqt) .: (id (1 -tuples_on seqt)) is functional V36() FinSequence-membered Element of bool (seqt *)
bool (seqt *) is non empty non trivial non finite non empty-membered set
chi ((K295(seqt) .: (id (1 -tuples_on seqt))),(2 -tuples_on seqt)) is non empty Relation-like 2 -tuples_on seqt -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on seqt),BOOLEAN:]
[a,D2] `1 is set
([a,D2] `1) \+\ a is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[a,D2] `2 is set
([a,D2] `2) \+\ D2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(X) . m is set
[m,[a,D2]] is non empty V26() set
dom (X) is Element of bool (bool (X))
bool (bool (X)) is non empty set
U is Relation-like X -correct (X) Element of bool (X)
II1 is (X) (X) Element of (X)
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
II1 `1 is finite countable (X) set
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
II1 `2 is set
II2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ II2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
I2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ II2) ^ I2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
{((<*(TheEqSymbOf X)*> ^ II2) ^ I2)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
<*(TheEqSymbOf X)*> ^ I2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ I2) ^ II2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
HC -AtomicEval ((<*(TheEqSymbOf X)*> ^ II2) ^ I2) is boolean Element of BOOLEAN
HC === is Relation-like Function-like Function-yielding V156() X,seqt -interpreter-like HC -extension set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
(TheEqSymbOf X) .--> (seqt -deltaInterpreter) is non empty trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on seqt),BOOLEAN:] -valued Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element countable set
{(TheEqSymbOf X)} --> (seqt -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on seqt),BOOLEAN:] -valued {(seqt -deltaInterpreter)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:]
{(seqt -deltaInterpreter)} is non empty trivial functional finite 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:] is non empty Relation-like finite countable set
bool [:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:] is non empty finite V36() countable set
HC +* ((TheEqSymbOf X) .--> (seqt -deltaInterpreter)) is non empty Relation-like Function-like Function-yielding V156() set
(X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ I2) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(HC ===) . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ I2)) is non empty Relation-like (abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ I2)))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ I2),seqt
ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ I2)) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ I2)) is set
abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ I2))) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ I2)))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
SubTerms ((<*(TheEqSymbOf X)*> ^ II2) ^ I2) is Relation-like NAT -defined (proj2 ((<*(TheEqSymbOf X)*> ^ II2) ^ I2)) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ I2))) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 ((<*(TheEqSymbOf X)*> ^ II2) ^ I2) is non empty finite countable set
(proj2 ((<*(TheEqSymbOf X)*> ^ II2) ^ I2)) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 ((<*(TheEqSymbOf X)*> ^ II2) ^ I2)
(TermSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V36() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf X) *) *)
(SubTerms ((<*(TheEqSymbOf X)*> ^ II2) ^ I2)) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite countable V209() set
((HC ===) . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ II2) ^ I2))) . ((SubTerms ((<*(TheEqSymbOf X)*> ^ II2) ^ I2)) * (HC -TermEval)) is set
HC -TruthEval ((<*(TheEqSymbOf X)*> ^ II2) ^ I2) is boolean Element of BOOLEAN
(HC -TermEval) . II2 is set
(HC -TermEval) . I2 is set
HC -AtomicEval ((<*(TheEqSymbOf X)*> ^ I2) ^ II2) is boolean Element of BOOLEAN
(X -firstChar) . ((<*(TheEqSymbOf X)*> ^ I2) ^ II2) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(HC ===) . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ I2) ^ II2)) is non empty Relation-like (abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ I2) ^ II2)))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . ((<*(TheEqSymbOf X)*> ^ I2) ^ II2),seqt
ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ I2) ^ II2)) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ I2) ^ II2)) is set
abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ I2) ^ II2))) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ I2) ^ II2)))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
SubTerms ((<*(TheEqSymbOf X)*> ^ I2) ^ II2) is Relation-like NAT -defined (proj2 ((<*(TheEqSymbOf X)*> ^ I2) ^ II2)) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ I2) ^ II2))) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 ((<*(TheEqSymbOf X)*> ^ I2) ^ II2) is non empty finite countable set
(proj2 ((<*(TheEqSymbOf X)*> ^ I2) ^ II2)) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 ((<*(TheEqSymbOf X)*> ^ I2) ^ II2)
(SubTerms ((<*(TheEqSymbOf X)*> ^ I2) ^ II2)) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite countable V209() set
((HC ===) . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ I2) ^ II2))) . ((SubTerms ((<*(TheEqSymbOf X)*> ^ I2) ^ II2)) * (HC -TermEval)) is set
HC -TruthEval ((<*(TheEqSymbOf X)*> ^ I2) ^ II2) is boolean Element of BOOLEAN
HC -TruthEval D2 is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
m is set
seqt is non empty set
seqt -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
seqt * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of seqt
seqt \/ BOOLEAN is non empty set
K491((seqt *),(seqt \/ BOOLEAN)) is non empty functional M30(seqt * ,seqt \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((seqt *),(seqt \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((seqt *),(seqt \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) : b1 is X,seqt -interpreter-like } is set
HC is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,seqt -interpreter-like Element of seqt -InterpretersOf X
a is HC -satisfied set
D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[a,D2] is non empty V26() set
HC -TermEval is non empty Relation-like AllTermsOf X -defined seqt -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),seqt:]
[:(AllTermsOf X),seqt:] is non empty Relation-like set
bool [:(AllTermsOf X),seqt:] is non empty set
seqt -deltaInterpreter is non empty Relation-like 2 -tuples_on seqt -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on seqt),BOOLEAN:]
2 -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
[:(2 -tuples_on seqt),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on seqt),BOOLEAN:] is non empty set
[:(seqt *),(seqt *):] is non empty non trivial Relation-like non finite non empty-membered set
K295(seqt) is non empty Relation-like [:(seqt *),(seqt *):] -defined seqt * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:(seqt *),(seqt *):],(seqt *):]
[:[:(seqt *),(seqt *):],(seqt *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(seqt *),(seqt *):],(seqt *):] is non empty non trivial non finite non empty-membered set
1 -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
id (1 -tuples_on seqt) is non empty Relation-like non-empty non empty-yielding 1 -tuples_on seqt -defined 1 -tuples_on seqt -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(1 -tuples_on seqt),(1 -tuples_on seqt):]
[:(1 -tuples_on seqt),(1 -tuples_on seqt):] is non empty Relation-like set
bool [:(1 -tuples_on seqt),(1 -tuples_on seqt):] is non empty set
K295(seqt) .: (id (1 -tuples_on seqt)) is functional V36() FinSequence-membered Element of bool (seqt *)
bool (seqt *) is non empty non trivial non finite non empty-membered set
chi ((K295(seqt) .: (id (1 -tuples_on seqt))),(2 -tuples_on seqt)) is non empty Relation-like 2 -tuples_on seqt -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on seqt),BOOLEAN:]
[a,D2] `1 is set
([a,D2] `1) \+\ a is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[a,D2] `2 is set
([a,D2] `2) \+\ D2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(X) . m is set
[m,[a,D2]] is non empty V26() set
dom (X) is Element of bool (bool (X))
bool (bool (X)) is non empty set
U is Relation-like X -correct (X) Element of bool (X)
II1 is (X) (X) Element of (X)
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
II1 `1 is finite countable (X) set
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
II1 `2 is set
II2 is low-compounding ofAtomicFormula Element of AllSymbolsOf X
ar II2 is non empty complex ext-real finite V40() V41() countable Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X . II2 is set
abs (ar II2) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
Seg (abs (ar II2)) is non empty finite abs (ar II2) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar II2) ) } is set
[:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
I2 is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar II2) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
I1 is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar II2) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } is set
II2 -compound I2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
<*II2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,II2] is non empty V26() set
{[1,II2]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
(X -multiCat) . I2 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*II2*> ^ ((X -multiCat) . I2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
<*(TheEqSymbOf X)*> ^ (II2 -compound I2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
II2 -compound I1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(X -multiCat) . I1 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*II2*> ^ ((X -multiCat) . I1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(<*(TheEqSymbOf X)*> ^ (II2 -compound I2)) ^ (II2 -compound I1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
c26 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
c26 . 1 is set
(c26 . 1) \+\ II2 is set
I02 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
I02 . 1 is set
(I02 . 1) \+\ II2 is set
(X -firstChar) . c26 is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
(X -firstChar) . I02 is non relational termal own ofAtomicFormula Element of AllSymbolsOf X
SubTerms c26 is Relation-like NAT -defined (proj2 c26) * -valued AllTermsOf X -valued Function-like finite abs (ar c26) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 c26 is non empty finite countable set
(proj2 c26) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 c26
AllTermsOf X is non empty functional V36() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
ar c26 is complex ext-real finite V40() V41() countable Element of INT
ar ((X -firstChar) . c26) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . c26) is set
abs (ar c26) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf X) *) *)
SubTerms I02 is Relation-like NAT -defined (proj2 I02) * -valued AllTermsOf X -valued Function-like finite abs (ar I02) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 I02 is non empty finite countable set
(proj2 I02) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 I02
ar I02 is complex ext-real finite V40() V41() countable Element of INT
ar ((X -firstChar) . I02) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . I02) is set
abs (ar I02) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(HC -TermEval) . c26 is set
HC . II2 is Relation-like Function-like set
I2 * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite abs (ar II2) -element len I2 -element FinSequence-like FinSubsequence-like countable V209() set
len I2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(HC . II2) . (I2 * (HC -TermEval)) is set
(HC -TermEval) . I02 is set
I1 * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite abs (ar II2) -element len I1 -element FinSequence-like FinSubsequence-like countable V209() set
len I1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(HC . II2) . (I1 * (HC -TermEval)) is set
bool a is non empty set
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } null {} is set
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } \typed/ {} is Element of bool ( { ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } \/ {})
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } \/ {} is set
bool ( { ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } \/ {}) is non empty set
len (I2 * (HC -TermEval)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
len (I1 * (HC -TermEval)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
X2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
X2 - X2 is complex ext-real finite V40() V41() countable set
(abs (ar II2)) - X2 is complex ext-real finite V40() V41() countable set
I2 null 0 is Relation-like NAT -defined 0 \/ (proj1 I2) -defined Seg ((abs (ar II2)) + 0) -defined 0 \/ (proj2 I2) -valued Function-like total finite len I2 -element FinSequence-like FinSubsequence-like countable V209() set
proj1 I2 is finite abs (ar II2) -element countable set
0 \/ (proj1 I2) is finite countable set
(abs (ar II2)) + 0 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
Seg ((abs (ar II2)) + 0) is non empty finite (abs (ar II2)) + 0 -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= (abs (ar II2)) + 0 ) } is set
proj2 I2 is finite countable set
0 \/ (proj2 I2) is finite countable set
I2 \typed/ 0 is Relation-like NAT -defined finite countable Element of bool (I2 \/ 0)
I2 \/ 0 is Relation-like NAT -defined finite countable set
bool (I2 \/ 0) is non empty finite V36() countable set
I2 ^ 0 is non empty Relation-like NAT -defined Function-like finite (abs (ar II2)) + {} -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
(abs (ar II2)) + {} is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
0 ^ I2 is Relation-like NAT -defined Function-like finite {} + (abs (ar II2)) -element {} + (abs (ar II2)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
{} + (abs (ar II2)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
{} + (abs (ar II2)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
dom (I2 null 0) is finite len I2 -element countable Element of bool NAT
I1 null 0 is Relation-like NAT -defined 0 \/ (proj1 I1) -defined Seg ((abs (ar II2)) + 0) -defined 0 \/ (proj2 I1) -valued Function-like total finite len I1 -element FinSequence-like FinSubsequence-like countable V209() set
proj1 I1 is finite abs (ar II2) -element countable set
0 \/ (proj1 I1) is finite countable set
proj2 I1 is finite countable set
0 \/ (proj2 I1) is finite countable set
I1 \typed/ 0 is Relation-like NAT -defined finite countable Element of bool (I1 \/ 0)
I1 \/ 0 is Relation-like NAT -defined finite countable set
bool (I1 \/ 0) is non empty finite V36() countable set
I1 ^ 0 is non empty Relation-like NAT -defined Function-like finite (abs (ar II2)) + {} -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
0 ^ I1 is Relation-like NAT -defined Function-like finite {} + (abs (ar II2)) -element {} + (abs (ar II2)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
dom (I1 null 0) is finite len I1 -element countable Element of bool NAT
Funcs ((Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}})) is non empty functional FUNCTION_DOMAIN of Seg (abs (ar II2)),((AllSymbolsOf X) *) \ {{}}
I is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
U is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
I + U is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
I2 . I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{(I2 . I)} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
{(I2 . I)} \ (AllTermsOf X) is trivial functional finite V36() with_common_domain countable Element of bool {(I2 . I)}
bool {(I2 . I)} is non empty finite V36() countable set
{(I2 . I)} typed\ (AllTermsOf X) is trivial functional finite V36() with_common_domain countable Element of bool {(I2 . I)}
I1 . I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{(I1 . I)} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
{(I1 . I)} \ (AllTermsOf X) is trivial functional finite V36() with_common_domain countable Element of bool {(I1 . I)}
bool {(I1 . I)} is non empty finite V36() countable set
{(I1 . I)} typed\ (AllTermsOf X) is trivial functional finite V36() with_common_domain countable Element of bool {(I1 . I)}
I2 . X2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
I1 . X2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
F2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ F2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
F1 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ F2) ^ F1 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
phi is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):]
X22 is Element of Seg (abs (ar II2))
phi . X22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(HC -TermEval) . (phi . X22) is set
(HC -TermEval) * phi is Relation-like Seg (abs (ar II2)) -defined seqt -valued Function-like finite countable V209() Element of bool [:(Seg (abs (ar II2))),seqt:]
[:(Seg (abs (ar II2))),seqt:] is non empty Relation-like set
bool [:(Seg (abs (ar II2))),seqt:] is non empty set
((HC -TermEval) * phi) . X22 is set
((HC -TermEval) . (phi . X22)) \+\ (((HC -TermEval) * phi) . X22) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
l22 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):]
l22 . X22 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(HC -TermEval) . (l22 . X22) is set
(HC -TermEval) * l22 is Relation-like Seg (abs (ar II2)) -defined seqt -valued Function-like finite countable V209() Element of bool [:(Seg (abs (ar II2))),seqt:]
((HC -TermEval) * l22) . X22 is set
((HC -TermEval) . (l22 . X22)) \+\ (((HC -TermEval) * l22) . X22) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
<*F2,F1*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V209() set
<*F2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,F2] is non empty V26() set
{[1,F2]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*F1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,F1] is non empty V26() set
{[1,F1]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*F2*> ^ <*F1*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element 1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
<*(TheEqSymbOf X)*> ^ (phi . X22) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ (phi . X22)) ^ (l22 . X22) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
I1 is HC -satisfied Element of bool a
F5 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
HC -TruthEval F5 is boolean Element of BOOLEAN
HC -AtomicEval F5 is boolean Element of BOOLEAN
HC === is Relation-like Function-like Function-yielding V156() X,seqt -interpreter-like HC -extension set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
(TheEqSymbOf X) .--> (seqt -deltaInterpreter) is non empty trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on seqt),BOOLEAN:] -valued Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element countable set
{(TheEqSymbOf X)} --> (seqt -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on seqt),BOOLEAN:] -valued {(seqt -deltaInterpreter)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:]
{(seqt -deltaInterpreter)} is non empty trivial functional finite 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:] is non empty Relation-like finite countable set
bool [:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:] is non empty finite V36() countable set
HC +* ((TheEqSymbOf X) .--> (seqt -deltaInterpreter)) is non empty Relation-like Function-like Function-yielding V156() set
(X -firstChar) . F5 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(HC ===) . ((X -firstChar) . F5) is non empty Relation-like (abs (ar ((X -firstChar) . F5))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . F5,seqt
ar ((X -firstChar) . F5) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . F5) is set
abs (ar ((X -firstChar) . F5)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar ((X -firstChar) . F5))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
SubTerms F5 is Relation-like NAT -defined (proj2 F5) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . F5)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 F5 is non empty finite countable set
(proj2 F5) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 F5
(TermSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of TermSymbolsOf X
(SubTerms F5) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite abs (ar ((X -firstChar) . F5)) -element len (SubTerms F5) -element FinSequence-like FinSubsequence-like countable V209() set
len (SubTerms F5) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
((HC ===) . ((X -firstChar) . F5)) . ((SubTerms F5) * (HC -TermEval)) is set
(I2 * (HC -TermEval)) . X2 is set
(I1 * (HC -TermEval)) . X2 is set
<*(TheEqSymbOf X)*> ^ c26 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ c26) ^ I02 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
HC -AtomicEval ((<*(TheEqSymbOf X)*> ^ c26) ^ I02) is boolean Element of BOOLEAN
(X -firstChar) . ((<*(TheEqSymbOf X)*> ^ c26) ^ I02) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(HC ===) . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ c26) ^ I02)) is non empty Relation-like (abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ c26) ^ I02)))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . ((<*(TheEqSymbOf X)*> ^ c26) ^ I02),seqt
ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ c26) ^ I02)) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ c26) ^ I02)) is set
abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ c26) ^ I02))) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ c26) ^ I02)))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
SubTerms ((<*(TheEqSymbOf X)*> ^ c26) ^ I02) is Relation-like NAT -defined (proj2 ((<*(TheEqSymbOf X)*> ^ c26) ^ I02)) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ c26) ^ I02))) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 ((<*(TheEqSymbOf X)*> ^ c26) ^ I02) is non empty finite countable set
(proj2 ((<*(TheEqSymbOf X)*> ^ c26) ^ I02)) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 ((<*(TheEqSymbOf X)*> ^ c26) ^ I02)
(SubTerms ((<*(TheEqSymbOf X)*> ^ c26) ^ I02)) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite abs (ar ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ c26) ^ I02))) -element len (SubTerms ((<*(TheEqSymbOf X)*> ^ c26) ^ I02)) -element FinSequence-like FinSubsequence-like countable V209() set
len (SubTerms ((<*(TheEqSymbOf X)*> ^ c26) ^ I02)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
((HC ===) . ((X -firstChar) . ((<*(TheEqSymbOf X)*> ^ c26) ^ I02))) . ((SubTerms ((<*(TheEqSymbOf X)*> ^ c26) ^ I02)) * (HC -TermEval)) is set
HC -TruthEval ((<*(TheEqSymbOf X)*> ^ c26) ^ I02) is boolean Element of BOOLEAN
HC -TruthEval D2 is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
X -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
[:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -multiCat is non empty Relation-like ((AllSymbolsOf X) *) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(((AllSymbolsOf X) *) *),((AllSymbolsOf X) *):]
K295((AllSymbolsOf X)) is non empty Relation-like [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):],((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
MultPlace K295((AllSymbolsOf X)) is non empty Relation-like (((AllSymbolsOf X) *) *) \ {{}} -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):]
(((AllSymbolsOf X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) *)
bool (((AllSymbolsOf X) *) *) is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool (((AllSymbolsOf X) *) *)
[:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((((AllSymbolsOf X) *) *) \ {{}}),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* (MultPlace K295((AllSymbolsOf X))) is non empty Relation-like Function-like Function-yielding V156() set
m is set
seqt is non empty set
seqt -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
seqt * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of seqt
seqt \/ BOOLEAN is non empty set
K491((seqt *),(seqt \/ BOOLEAN)) is non empty functional M30(seqt * ,seqt \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((seqt *),(seqt \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((seqt *),(seqt \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) : b1 is X,seqt -interpreter-like } is set
HC is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,seqt -interpreter-like Element of seqt -InterpretersOf X
a is HC -satisfied set
D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[a,D2] is non empty V26() set
HC -TermEval is non empty Relation-like AllTermsOf X -defined seqt -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),seqt:]
[:(AllTermsOf X),seqt:] is non empty Relation-like set
bool [:(AllTermsOf X),seqt:] is non empty set
seqt -deltaInterpreter is non empty Relation-like 2 -tuples_on seqt -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on seqt),BOOLEAN:]
2 -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
[:(2 -tuples_on seqt),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on seqt),BOOLEAN:] is non empty set
[:(seqt *),(seqt *):] is non empty non trivial Relation-like non finite non empty-membered set
K295(seqt) is non empty Relation-like [:(seqt *),(seqt *):] -defined seqt * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:(seqt *),(seqt *):],(seqt *):]
[:[:(seqt *),(seqt *):],(seqt *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(seqt *),(seqt *):],(seqt *):] is non empty non trivial non finite non empty-membered set
1 -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
id (1 -tuples_on seqt) is non empty Relation-like non-empty non empty-yielding 1 -tuples_on seqt -defined 1 -tuples_on seqt -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(1 -tuples_on seqt),(1 -tuples_on seqt):]
[:(1 -tuples_on seqt),(1 -tuples_on seqt):] is non empty Relation-like set
bool [:(1 -tuples_on seqt),(1 -tuples_on seqt):] is non empty set
K295(seqt) .: (id (1 -tuples_on seqt)) is functional V36() FinSequence-membered Element of bool (seqt *)
bool (seqt *) is non empty non trivial non finite non empty-membered set
chi ((K295(seqt) .: (id (1 -tuples_on seqt))),(2 -tuples_on seqt)) is non empty Relation-like 2 -tuples_on seqt -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on seqt),BOOLEAN:]
[a,D2] `1 is set
([a,D2] `1) \+\ a is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[a,D2] `2 is set
([a,D2] `2) \+\ D2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(X) . m is set
[m,[a,D2]] is non empty V26() set
dom (X) is Element of bool (bool (X))
bool (bool (X)) is non empty set
U is Relation-like X -correct (X) Element of bool (X)
II1 is (X) (X) Element of (X)
(((AllSymbolsOf X) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((AllSymbolsOf X) *) \ {{}}
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool ((((AllSymbolsOf X) *) \ {{}}) *)
bool ((((AllSymbolsOf X) *) \ {{}}) *) is non empty non trivial non finite non empty-membered set
II1 `1 is finite countable (X) set
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
II1 `2 is set
II2 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
ar II2 is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X . II2 is set
abs (ar II2) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
I2 is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar II2) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
II2 -compound I2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
AtomicFormulaSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
TheNorSymbOf X is set
{(TheNorSymbOf X)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf X) \ {(TheNorSymbOf X)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) typed\ {(TheNorSymbOf X)} is Element of bool (AllSymbolsOf X)
<*II2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,II2] is non empty V26() set
{[1,II2]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
((AllSymbolsOf X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf X) *
(X -multiCat) . I2 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*II2*> ^ ((X -multiCat) . I2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{(II2 -compound I2)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
Seg (abs (ar II2)) is non empty finite abs (ar II2) -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= abs (ar II2) ) } is set
[:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
I1 is Relation-like NAT -defined AllTermsOf X -valued Function-like finite abs (ar II2) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } is set
{(II2 -compound I2)} \/ { ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } is non empty set
II2 -compound I1 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
(X -multiCat) . I1 is Relation-like NAT -defined AllSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of (AllSymbolsOf X) *
<*II2*> ^ ((X -multiCat) . I1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
c26 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
(X -firstChar) . c26 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
bool a is non empty set
I02 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
{I02} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } null {I02} is set
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } \typed/ {I02} is Element of bool ( { ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } \/ {I02})
{ ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } \/ {I02} is non empty set
bool ( { ((<*(TheEqSymbOf X)*> ^ (b2 . b1)) ^ (b3 . b1)) where b1 is Element of Seg (abs (ar II2)), b2, b3 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):] : ( b2 = I2 & b3 = I1 ) } \/ {I02}) is non empty set
(X -multiCat) . I2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
<*II2*> ^ ((X -multiCat) . I2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(<*II2*> ^ ((X -multiCat) . I2)) . 1 is set
((<*II2*> ^ ((X -multiCat) . I2)) . 1) \+\ II2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(X -multiCat) . I1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
<*II2*> ^ ((X -multiCat) . I1) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(<*II2*> ^ ((X -multiCat) . I1)) . 1 is set
((<*II2*> ^ ((X -multiCat) . I1)) . 1) \+\ II2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(X -firstChar) . I02 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
I1 is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
SubTerms I02 is Relation-like NAT -defined (proj2 I02) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . I02)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
ar ((X -firstChar) . I02) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . I02) is set
abs (ar ((X -firstChar) . I02)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
proj2 I02 is non empty finite countable set
(proj2 I02) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 I02
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
(TermSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of TermSymbolsOf X
AllTermsOf X is non empty functional V36() FinSequence-membered AllSymbolsOf X -prefix X -prefix Element of bool ((AllSymbolsOf X) *)
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf X) *) *)
SubTerms c26 is Relation-like NAT -defined (proj2 c26) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . c26)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
ar ((X -firstChar) . c26) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . c26) is set
abs (ar ((X -firstChar) . c26)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
proj2 c26 is non empty finite countable set
(proj2 c26) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 c26
I2 is HC -satisfied Element of bool a
{I02} null I2 is finite countable (X) set
{I02} \typed/ I2 is Element of bool ({I02} \/ I2)
{I02} \/ I2 is non empty set
bool ({I02} \/ I2) is non empty set
X1 is HC -satisfied Element of bool a
I2 * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite abs (ar II2) -element len I2 -element FinSequence-like FinSubsequence-like countable V209() set
len I2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
I1 * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite abs (ar II2) -element len I1 -element FinSequence-like FinSubsequence-like countable V209() set
len I1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
len (I2 * (HC -TermEval)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
len (I1 * (HC -TermEval)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
U is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
U - U is complex ext-real finite V40() V41() countable set
(abs (ar II2)) - U is complex ext-real finite V40() V41() countable set
I2 null 0 is Relation-like NAT -defined 0 \/ (proj1 I2) -defined Seg ((abs (ar II2)) + 0) -defined 0 \/ (proj2 I2) -valued Function-like total finite len I2 -element FinSequence-like FinSubsequence-like countable V209() set
proj1 I2 is finite abs (ar II2) -element countable set
0 \/ (proj1 I2) is finite countable set
(abs (ar II2)) + 0 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
Seg ((abs (ar II2)) + 0) is non empty finite (abs (ar II2)) + 0 -element countable Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT : ( 1 <= b1 & b1 <= (abs (ar II2)) + 0 ) } is set
proj2 I2 is finite countable set
0 \/ (proj2 I2) is finite countable set
I2 \typed/ 0 is Relation-like NAT -defined finite countable Element of bool (I2 \/ 0)
I2 \/ 0 is Relation-like NAT -defined finite countable set
bool (I2 \/ 0) is non empty finite V36() countable set
I2 ^ 0 is non empty Relation-like NAT -defined Function-like finite (abs (ar II2)) + {} -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
(abs (ar II2)) + {} is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
0 ^ I2 is Relation-like NAT -defined Function-like finite {} + (abs (ar II2)) -element {} + (abs (ar II2)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
{} + (abs (ar II2)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
{} + (abs (ar II2)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
dom (I2 null 0) is finite len I2 -element countable Element of bool NAT
I1 null 0 is Relation-like NAT -defined 0 \/ (proj1 I1) -defined Seg ((abs (ar II2)) + 0) -defined 0 \/ (proj2 I1) -valued Function-like total finite len I1 -element FinSequence-like FinSubsequence-like countable V209() set
proj1 I1 is finite abs (ar II2) -element countable set
0 \/ (proj1 I1) is finite countable set
proj2 I1 is finite countable set
0 \/ (proj2 I1) is finite countable set
I1 \typed/ 0 is Relation-like NAT -defined finite countable Element of bool (I1 \/ 0)
I1 \/ 0 is Relation-like NAT -defined finite countable set
bool (I1 \/ 0) is non empty finite V36() countable set
I1 ^ 0 is non empty Relation-like NAT -defined Function-like finite (abs (ar II2)) + {} -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
0 ^ I1 is Relation-like NAT -defined Function-like finite {} + (abs (ar II2)) -element {} + (abs (ar II2)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
dom (I1 null 0) is finite len I1 -element countable Element of bool NAT
Funcs ((Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}})) is non empty functional FUNCTION_DOMAIN of Seg (abs (ar II2)),((AllSymbolsOf X) *) \ {{}}
l22 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
l22 + phi is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
I2 . l22 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{(I2 . l22)} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
{(I2 . l22)} \ (AllTermsOf X) is trivial functional finite V36() with_common_domain countable Element of bool {(I2 . l22)}
bool {(I2 . l22)} is non empty finite V36() countable set
{(I2 . l22)} typed\ (AllTermsOf X) is trivial functional finite V36() with_common_domain countable Element of bool {(I2 . l22)}
I1 . l22 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{(I1 . l22)} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
{(I1 . l22)} \ (AllTermsOf X) is trivial functional finite V36() with_common_domain countable Element of bool {(I1 . l22)}
bool {(I1 . l22)} is non empty finite V36() countable set
{(I1 . l22)} typed\ (AllTermsOf X) is trivial functional finite V36() with_common_domain countable Element of bool {(I1 . l22)}
I2 . U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
I1 . U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
F5 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheEqSymbOf X)*> ^ F5 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
seqt2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ F5) ^ seqt2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
F2 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):]
I is Element of Seg (abs (ar II2))
F2 . I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(HC -TermEval) . (F2 . I) is set
(HC -TermEval) * F2 is Relation-like Seg (abs (ar II2)) -defined seqt -valued Function-like finite countable V209() Element of bool [:(Seg (abs (ar II2))),seqt:]
[:(Seg (abs (ar II2))),seqt:] is non empty Relation-like set
bool [:(Seg (abs (ar II2))),seqt:] is non empty set
((HC -TermEval) * F2) . I is set
((HC -TermEval) . (F2 . I)) \+\ (((HC -TermEval) * F2) . I) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
F1 is non empty Relation-like non-empty non empty-yielding Seg (abs (ar II2)) -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total finite Function-yielding V156() countable V208() V209() Element of bool [:(Seg (abs (ar II2))),(((AllSymbolsOf X) *) \ {{}}):]
F1 . I is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(HC -TermEval) . (F1 . I) is set
(HC -TermEval) * F1 is Relation-like Seg (abs (ar II2)) -defined seqt -valued Function-like finite countable V209() Element of bool [:(Seg (abs (ar II2))),seqt:]
((HC -TermEval) * F1) . I is set
((HC -TermEval) . (F1 . I)) \+\ (((HC -TermEval) * F1) . I) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
<*F5,seqt2*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V209() set
<*F5*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,F5] is non empty V26() set
{[1,F5]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*seqt2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() FuncSeq-like countable V208() V209() set
[1,seqt2] is non empty V26() set
{[1,seqt2]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*F5*> ^ <*seqt2*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element 1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() set
<*(TheEqSymbOf X)*> ^ (F2 . I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheEqSymbOf X)*> ^ (F2 . I)) ^ (F1 . I) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
z is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf X) *) \ {{}}
HC -TruthEval z is boolean Element of BOOLEAN
HC -AtomicEval z is boolean Element of BOOLEAN
HC === is Relation-like Function-like Function-yielding V156() X,seqt -interpreter-like HC -extension set
TheEqSymbOf X is Element of AtomicFormulaSymbolsOf X
(TheEqSymbOf X) .--> (seqt -deltaInterpreter) is non empty trivial Relation-like AtomicFormulaSymbolsOf X -defined {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on seqt),BOOLEAN:] -valued Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{(TheEqSymbOf X)} is non empty trivial finite 1 -element countable set
{(TheEqSymbOf X)} --> (seqt -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf X)} -defined bool [:(2 -tuples_on seqt),BOOLEAN:] -valued {(seqt -deltaInterpreter)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:]
{(seqt -deltaInterpreter)} is non empty trivial functional finite 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:] is non empty Relation-like finite countable set
bool [:{(TheEqSymbOf X)},{(seqt -deltaInterpreter)}:] is non empty finite V36() countable set
HC +* ((TheEqSymbOf X) .--> (seqt -deltaInterpreter)) is non empty Relation-like Function-like Function-yielding V156() set
(X -firstChar) . z is low-compounding relational ofAtomicFormula Element of AllSymbolsOf X
(HC ===) . ((X -firstChar) . z) is non empty Relation-like (abs (ar ((X -firstChar) . z))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . z,seqt
ar ((X -firstChar) . z) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of X . ((X -firstChar) . z) is set
abs (ar ((X -firstChar) . z)) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar ((X -firstChar) . z))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
SubTerms z is Relation-like NAT -defined (proj2 z) * -valued (TermSymbolsOf X) * -valued AllTermsOf X -valued Function-like finite abs (ar ((X -firstChar) . z)) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf X) *
proj2 z is non empty finite countable set
(proj2 z) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 z
(SubTerms z) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite countable V209() set
((HC ===) . ((X -firstChar) . z)) . ((SubTerms z) * (HC -TermEval)) is set
(I2 * (HC -TermEval)) . U is set
(I1 * (HC -TermEval)) . U is set
HC -AtomicEval c26 is boolean Element of BOOLEAN
(HC ===) . ((X -firstChar) . c26) is non empty Relation-like (abs (ar ((X -firstChar) . c26))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . c26,seqt
(abs (ar ((X -firstChar) . c26))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
(SubTerms c26) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite countable V209() set
((HC ===) . ((X -firstChar) . c26)) . ((SubTerms c26) * (HC -TermEval)) is set
HC -TruthEval c26 is boolean Element of BOOLEAN
HC -AtomicEval I02 is boolean Element of BOOLEAN
(HC ===) . ((X -firstChar) . I02) is non empty Relation-like (abs (ar ((X -firstChar) . I02))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . I02,seqt
(abs (ar ((X -firstChar) . I02))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
(SubTerms I02) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite countable V209() set
((HC ===) . ((X -firstChar) . I02)) . ((SubTerms I02) * (HC -TermEval)) is set
HC -TruthEval I02 is boolean Element of BOOLEAN
HC -TruthEval D2 is boolean Element of BOOLEAN
HC -AtomicEval c26 is boolean Element of BOOLEAN
(HC ===) . ((X -firstChar) . c26) is non empty Relation-like (abs (ar ((X -firstChar) . c26))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . c26,seqt
(abs (ar ((X -firstChar) . c26))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
(SubTerms c26) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite countable V209() set
((HC ===) . ((X -firstChar) . c26)) . ((SubTerms c26) * (HC -TermEval)) is set
HC -TruthEval c26 is boolean Element of BOOLEAN
HC -AtomicEval I02 is boolean Element of BOOLEAN
(HC ===) . ((X -firstChar) . I02) is non empty Relation-like (abs (ar ((X -firstChar) . I02))) -tuples_on seqt -defined seqt \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (X -firstChar) . I02,seqt
(abs (ar ((X -firstChar) . I02))) -tuples_on seqt is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of seqt
(SubTerms I02) * (HC -TermEval) is Relation-like NAT -defined seqt -valued Function-like finite countable V209() set
((HC ===) . ((X -firstChar) . I02)) . ((SubTerms I02) * (HC -TermEval)) is set
HC -TruthEval I02 is boolean Element of BOOLEAN
HC -TruthEval D2 is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
H is set
m is non empty set
m -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((m *),(m \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
m * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of m
m \/ BOOLEAN is non empty set
K491((m *),(m \/ BOOLEAN)) is non empty functional M30(m * ,m \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((m *),(m \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((m *),(m \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((m *),(m \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((m *),(m \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((m *),(m \/ BOOLEAN))) : b1 is X,m -interpreter-like } is set
HH is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,m -interpreter-like Element of m -InterpretersOf X
HC is HH -satisfied set
a is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[HC,a] is non empty V26() set
[HC,a] `1 is set
([HC,a] `1) \+\ HC is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[HC,a] `2 is set
([HC,a] `2) \+\ a is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(X) . H is set
[H,[HC,a]] is non empty V26() set
dom (X) is Element of bool (bool (X))
bool (bool (X)) is non empty set
sub1 is Relation-like X -correct (X) Element of bool (X)
sub2 is (X) (X) Element of (X)
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
sub2 `1 is finite countable (X) set
sub2 `2 is set
inf is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
II1 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}}
U is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(inf,II1) SubstIn U is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
Funcs ((AllFormulasOf X),(AllFormulasOf X)) is non empty functional FUNCTION_DOMAIN of AllFormulasOf X, AllFormulasOf X
inf Subst1 II1 is Relation-like AllFormulasOf X -defined AllFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of Funcs ((AllFormulasOf X),(AllFormulasOf X))
id (AllFormulasOf X) is non empty Relation-like non-empty non empty-yielding AllFormulasOf X -defined AllFormulasOf X -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(AllFormulasOf X),(AllFormulasOf X):]
[:(AllFormulasOf X),(AllFormulasOf X):] is non empty Relation-like set
bool [:(AllFormulasOf X),(AllFormulasOf X):] is non empty set
inf AtomicSubst II1 is non empty Relation-like non-empty non empty-yielding AtomicFormulasOf X -defined AtomicFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(AtomicFormulasOf X),(AtomicFormulasOf X):]
AtomicFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : b1 is 0wff } is set
[:(AtomicFormulasOf X),(AtomicFormulasOf X):] is non empty Relation-like set
bool [:(AtomicFormulasOf X),(AtomicFormulasOf X):] is non empty set
(id (AllFormulasOf X)) +* (inf AtomicSubst II1) is non empty Relation-like non-empty Function-like Function-yielding V156() set
(inf,II1) Subst4 (inf Subst1 II1) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf X),(AllFormulasOf X)) -valued Function-like total quasi_total Function-yielding V156() Element of bool [:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):]
[:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):] is non empty non trivial non finite non empty-membered set
Depth U is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
((inf,II1) Subst4 (inf Subst1 II1)) . (Depth U) is Relation-like Function-like Function-yielding V156() V208() Element of Funcs ((AllFormulasOf X),(AllFormulasOf X))
(((inf,II1) Subst4 (inf Subst1 II1)) . (Depth U)) . U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((inf,II1) SubstIn U)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
<*inf*> is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
[1,inf] is non empty V26() set
{[1,inf]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*inf*> ^ U is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff 1 + (Depth U) -wff non Depth U -wff wff exal Element of ((AllSymbolsOf X) *) \ {{}}
1 + (Depth U) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
II2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of AllTermsOf X
(inf,II2) SubstIn U is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
inf Subst1 II2 is Relation-like AllFormulasOf X -defined AllFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of Funcs ((AllFormulasOf X),(AllFormulasOf X))
inf AtomicSubst II2 is non empty Relation-like non-empty non empty-yielding AtomicFormulasOf X -defined AtomicFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:(AtomicFormulasOf X),(AtomicFormulasOf X):]
(id (AllFormulasOf X)) +* (inf AtomicSubst II2) is non empty Relation-like non-empty Function-like Function-yielding V156() set
(inf,II2) Subst4 (inf Subst1 II2) is non empty Relation-like NAT -defined Funcs ((AllFormulasOf X),(AllFormulasOf X)) -valued Function-like total quasi_total Function-yielding V156() Element of bool [:NAT,(Funcs ((AllFormulasOf X),(AllFormulasOf X))):]
((inf,II2) Subst4 (inf Subst1 II2)) . (Depth U) is Relation-like Function-like Function-yielding V156() V208() Element of Funcs ((AllFormulasOf X),(AllFormulasOf X))
(((inf,II2) Subst4 (inf Subst1 II2)) . (Depth U)) . U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
HH -TermEval is non empty Relation-like AllTermsOf X -defined m -valued Function-like total quasi_total Element of bool [:(AllTermsOf X),m:]
[:(AllTermsOf X),m:] is non empty Relation-like set
bool [:(AllTermsOf X),m:] is non empty set
(HH -TermEval) . II2 is Element of m
I1 is Element of m
(inf,I1) ReassignIn HH is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,m -interpreter-like Element of m -InterpretersOf X
{} .--> I1 is non empty trivial Relation-like {{}} -defined m -valued Function-like one-to-one constant finite 1 -element countable V209() set
{{}} --> I1 is non empty Relation-like {{}} -defined m -valued {I1} -valued Function-like constant total quasi_total finite countable V209() Element of bool [:{{}},{I1}:]
{I1} is non empty trivial finite 1 -element countable set
[:{{}},{I1}:] is non empty Relation-like finite countable set
bool [:{{}},{I1}:] is non empty finite V36() countable set
inf .--> ({} .--> I1) is non empty trivial Relation-like AllSymbolsOf X -defined {inf} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{inf} is non empty trivial finite 1 -element countable set
{inf} --> ({} .--> I1) is non empty Relation-like non-empty non empty-yielding {inf} -defined {({} .--> I1)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{inf},{({} .--> I1)}:]
{({} .--> I1)} is non empty trivial functional finite V36() 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{inf},{({} .--> I1)}:] is non empty Relation-like finite countable set
bool [:{inf},{({} .--> I1)}:] is non empty finite V36() countable set
HH +* (inf .--> ({} .--> I1)) is non empty Relation-like Function-like Function-yielding V156() set
I2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{I2} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
HH -TruthEval I2 is boolean Element of BOOLEAN
c26 is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,m -interpreter-like Element of m -InterpretersOf X
c26 -TruthEval U is boolean Element of BOOLEAN
HH -TruthEval a is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
[:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) -firstChar is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
(AllSymbolsOf X) -pr1 is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
[:(AllSymbolsOf X),(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf X),(AllSymbolsOf X)) is non empty Relation-like [:(AllSymbolsOf X),(AllSymbolsOf X):] -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf X),(AllSymbolsOf X):],(AllSymbolsOf X):]
MultPlace ((AllSymbolsOf X) -pr1) is non empty Relation-like ((AllSymbolsOf X) *) \ {{}} -defined AllSymbolsOf X -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf X) *) \ {{}}),(AllSymbolsOf X):]
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
m is set
seqt is non empty set
seqt -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))))
seqt * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of seqt
seqt \/ BOOLEAN is non empty set
K491((seqt *),(seqt \/ BOOLEAN)) is non empty functional M30(seqt * ,seqt \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((seqt *),(seqt \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((seqt *),(seqt \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((seqt *),(seqt \/ BOOLEAN))) : b1 is X,seqt -interpreter-like } is set
HC is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,seqt -interpreter-like Element of seqt -InterpretersOf X
a is HC -satisfied set
D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[a,D2] is non empty V26() set
[a,D2] `1 is set
([a,D2] `1) \+\ a is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[a,D2] `2 is set
([a,D2] `2) \+\ D2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
dom (X) is Element of bool (bool (X))
bool (bool (X)) is non empty set
(X) . m is set
[m,[a,D2]] is non empty V26() set
sub2 is Relation-like X -correct (X) Element of bool (X)
inf is (X) (X) Element of (X)
inf `1 is finite countable (X) set
inf `2 is set
{(inf `2)} is non empty trivial finite 1 -element countable set
II2 is set
U is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
<*U*> is non empty trivial Relation-like NAT -defined TermSymbolsOf X -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() termal 0 -termal Element of ((AllSymbolsOf X) *) \ {{}}
TermSymbolsOf X is non empty set
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
[1,U] is non empty V26() set
{[1,U]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
I2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
<*U*> ^ I2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{(<*U*> ^ I2)} is non empty trivial functional finite V36() 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
II2 \/ {(<*U*> ^ I2)} is non empty set
{I2} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
II2 \/ {I2} is non empty set
(II2 \/ {I2}) \/ {(inf `2)} is non empty set
II1 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf X
U SubstWith II1 is non empty Relation-like (AllSymbolsOf X) * -defined (AllSymbolsOf X) * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):]
[:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:((AllSymbolsOf X) *),((AllSymbolsOf X) *):] is non empty non trivial non finite non empty-membered set
(U SubstWith II1) . I2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((U SubstWith II1) . I2)} is non empty trivial functional finite V36() 1 -element with_common_domain countable set
II2 \/ {((U SubstWith II1) . I2)} is non empty set
[(II2 \/ {((U SubstWith II1) . I2)}),(inf `2)] is non empty V26() set
{(<*U*> ^ I2)} null II2 is set
{(<*U*> ^ I2)} \typed/ II2 is Element of bool ({(<*U*> ^ I2)} \/ II2)
{(<*U*> ^ I2)} \/ II2 is non empty set
bool ({(<*U*> ^ I2)} \/ II2) is non empty set
I1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
I1 . 1 is set
U \+\ (I1 . 1) is set
(X -firstChar) . I1 is Element of AllSymbolsOf X
c26 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff wff exal Element of ((AllSymbolsOf X) *) \ {{}}
head c26 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
SubWffsOf c26 is set
(SubWffsOf c26) `1 is set
I02 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{I02} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
II2 \/ {I02} is non empty set
{D2} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
{D2} null (II2 \/ {I02}) is finite countable (X) set
{D2} \typed/ (II2 \/ {I02}) is Element of bool ({D2} \/ (II2 \/ {I02}))
{D2} \/ (II2 \/ {I02}) is non empty set
bool ({D2} \/ (II2 \/ {I02})) is non empty set
(II2 \/ {I02}) \/ {D2} is non empty set
bool ((II2 \/ {I02}) \/ {D2}) is non empty set
II2 \/ {D2} is non empty set
{I02} null (II2 \/ {D2}) is finite countable (X) set
{I02} \typed/ (II2 \/ {D2}) is Element of bool ({I02} \/ (II2 \/ {D2}))
{I02} \/ (II2 \/ {D2}) is non empty set
bool ({I02} \/ (II2 \/ {D2})) is non empty set
{I02} \/ {D2} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
II2 \/ ({I02} \/ {D2}) is non empty set
II2 null ({I02} \/ {D2}) is set
II2 \typed/ ({I02} \/ {D2}) is Element of bool (II2 \/ ({I02} \/ {D2}))
bool (II2 \/ ({I02} \/ {D2})) is non empty set
<*U*> ^ I02 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff 1 + (Depth I02) -wff non Depth I02 -wff wff exal Element of ((AllSymbolsOf X) *) \ {{}}
Depth I02 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
1 + (Depth I02) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
tail c26 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued AllSymbolsOf X -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of (AllSymbolsOf X) *
(SubWffsOf c26) `2 is set
(<*U*> ^ I02) ^ (tail c26) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(<*U*> ^ I02) null (tail c26) is Relation-like NAT -defined (tail c26) \/ (proj1 (<*U*> ^ I02)) -defined (tail c26) \/ (proj2 (<*U*> ^ I02)) -valued Function-like finite len (<*U*> ^ I02) -element FinSequence-like FinSubsequence-like countable V209() set
proj1 (<*U*> ^ I02) is non empty finite countable set
(tail c26) \/ (proj1 (<*U*> ^ I02)) is non empty finite countable set
proj2 (<*U*> ^ I02) is non empty finite countable set
(tail c26) \/ (proj2 (<*U*> ^ I02)) is non empty finite countable set
len (<*U*> ^ I02) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(<*U*> ^ I02) \typed/ (tail c26) is Relation-like NAT -defined finite countable Element of bool ((<*U*> ^ I02) \/ (tail c26))
(<*U*> ^ I02) \/ (tail c26) is non empty Relation-like NAT -defined finite countable set
bool ((<*U*> ^ I02) \/ (tail c26)) is non empty finite V36() countable set
(tail c26) ^ (<*U*> ^ I02) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
I1 is non empty Element of bool ((II2 \/ {I02}) \/ {D2})
I1 null ((II2 \/ {I02}) \/ {D2}) is set
((II2 \/ {I02}) \/ {D2}) /\ I1 is Element of bool ((II2 \/ {I02}) \/ {D2})
((II2 \/ {I02}) \/ {D2}) typed/\ I1 is Element of bool ((II2 \/ {I02}) \/ {D2})
((II2 \/ {I02}) \/ {D2}) /\ I1 is set
((II2 \/ {I02}) \/ {D2}) /\typed I1 is Element of bool I1
bool I1 is non empty set
I1 \typed/ ((II2 \/ {I02}) \/ {D2}) is Element of bool (I1 \/ ((II2 \/ {I02}) \/ {D2}))
I1 \/ ((II2 \/ {I02}) \/ {D2}) is non empty set
bool (I1 \/ ((II2 \/ {I02}) \/ {D2})) is non empty set
I2 is non empty Element of bool ((II2 \/ {I02}) \/ {D2})
I2 null ((II2 \/ {I02}) \/ {D2}) is set
((II2 \/ {I02}) \/ {D2}) /\ I2 is Element of bool ((II2 \/ {I02}) \/ {D2})
((II2 \/ {I02}) \/ {D2}) typed/\ I2 is Element of bool ((II2 \/ {I02}) \/ {D2})
((II2 \/ {I02}) \/ {D2}) /\ I2 is set
((II2 \/ {I02}) \/ {D2}) /\typed I2 is Element of bool I2
bool I2 is non empty set
I2 \typed/ ((II2 \/ {I02}) \/ {D2}) is Element of bool (I2 \/ ((II2 \/ {I02}) \/ {D2}))
I2 \/ ((II2 \/ {I02}) \/ {D2}) is non empty set
bool (I2 \/ ((II2 \/ {I02}) \/ {D2})) is non empty set
X1 is Element of bool ((II2 \/ {I02}) \/ {D2})
X1 null ((II2 \/ {I02}) \/ {D2}) is set
((II2 \/ {I02}) \/ {D2}) /\ X1 is Element of bool ((II2 \/ {I02}) \/ {D2})
((II2 \/ {I02}) \/ {D2}) typed/\ X1 is Element of bool ((II2 \/ {I02}) \/ {D2})
((II2 \/ {I02}) \/ {D2}) /\ X1 is set
((II2 \/ {I02}) \/ {D2}) /\typed X1 is Element of bool X1
bool X1 is non empty set
X1 \typed/ ((II2 \/ {I02}) \/ {D2}) is Element of bool (X1 \/ ((II2 \/ {I02}) \/ {D2}))
X1 \/ ((II2 \/ {I02}) \/ {D2}) is non empty set
bool (X1 \/ ((II2 \/ {I02}) \/ {D2})) is non empty set
(U,II1) -SymbolSubstIn I02 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
I02 +~ (U,II1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
bool a is non empty set
{c26} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
II2 null {c26} is set
II2 \typed/ {c26} is Element of bool (II2 \/ {c26})
II2 \/ {c26} is non empty set
bool (II2 \/ {c26}) is non empty set
{c26} null II2 is finite countable (X) set
{c26} \typed/ II2 is Element of bool ({c26} \/ II2)
{c26} \/ II2 is non empty set
bool ({c26} \/ II2) is non empty set
U is HC -satisfied Element of bool a
HC -TruthEval c26 is boolean Element of BOOLEAN
I is Element of seqt
(U,I) ReassignIn HC is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,seqt -interpreter-like Element of seqt -InterpretersOf X
{} .--> I is non empty trivial Relation-like {{}} -defined seqt -valued Function-like one-to-one constant finite 1 -element countable V209() set
{{}} --> I is non empty Relation-like {{}} -defined seqt -valued {I} -valued Function-like constant total quasi_total finite countable V209() Element of bool [:{{}},{I}:]
{I} is non empty trivial finite 1 -element countable set
[:{{}},{I}:] is non empty Relation-like finite countable set
bool [:{{}},{I}:] is non empty finite V36() countable set
U .--> ({} .--> I) is non empty trivial Relation-like AllSymbolsOf X -defined {U} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{U} is non empty trivial finite 1 -element countable set
{U} --> ({} .--> I) is non empty Relation-like non-empty non empty-yielding {U} -defined {({} .--> I)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{U},{({} .--> I)}:]
{({} .--> I)} is non empty trivial functional finite V36() 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{U},{({} .--> I)}:] is non empty Relation-like finite countable set
bool [:{U},{({} .--> I)}:] is non empty finite V36() countable set
HC +* (U .--> ({} .--> I)) is non empty Relation-like Function-like Function-yielding V156() set
((U,I) ReassignIn HC) -TruthEval I02 is boolean Element of BOOLEAN
II1 .--> ({} .--> I) is non empty trivial Relation-like AllSymbolsOf X -defined {II1} -defined Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{II1} is non empty trivial finite 1 -element countable set
{II1} --> ({} .--> I) is non empty Relation-like non-empty non empty-yielding {II1} -defined {({} .--> I)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{II1},{({} .--> I)}:]
[:{II1},{({} .--> I)}:] is non empty Relation-like finite countable set
bool [:{II1},{({} .--> I)}:] is non empty finite V36() countable set
(II1,I) ReassignIn HC is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,seqt -interpreter-like Element of seqt -InterpretersOf X
HC +* (II1 .--> ({} .--> I)) is non empty Relation-like Function-like Function-yielding V156() set
proj2 I02 is non empty finite countable set
F2 is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,seqt -interpreter-like Element of seqt -InterpretersOf X
X2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
F2 -TruthEval X2 is boolean Element of BOOLEAN
{X2} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
proj2 D2 is non empty finite countable set
{II1} is non empty trivial finite 1 -element countable Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
dom (II1 .--> ({} .--> I)) is non empty trivial finite 1 -element countable Element of bool {II1}
bool {II1} is non empty finite V36() countable set
F2 | (proj2 D2) is Relation-like proj2 D2 -defined OwnSymbolsOf X -defined Function-like finite Function-yielding V156() countable V209() set
HC | (proj2 D2) is Relation-like proj2 D2 -defined OwnSymbolsOf X -defined Function-like finite Function-yielding V156() countable V209() set
(II1 .--> ({} .--> I)) | (proj2 D2) is Relation-like proj2 D2 -defined AllSymbolsOf X -defined Function-like constant finite Function-yielding V156() countable V209() set
(HC | (proj2 D2)) +* ((II1 .--> ({} .--> I)) | (proj2 D2)) is Relation-like Function-like finite Function-yielding V156() countable V209() set
(HC | (proj2 D2)) +* {} is Relation-like Function-like finite Function-yielding V156() countable V209() set
(proj2 D2) /\ (OwnSymbolsOf X) is finite countable Element of bool (AllSymbolsOf X)
(proj2 D2) typed/\ (OwnSymbolsOf X) is finite countable Element of bool (proj2 D2)
bool (proj2 D2) is non empty finite V36() countable set
(proj2 D2) /\ (OwnSymbolsOf X) is finite countable set
(proj2 D2) /\typed (OwnSymbolsOf X) is Element of bool (OwnSymbolsOf X)
bool (OwnSymbolsOf X) is non empty set
HC | ((proj2 D2) /\ (OwnSymbolsOf X)) is Relation-like (proj2 D2) /\ (OwnSymbolsOf X) -defined OwnSymbolsOf X -defined Function-like finite Function-yielding V156() countable V209() set
(F2 | (proj2 D2)) | (OwnSymbolsOf X) is Relation-like OwnSymbolsOf X -defined OwnSymbolsOf X -defined Function-like finite Function-yielding V156() countable V209() set
(F2 | (proj2 D2)) null (OwnSymbolsOf X) is Relation-like (OwnSymbolsOf X) \/ (proj1 (F2 | (proj2 D2))) -defined (OwnSymbolsOf X) \/ (proj2 (F2 | (proj2 D2))) -valued Function-like set
proj1 (F2 | (proj2 D2)) is finite countable set
(OwnSymbolsOf X) \/ (proj1 (F2 | (proj2 D2))) is non empty set
proj2 (F2 | (proj2 D2)) is finite countable set
(OwnSymbolsOf X) \/ (proj2 (F2 | (proj2 D2))) is non empty set
(F2 | (proj2 D2)) \typed/ (OwnSymbolsOf X) is Element of bool ((F2 | (proj2 D2)) \/ (OwnSymbolsOf X))
(F2 | (proj2 D2)) \/ (OwnSymbolsOf X) is non empty set
bool ((F2 | (proj2 D2)) \/ (OwnSymbolsOf X)) is non empty set
F2 | ((proj2 D2) /\ (OwnSymbolsOf X)) is Relation-like (proj2 D2) /\ (OwnSymbolsOf X) -defined OwnSymbolsOf X -defined Function-like finite Function-yielding V156() countable V209() set
X22 is HC -satisfied Element of bool a
F5 is HC -satisfied F2 -satisfied Element of bool a
F1 is F2 -satisfied set
F5 \/ F1 is F2 -satisfied set
seqt2 is F2 -satisfied set
[seqt2,D2] is non empty V26() set
F2 -TruthEval D2 is boolean Element of BOOLEAN
HC -TruthEval D2 is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
D is set
Y is non empty set
Y -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((Y *),(Y \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
Y * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of Y
Y \/ BOOLEAN is non empty set
K491((Y *),(Y \/ BOOLEAN)) is non empty functional M30(Y * ,Y \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((Y *),(Y \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((Y *),(Y \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((Y *),(Y \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((Y *),(Y \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((Y *),(Y \/ BOOLEAN))) : b1 is X,Y -interpreter-like } is set
psi is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,Y -interpreter-like Element of Y -InterpretersOf X
H is psi -satisfied set
m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[H,m] is non empty V26() set
dom (X) is Element of bool (bool (X))
bool (bool (X)) is non empty set
[H,m] `1 is set
[H,m] `2 is set
(X) . D is set
[D,[H,m]] is non empty V26() set
HH is Relation-like X -correct (X) Element of bool (X)
HC is (X) (X) Element of (X)
HC `1 is finite countable (X) set
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
HC `2 is set
a is set
D2 is set
a `1 is set
D2 `1 is set
a `2 is set
sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ sub1) ^ sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth sub1),(Depth sub1)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot sub1),(xnot sub1)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth sub1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth sub1),(Depth sub1)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
xnot sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{(xnot sub1),(xnot sub1)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
D2 `2 is set
sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ sub2) ^ sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth sub2),(Depth sub2)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot sub2),(xnot sub2)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth sub2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth sub2),(Depth sub2)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
xnot sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{(xnot sub2),(xnot sub2)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
(<*(TheNorSymbOf X)*> ^ sub1) ^ sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth sub1),(Depth sub2)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot sub1),(xnot sub2)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth sub1),(Depth sub2)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot sub1),(xnot sub2)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[H,((<*(TheNorSymbOf X)*> ^ sub1) ^ sub1)] is non empty V26() set
[H,((<*(TheNorSymbOf X)*> ^ sub2) ^ sub2)] is non empty V26() set
psi -TruthEval ((<*(TheNorSymbOf X)*> ^ sub1) ^ sub1) is boolean Element of BOOLEAN
psi -TruthEval ((<*(TheNorSymbOf X)*> ^ sub2) ^ sub2) is boolean Element of BOOLEAN
psi -TruthEval sub1 is boolean Element of BOOLEAN
psi -TruthEval sub2 is boolean Element of BOOLEAN
psi -TruthEval m is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
D is set
Y is non empty set
Y -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((Y *),(Y \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
Y * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of Y
Y \/ BOOLEAN is non empty set
K491((Y *),(Y \/ BOOLEAN)) is non empty functional M30(Y * ,Y \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((Y *),(Y \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((Y *),(Y \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((Y *),(Y \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((Y *),(Y \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((Y *),(Y \/ BOOLEAN))) : b1 is X,Y -interpreter-like } is set
psi is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,Y -interpreter-like Element of Y -InterpretersOf X
H is psi -satisfied set
m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[H,m] is non empty V26() set
dom (X) is Element of bool (bool (X))
bool (bool (X)) is non empty set
[H,m] `1 is set
[H,m] `2 is set
(X) . D is set
[D,[H,m]] is non empty V26() set
HH is Relation-like X -correct (X) Element of bool (X)
HC is (X) (X) Element of (X)
HC `1 is finite countable (X) set
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
HC `2 is set
a is set
a `1 is set
a `2 is set
D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ D2) ^ sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth D2),(Depth sub1)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot D2),(xnot sub1)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth D2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth sub1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth D2),(Depth sub1)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
xnot D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ D2) ^ D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth D2),(Depth D2)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot D2),(xnot D2)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth D2),(Depth D2)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot D2),(xnot D2)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
xnot sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ sub1) ^ sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth sub1),(Depth sub1)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot sub1),(xnot sub1)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth sub1),(Depth sub1)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot sub1),(xnot sub1)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
{(xnot D2),(xnot sub1)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
(<*(TheNorSymbOf X)*> ^ sub1) ^ D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth sub1),(Depth D2)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot sub1),(xnot D2)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth sub1),(Depth D2)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot sub1),(xnot D2)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[H,((<*(TheNorSymbOf X)*> ^ D2) ^ sub1)] is non empty V26() set
psi -TruthEval ((<*(TheNorSymbOf X)*> ^ D2) ^ sub1) is boolean Element of BOOLEAN
psi -TruthEval D2 is boolean Element of BOOLEAN
psi -TruthEval sub1 is boolean Element of BOOLEAN
psi -TruthEval m is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
the U2 of X is Element of the U1 of X
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
D is set
Y is non empty set
Y -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((Y *),(Y \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
Y * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of Y
Y \/ BOOLEAN is non empty set
K491((Y *),(Y \/ BOOLEAN)) is non empty functional M30(Y * ,Y \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((Y *),(Y \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((Y *),(Y \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((Y *),(Y \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((Y *),(Y \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((Y *),(Y \/ BOOLEAN))) : b1 is X,Y -interpreter-like } is set
psi is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,Y -interpreter-like Element of Y -InterpretersOf X
H is psi -satisfied set
m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[H,m] is non empty V26() set
[H,m] `1 is set
([H,m] `1) \+\ H is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
[H,m] `2 is set
([H,m] `2) \+\ m is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(X) . D is set
[D,[H,m]] is non empty V26() set
dom (X) is Element of bool (bool (X))
bool (bool (X)) is non empty set
HH is Relation-like X -correct (X) Element of bool (X)
HC is (X) (X) Element of (X)
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
HC `1 is finite countable (X) set
HC `2 is set
a is set
D2 is set
a `1 is set
D2 `1 is set
a `2 is set
sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
D2 `2 is set
<*(TheNorSymbOf X)*> ^ sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ sub2) ^ inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth sub2),(Depth inf)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot sub2),(xnot inf)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth sub2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
Depth inf is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth sub2),(Depth inf)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
xnot sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ sub2) ^ sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth sub2),(Depth sub2)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot sub2),(xnot sub2)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth sub2),(Depth sub2)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot sub2),(xnot sub2)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
xnot inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ inf) ^ inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth inf),(Depth inf)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot inf),(xnot inf)}) Element of ((AllSymbolsOf X) *) \ {{}}
max ((Depth inf),(Depth inf)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot inf),(xnot inf)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
{(xnot sub2),(xnot inf)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{sub1} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (X) Element of bool (((AllSymbolsOf X) *) \ {{}})
{sub1} \/ (HC `1) is non empty finite countable (X) set
<*(TheNorSymbOf X)*> ^ sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ sub1) ^ sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth sub1),(Depth sub1)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot sub1),(xnot sub1)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth sub1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth sub1),(Depth sub1)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
xnot sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
{(xnot sub1),(xnot sub1)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
U is non empty Relation-like (X) Element of bool (X)
II1 is Element of U
II1 `1 is set
{sub1} \/ H is non empty set
I2 is finite countable (X) set
psi -TruthEval sub1 is boolean Element of BOOLEAN
I1 is psi -satisfied set
I1 \/ H is psi -satisfied set
c26 is psi -satisfied set
[c26,sub2] is non empty V26() set
[c26,((<*(TheNorSymbOf X)*> ^ sub2) ^ inf)] is non empty V26() set
psi -TruthEval sub2 is boolean Element of BOOLEAN
psi -TruthEval ((<*(TheNorSymbOf X)*> ^ sub2) ^ inf) is boolean Element of BOOLEAN
psi -TruthEval m is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
(X,C) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{} null X is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined X \/ (proj1 {}) -defined X \/ (proj1 {}) -defined {{}} -valued X -valued {{}} -valued X \/ (proj2 {}) -valued X \/ (proj2 {}) -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element len {} -element len {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() X -correct (X) (X) set
X \/ (proj1 {}) is set
X \/ (proj2 {}) is set
{} \typed/ X is Element of bool ({} \/ X)
{} \/ X is set
bool ({} \/ X) is non empty set
{} null (X) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined (X) \/ (proj1 {}) -defined {{}} -valued (X) -valued (X) \/ (proj2 {}) -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element len {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(X) \/ (proj1 {}) is non empty Relation-like set
(X) \/ (proj2 {}) is non empty Relation-like set
{} \typed/ (X) is Relation-like Element of bool ({} \/ (X))
{} \/ (X) is non empty Relation-like set
bool ({} \/ (X)) is non empty set
dom (X,C) is Element of bool (bool (X))
bool (bool (X)) is non empty set
proj2 (X,C) is set
(X,C,0) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
iter ((X,C),0) is Relation-like Function-like set
field (X,C) is set
proj1 (X,C) is set
(proj1 (X,C)) \/ (proj2 (X,C)) is set
id (field (X,C)) is Relation-like field (X,C) -defined field (X,C) -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:(field (X,C)),(field (X,C)):]
[:(field (X,C)),(field (X,C)):] is Relation-like set
bool [:(field (X,C)),(field (X,C)):] is non empty set
FF is Element of bool (bool (X))
(bool (X)) \/ FF is non empty Element of bool (bool (X))
(bool (X)) null FF is set
(bool (X)) \typed/ FF is Element of bool ((bool (X)) \/ FF)
(bool (X)) \/ FF is non empty set
bool ((bool (X)) \/ FF) is non empty set
id ((bool (X)) \/ FF) is non empty Relation-like (bool (X)) \/ FF -defined (bool (X)) \/ FF -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:((bool (X)) \/ FF),((bool (X)) \/ FF):]
[:((bool (X)) \/ FF),((bool (X)) \/ FF):] is non empty Relation-like set
bool [:((bool (X)) \/ FF),((bool (X)) \/ FF):] is non empty set
id (bool (X)) is non empty Relation-like bool (X) -defined bool (X) -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:(bool (X)),(bool (X)):]
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
Y is Relation-like X -correct (X) Element of bool (X)
(X,C,0) . Y is Relation-like (X) Element of bool (X)
(id (bool (X))) . Y is Relation-like (X) Element of bool (X)
((id (bool (X))) . Y) \+\ Y is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() (X) Element of bool (X)
D is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X,C,D) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
iter ((X,C),D) is Relation-like Function-like set
D + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(X,C,(D + 1)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
iter ((X,C),(D + 1)) is Relation-like Function-like set
Y is Relation-like X -correct (X) Element of bool (X)
(X,C,(D + 1)) . Y is Relation-like (X) Element of bool (X)
dom (X,C,D) is Element of bool (bool (X))
(X,C,D) . Y is Relation-like (X) Element of bool (X)
(X,C) * (X,C,D) is non empty Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of bool [:(bool (X)),(bool (X)):]
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
m is non empty set
m -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((m *),(m \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
m * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of m
m \/ BOOLEAN is non empty set
K491((m *),(m \/ BOOLEAN)) is non empty functional M30(m * ,m \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((m *),(m \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((m *),(m \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((m *),(m \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((m *),(m \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((m *),(m \/ BOOLEAN))) : b1 is X,m -interpreter-like } is set
HH is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,m -interpreter-like Element of m -InterpretersOf X
HC is HH -satisfied set
a is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[HC,a] is non empty V26() set
[:(bool (X)),(bool (X)):] is non empty Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):]
[:(bool (X)),(bool (X)):] is non empty Relation-like set
bool [:(bool (X)),(bool (X)):] is non empty set
bool [:(bool (X)),(bool (X)):] is non empty set
H is Relation-like X -correct (X) Element of bool (X)
{H} is non empty trivial finite 1 -element countable Element of bool (bool (X))
{ (b1 .: {H}) where b1 is Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):] : b1 in C } is set
(X,C) . H is Relation-like (X) Element of bool (X)
union { (b1 .: {H}) where b1 is Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):] : b1 in C } is set
union (union { (b1 .: {H}) where b1 is Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):] : b1 in C } ) is set
sub1 is set
sub2 is set
inf is Relation-like bool (X) -defined bool (X) -valued Element of bool [:(bool (X)),(bool (X)):]
inf .: {H} is Element of bool (bool (X))
U is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
U . H is Relation-like (X) Element of bool (X)
dom U is Element of bool (bool (X))
Im (inf,H) is set
{H} is non empty trivial finite 1 -element countable set
inf .: {H} is set
Im (U,H) is set
U .: {H} is finite countable set
{(U . H)} is non empty trivial finite 1 -element countable Element of bool (bool (X))
II1 is Relation-like X -correct (X) Element of bool (X)
HH -TruthEval a is boolean Element of BOOLEAN
Y is set
D is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
phii is set
psi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[phii,D] is non empty V26() set
bool Y is non empty set
(X,C,psi) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
iter ((X,C),psi) is Relation-like Function-like set
DD is Relation-like X -correct (X) Element of bool (X)
(X,C,psi) . DD is Relation-like (X) Element of bool (X)
HH is non empty set
HH -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((HH *),(HH \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
HH * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of HH
HH \/ BOOLEAN is non empty set
K491((HH *),(HH \/ BOOLEAN)) is non empty functional M30(HH * ,HH \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((HH *),(HH \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((HH *),(HH \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((HH *),(HH \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((HH *),(HH \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((HH *),(HH \/ BOOLEAN))) : b1 is X,HH -interpreter-like } is set
a is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,HH -interpreter-like Element of HH -InterpretersOf X
D2 is a -satisfied set
bool D2 is non empty set
H is Element of bool Y
sub1 is a -satisfied Element of bool D2
[sub1,D] is non empty V26() Element of [:(bool D2),(((AllSymbolsOf X) *) \ {{}}):]
[:(bool D2),(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
seqt is Relation-like X -correct (X) Element of bool (X)
a -TruthEval D is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
{C} is non empty trivial functional finite 1 -element with_common_domain countable Element of bool (Funcs ((bool (X)),(bool (X))))
S is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
S is functional Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is functional (2,X) Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X),(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
{(X),(X),(X),(X),(X),(X),(X),(X)} \/ {(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
DD is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
DD is functional Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
S is Relation-like (X) Element of bool (X)
DD is Relation-like (X) Element of bool (X)
Y is set
(X) . S is Relation-like (X) Element of bool (X)
[S,Y] is non empty V26() set
phii is (X) (X) Element of (X)
phii `2 is set
phii `1 is finite countable (X) set
psi is set
H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
psi `1 is set
psi `2 is set
xnot H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf X)*> ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ H) ^ H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth H),(Depth H)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot H),(xnot H)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth H is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth H),(Depth H)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(xnot H),(xnot H)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
xnot (xnot H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ (xnot H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ (xnot H)) ^ (xnot H) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth (xnot H)),(Depth (xnot H))) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot (xnot H)),(xnot (xnot H))}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth (xnot H) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth (xnot H)),(Depth (xnot H))) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot (xnot H)),(xnot (xnot H))} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[DD,phii] is non empty V26() Element of [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
(X) . DD is Relation-like (X) Element of bool (X)
S is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
X is V51() V53() eligible Language-like
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
C is finite countable (X) set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
[C,phi] is non empty V26() (X) (X) set
[C,phi] null 1 is set
[C,phi] \typed/ 1 is Element of bool ([C,phi] \/ 1)
[C,phi] \/ 1 is non empty set
bool ([C,phi] \/ 1) is non empty set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
xnot phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
the U3 of X is Element of the U1 of X
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf X)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ phi) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth phi)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot phi),(xnot phi)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth phi),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) (X) Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(xnot phi),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
xnot (xnot phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ (xnot phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ (xnot phi)) ^ (xnot phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth (xnot phi)),(Depth (xnot phi))) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot (xnot phi)),(xnot (xnot phi))}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth (xnot phi) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth (xnot phi)),(Depth (xnot phi))) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot (xnot phi)),(xnot (xnot phi))} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
[C,(xnot (xnot phi))] is non empty V26() (X) (X) set
{[C,(xnot (xnot phi))]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (X) set
H is (X) (X) Element of (X)
H `2 is set
(H `2) \+\ phi is set
[C,(xnot (xnot phi))] `1 is finite countable (X) set
([C,(xnot (xnot phi))] `1) \+\ C is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
H `1 is finite countable (X) set
(H `1) \+\ C is finite countable set
[C,(xnot (xnot phi))] `2 is set
([C,(xnot (xnot phi))] `2) \+\ (xnot (xnot phi)) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
m is Relation-like (X) Element of bool (X)
[m,H] is non empty V26() Element of [:(bool (X)),(X):]
(X) . {[C,(xnot (xnot phi))]} is set
seqt is set
C is V51() V53() eligible Language-like
AtomicFormulaSymbolsOf C is non empty Element of bool (AllSymbolsOf C)
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
TheNorSymbOf C is set
the U3 of C is Element of the U1 of C
{(TheNorSymbOf C)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf C) \ {(TheNorSymbOf C)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) typed\ {(TheNorSymbOf C)} is Element of bool (AllSymbolsOf C)
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
X is set
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
TermSymbolsOf C is non empty set
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf C) *) \ {{}}
FF is non empty set
FF -InterpretersOf C is non empty functional Element of bool (Funcs ((OwnSymbolsOf C),K491((FF *),(FF \/ BOOLEAN))))
OwnSymbolsOf C is non empty Element of bool (AllSymbolsOf C)
{ the U2 of C, the U3 of C} is non empty finite countable set
the U1 of C \ { the U2 of C, the U3 of C} is Element of bool the U1 of C
the U1 of C typed\ { the U2 of C, the U3 of C} is Element of bool the U1 of C
FF * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of FF
FF \/ BOOLEAN is non empty set
K491((FF *),(FF \/ BOOLEAN)) is non empty functional M30(FF * ,FF \/ BOOLEAN)
Funcs ((OwnSymbolsOf C),K491((FF *),(FF \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf C,K491((FF *),(FF \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf C),K491((FF *),(FF \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf C -defined K491((FF *),(FF \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf C),K491((FF *),(FF \/ BOOLEAN))) : b1 is C,FF -interpreter-like } is set
Y is Relation-like OwnSymbolsOf C -defined Function-like total Function-yielding V156() C,FF -interpreter-like Element of FF -InterpretersOf C
Y -TermEval is non empty Relation-like AllTermsOf C -defined FF -valued Function-like total quasi_total Element of bool [:(AllTermsOf C),FF:]
AllTermsOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf C) *) \ {{}}))
bool (bool (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
C -termsOfMaxDepth is Relation-like Function-like set
proj2 (C -termsOfMaxDepth) is set
union (proj2 (C -termsOfMaxDepth)) is set
[:(AllTermsOf C),FF:] is non empty Relation-like set
bool [:(AllTermsOf C),FF:] is non empty set
(Y -TermEval) . the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}} is set
Y -TruthEval ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) is boolean Element of BOOLEAN
Y -AtomicEval ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) is boolean Element of BOOLEAN
Y === is Relation-like Function-like Function-yielding V156() C,FF -interpreter-like Y -extension set
TheEqSymbOf C is Element of AtomicFormulaSymbolsOf C
FF -deltaInterpreter is non empty Relation-like 2 -tuples_on FF -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on FF),BOOLEAN:]
2 -tuples_on FF is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of FF
[:(2 -tuples_on FF),BOOLEAN:] is non empty Relation-like set
bool [:(2 -tuples_on FF),BOOLEAN:] is non empty set
[:(FF *),(FF *):] is non empty non trivial Relation-like non finite non empty-membered set
K295(FF) is non empty Relation-like [:(FF *),(FF *):] -defined FF * -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:[:(FF *),(FF *):],(FF *):]
[:[:(FF *),(FF *):],(FF *):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(FF *),(FF *):],(FF *):] is non empty non trivial non finite non empty-membered set
1 -tuples_on FF is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of FF
id (1 -tuples_on FF) is non empty Relation-like non-empty non empty-yielding 1 -tuples_on FF -defined 1 -tuples_on FF -valued Function-like one-to-one total quasi_total onto bijective Function-yielding V156() reflexive symmetric antisymmetric transitive V208() Element of bool [:(1 -tuples_on FF),(1 -tuples_on FF):]
[:(1 -tuples_on FF),(1 -tuples_on FF):] is non empty Relation-like set
bool [:(1 -tuples_on FF),(1 -tuples_on FF):] is non empty set
K295(FF) .: (id (1 -tuples_on FF)) is functional V36() FinSequence-membered Element of bool (FF *)
bool (FF *) is non empty non trivial non finite non empty-membered set
chi ((K295(FF) .: (id (1 -tuples_on FF))),(2 -tuples_on FF)) is non empty Relation-like 2 -tuples_on FF -defined BOOLEAN -valued Function-like total quasi_total boolean-valued Element of bool [:(2 -tuples_on FF),BOOLEAN:]
(TheEqSymbOf C) .--> (FF -deltaInterpreter) is non empty trivial Relation-like AtomicFormulaSymbolsOf C -defined {(TheEqSymbOf C)} -defined bool [:(2 -tuples_on FF),BOOLEAN:] -valued Function-like one-to-one constant finite 1 -element Function-yielding V156() countable V209() set
{(TheEqSymbOf C)} is non empty trivial finite 1 -element countable set
{(TheEqSymbOf C)} --> (FF -deltaInterpreter) is non empty Relation-like non-empty non empty-yielding {(TheEqSymbOf C)} -defined bool [:(2 -tuples_on FF),BOOLEAN:] -valued {(FF -deltaInterpreter)} -valued Function-like constant total quasi_total finite Function-yielding V156() countable V209() Element of bool [:{(TheEqSymbOf C)},{(FF -deltaInterpreter)}:]
{(FF -deltaInterpreter)} is non empty trivial functional finite 1 -element with_non-empty_elements non empty-membered with_common_domain countable set
[:{(TheEqSymbOf C)},{(FF -deltaInterpreter)}:] is non empty Relation-like finite countable set
bool [:{(TheEqSymbOf C)},{(FF -deltaInterpreter)}:] is non empty finite V36() countable set
Y +* ((TheEqSymbOf C) .--> (FF -deltaInterpreter)) is non empty Relation-like Function-like Function-yielding V156() set
C -firstChar is non empty Relation-like ((AllSymbolsOf C) *) \ {{}} -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):]
[:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) -firstChar is non empty Relation-like ((AllSymbolsOf C) *) \ {{}} -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):]
(AllSymbolsOf C) -pr1 is non empty Relation-like [:(AllSymbolsOf C),(AllSymbolsOf C):] -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):]
[:(AllSymbolsOf C),(AllSymbolsOf C):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf C),(AllSymbolsOf C)) is non empty Relation-like [:(AllSymbolsOf C),(AllSymbolsOf C):] -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):]
MultPlace ((AllSymbolsOf C) -pr1) is non empty Relation-like ((AllSymbolsOf C) *) \ {{}} -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):]
(C -firstChar) . ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) is low-compounding relational ofAtomicFormula Element of AllSymbolsOf C
(Y ===) . ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}})) is non empty Relation-like (abs (ar ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}})))) -tuples_on FF -defined FF \/ BOOLEAN -valued Function-like total quasi_total Interpreter of (C -firstChar) . ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}),FF
ar ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}})) is non empty complex ext-real non positive negative finite V40() V41() countable Element of INT
the adicity of C . ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}})) is set
abs (ar ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}))) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(abs (ar ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}})))) -tuples_on FF is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of FF
SubTerms ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) is Relation-like NAT -defined (proj2 ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}})) * -valued (TermSymbolsOf C) * -valued AllTermsOf C -valued Function-like finite abs (ar ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}))) -element FinSequence-like FinSubsequence-like Function-yielding V156() countable V208() V209() Element of (AllTermsOf C) *
proj2 ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) is non empty finite countable set
(proj2 ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}})) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of proj2 ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}})
(TermSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of TermSymbolsOf C
AllTermsOf C is non empty functional V36() FinSequence-membered AllSymbolsOf C -prefix C -prefix Element of bool ((AllSymbolsOf C) *)
((AllSymbolsOf C) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (AllSymbolsOf C) *
(AllTermsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of bool (((AllSymbolsOf C) *) *)
bool (((AllSymbolsOf C) *) *) is non empty non trivial non finite non empty-membered set
(SubTerms ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}})) * (Y -TermEval) is Relation-like NAT -defined FF -valued Function-like finite countable V209() set
((Y ===) . ((C -firstChar) . ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}))) . ((SubTerms ((<*(TheEqSymbOf C)*> ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}) ^ the non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}})) * (Y -TermEval)) is set
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
X is set
AtomicFormulaSymbolsOf C is non empty Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
TheNorSymbOf C is set
the U3 of C is Element of the U1 of C
{(TheNorSymbOf C)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf C) \ {(TheNorSymbOf C)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) typed\ {(TheNorSymbOf C)} is Element of bool (AllSymbolsOf C)
the non empty Relation-like NAT -defined AtomicFormulaSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff X -implied Element of ((AllSymbolsOf C) *) \ {{}} is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff X -implied Element of ((AllSymbolsOf C) *) \ {{}}
X is V51() V53() eligible Language-like
C is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff C -implied Element of ((AllSymbolsOf X) *) \ {{}}
xnot phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
TheNorSymbOf X is non literal non low-compounding non relational non own Element of AllSymbolsOf X
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
<*(TheNorSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheNorSymbOf X)] is non empty V26() set
{[1,(TheNorSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf X)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ phi) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth phi)) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot phi),(xnot phi)}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth phi),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) (X) Element of bool (Funcs ((bool (X)),(bool (X))))
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X)} is non empty trivial functional finite 1 -element with_common_domain countable (X) (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X)} \/ {(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(xnot phi),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
xnot (xnot phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
<*(TheNorSymbOf X)*> ^ (xnot phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf X) *) \ {{}}
(<*(TheNorSymbOf X)*> ^ (xnot phi)) ^ (xnot phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth (xnot phi)),(Depth (xnot phi))) -wff wff non exal (X,{(X)} \/ {(X)},{(xnot (xnot phi)),(xnot (xnot phi))}) Element of ((AllSymbolsOf X) *) \ {{}}
Depth (xnot phi) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth (xnot phi)),(Depth (xnot phi))) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot (xnot phi)),(xnot (xnot phi))} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf X) *) \ {{}})
S is non empty set
S -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((S *),(S \/ BOOLEAN))))
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
S * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of S
S \/ BOOLEAN is non empty set
K491((S *),(S \/ BOOLEAN)) is non empty functional M30(S * ,S \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((S *),(S \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((S *),(S \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf X),K491((S *),(S \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((S *),(S \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((S *),(S \/ BOOLEAN))) : b1 is X,S -interpreter-like } is set
FF is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,S -interpreter-like Element of S -InterpretersOf X
FF -TruthEval phi is boolean Element of BOOLEAN
FF -TruthEval (xnot phi) is boolean Element of BOOLEAN
FF -TruthEval (xnot (xnot phi)) is boolean Element of BOOLEAN
'not' (FF -TruthEval phi) is boolean Element of BOOLEAN
1 - (FF -TruthEval phi) is set
('not' (FF -TruthEval phi)) \+\ (FF -TruthEval (xnot phi)) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
'not' (FF -TruthEval (xnot phi)) is boolean Element of BOOLEAN
1 - (FF -TruthEval (xnot phi)) is set
('not' (FF -TruthEval (xnot phi))) \+\ (FF -TruthEval (xnot (xnot phi))) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
ExFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
[:NAT,(ExFormulasOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(ExFormulasOf C):] is non empty non trivial non finite non empty-membered set
X is functional set
X \/ (AllFormulasOf C) is non empty functional set
bool (X \/ (AllFormulasOf C)) is non empty Element of bool (bool (X \/ (AllFormulasOf C)))
bool (X \/ (AllFormulasOf C)) is non empty set
bool (bool (X \/ (AllFormulasOf C))) is non empty set
[:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial non finite non empty-membered set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S is non empty Relation-like non-empty non empty-yielding NAT -defined ExFormulasOf C -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(ExFormulasOf C):]
X null (AllFormulasOf C) is set
X \typed/ (AllFormulasOf C) is functional Element of bool (X \/ (AllFormulasOf C))
psi is functional Element of bool (X \/ (AllFormulasOf C))
H is non empty Relation-like NAT -defined bool (X \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (X \/ (AllFormulasOf C))):]
H . 0 is functional Element of bool (X \/ (AllFormulasOf C))
m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
seqt is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
H . seqt is functional Element of bool (X \/ (AllFormulasOf C))
S . seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf C
(C,phi,(H . seqt),(S . seqt)) is functional Element of bool ((H . seqt) \/ (AllFormulasOf C))
(H . seqt) \/ (AllFormulasOf C) is non empty functional set
bool ((H . seqt) \/ (AllFormulasOf C)) is non empty set
(AllFormulasOf C) \/ (H . seqt) is non empty functional set
(AllFormulasOf C) \/ (X \/ (AllFormulasOf C)) is non empty functional set
(AllFormulasOf C) \/ (AllFormulasOf C) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) \ {{}})
((AllFormulasOf C) \/ (AllFormulasOf C)) \/ X is non empty functional set
m + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
H . (m + 1) is functional Element of bool (X \/ (AllFormulasOf C))
HH is functional Element of bool (X \/ (AllFormulasOf C))
HH null (X \/ (AllFormulasOf C)) is set
(X \/ (AllFormulasOf C)) /\ HH is functional Element of bool (X \/ (AllFormulasOf C))
(X \/ (AllFormulasOf C)) typed/\ HH is functional Element of bool (X \/ (AllFormulasOf C))
(X \/ (AllFormulasOf C)) /\ HH is functional set
(X \/ (AllFormulasOf C)) /\typed HH is functional Element of bool HH
bool HH is non empty set
HH \typed/ (X \/ (AllFormulasOf C)) is functional Element of bool (HH \/ (X \/ (AllFormulasOf C)))
HH \/ (X \/ (AllFormulasOf C)) is non empty functional set
bool (HH \/ (X \/ (AllFormulasOf C))) is non empty set
H . m is functional Element of bool (X \/ (AllFormulasOf C))
S . m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf C
(C,phi,(H . m),(S . m)) is functional Element of bool ((H . m) \/ (AllFormulasOf C))
(H . m) \/ (AllFormulasOf C) is non empty functional set
bool ((H . m) \/ (AllFormulasOf C)) is non empty set
m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
m + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
H . (m + 1) is functional Element of bool (X \/ (AllFormulasOf C))
H . m is functional Element of bool (X \/ (AllFormulasOf C))
S . m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf C
(C,phi,(H . m),(S . m)) is functional Element of bool ((H . m) \/ (AllFormulasOf C))
(H . m) \/ (AllFormulasOf C) is non empty functional set
bool ((H . m) \/ (AllFormulasOf C)) is non empty set
psi is non empty Relation-like NAT -defined bool (X \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (X \/ (AllFormulasOf C))):]
psi . 0 is functional Element of bool (X \/ (AllFormulasOf C))
H is non empty Relation-like NAT -defined bool (X \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (X \/ (AllFormulasOf C))):]
H . 0 is functional Element of bool (X \/ (AllFormulasOf C))
m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
m + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
psi . (m + 1) is functional Element of bool (X \/ (AllFormulasOf C))
psi . m is functional Element of bool (X \/ (AllFormulasOf C))
S . m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf C
(C,phi,(psi . m),(S . m)) is functional Element of bool ((psi . m) \/ (AllFormulasOf C))
(psi . m) \/ (AllFormulasOf C) is non empty functional set
bool ((psi . m) \/ (AllFormulasOf C)) is non empty set
seqt is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
seqt + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
psi . (seqt + 1) is functional Element of bool (X \/ (AllFormulasOf C))
psi . seqt is functional Element of bool (X \/ (AllFormulasOf C))
S . seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf C
(C,phi,(psi . seqt),(S . seqt)) is functional Element of bool ((psi . seqt) \/ (AllFormulasOf C))
(psi . seqt) \/ (AllFormulasOf C) is non empty functional set
bool ((psi . seqt) \/ (AllFormulasOf C)) is non empty set
m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
m + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
H . (m + 1) is functional Element of bool (X \/ (AllFormulasOf C))
H . m is functional Element of bool (X \/ (AllFormulasOf C))
S . m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf C
(C,phi,(H . m),(S . m)) is functional Element of bool ((H . m) \/ (AllFormulasOf C))
(H . m) \/ (AllFormulasOf C) is non empty functional set
bool ((H . m) \/ (AllFormulasOf C)) is non empty set
seqt is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
seqt + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
H . (seqt + 1) is functional Element of bool (X \/ (AllFormulasOf C))
H . seqt is functional Element of bool (X \/ (AllFormulasOf C))
S . seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf C
(C,phi,(H . seqt),(S . seqt)) is functional Element of bool ((H . seqt) \/ (AllFormulasOf C))
(H . seqt) \/ (AllFormulasOf C) is non empty functional set
bool ((H . seqt) \/ (AllFormulasOf C)) is non empty set
dom psi is non empty countable Element of bool NAT
dom H is non empty countable Element of bool NAT
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
ExFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
[:NAT,(ExFormulasOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(ExFormulasOf C):] is non empty non trivial non finite non empty-membered set
X is set
C is V51() V53() eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
{phi} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
X \/ {phi} is non empty set
S is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf C
<*S*> is non empty trivial Relation-like NAT -defined TermSymbolsOf C -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() termal 0 -termal Element of ((AllSymbolsOf C) *) \ {{}}
TermSymbolsOf C is non empty set
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
[1,S] is non empty V26() set
{[1,S]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*S*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff 1 + (Depth phi) -wff non Depth phi -wff wff exal Element of ((AllSymbolsOf C) *) \ {{}}
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
1 + (Depth phi) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
{(<*S*> ^ phi)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
X \/ {(<*S*> ^ phi)} is non empty set
DD is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf C
(S,DD) -SymbolSubstIn phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
phi +~ (S,DD) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((S,DD) -SymbolSubstIn phi)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
X \/ {((S,DD) -SymbolSubstIn phi)} is non empty set
FF is functional Element of bool (Funcs ((bool (C)),(bool (C))))
TheEqSymbOf C is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf C
the U2 of C is Element of the U1 of C
LettersOf C is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
the adicity of C " {0} is Element of bool ( the U1 of C \ { the U3 of C})
proj2 phi is non empty finite countable set
(proj2 phi) /\ (LettersOf C) is non empty finite countable Element of bool (AllSymbolsOf C)
(proj2 phi) typed/\ (LettersOf C) is finite countable Element of bool (proj2 phi)
bool (proj2 phi) is non empty finite V36() countable set
(proj2 phi) /\ (LettersOf C) is non empty finite countable set
(proj2 phi) /\typed (LettersOf C) is Element of bool (LettersOf C)
bool (LettersOf C) is non empty non trivial non finite non empty-membered set
the Element of (proj2 phi) /\ (LettersOf C) is Element of (proj2 phi) /\ (LettersOf C)
a is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf C
<*a*> is non empty trivial Relation-like NAT -defined TermSymbolsOf C -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() termal 0 -termal Element of ((AllSymbolsOf C) *) \ {{}}
[1,a] is non empty V26() set
{[1,a]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
AtomicFormulaSymbolsOf C is non empty Element of bool (AllSymbolsOf C)
TheNorSymbOf C is set
{(TheNorSymbOf C)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf C) \ {(TheNorSymbOf C)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) typed\ {(TheNorSymbOf C)} is Element of bool (AllSymbolsOf C)
<*(TheEqSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheEqSymbOf C)] is non empty V26() set
{[1,(TheEqSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
D2 is non empty Relation-like NAT -defined TermSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheEqSymbOf C)*> ^ D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheEqSymbOf C)*> ^ D2) ^ D2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf C) *) \ {{}}
sub2 is non empty Relation-like NAT -defined AtomicFormulaSymbolsOf C -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() 0wff 0 -wff wff Element of ((AllSymbolsOf C) *) \ {{}}
proj2 sub2 is non empty finite countable set
proj2 (<*(TheEqSymbOf C)*> ^ D2) is non empty finite countable set
proj2 D2 is non empty finite countable set
(proj2 (<*(TheEqSymbOf C)*> ^ D2)) \/ (proj2 D2) is non empty finite countable set
proj2 <*(TheEqSymbOf C)*> is non empty trivial finite 1 -element countable set
(proj2 <*(TheEqSymbOf C)*>) \/ (proj2 D2) is non empty finite countable set
((proj2 <*(TheEqSymbOf C)*>) \/ (proj2 D2)) \/ (proj2 D2) is non empty finite countable set
(proj2 D2) \/ (proj2 D2) is non empty finite countable set
(proj2 <*(TheEqSymbOf C)*>) \/ ((proj2 D2) \/ (proj2 D2)) is non empty finite countable set
{(TheEqSymbOf C)} is non empty trivial finite 1 -element countable Element of bool (AllSymbolsOf C)
{(TheEqSymbOf C)} \/ (proj2 D2) is non empty finite countable set
{a} is non empty trivial finite 1 -element countable Element of bool (AllSymbolsOf C)
{(TheEqSymbOf C)} \/ {a} is non empty finite countable Element of bool (AllSymbolsOf C)
inf is Element of proj2 phi
{inf} is non empty trivial finite 1 -element countable Element of bool (proj2 phi)
{(TheEqSymbOf C),(TheNorSymbOf C)} is non empty finite countable Element of bool (AllSymbolsOf C)
{inf} \/ {(TheEqSymbOf C),(TheNorSymbOf C)} is non empty finite countable set
(proj2 phi) \/ {(TheEqSymbOf C),(TheNorSymbOf C)} is non empty finite countable set
xnot sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() 0 + 1 -wff wff Element of ((AllSymbolsOf C) *) \ {{}}
0 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ sub2) ^ sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth sub2),(Depth sub2)) -wff 0 + 1 -wff wff non exal (C,{(C)} \/ {(C)},{(xnot sub2),(xnot sub2)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth sub2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
max ((Depth sub2),(Depth sub2)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot sub2),(xnot sub2)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
U is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
proj2 U is non empty finite countable set
proj2 (<*(TheNorSymbOf C)*> ^ sub2) is non empty finite countable set
(proj2 (<*(TheNorSymbOf C)*> ^ sub2)) \/ (proj2 sub2) is non empty finite countable set
proj2 <*(TheNorSymbOf C)*> is non empty trivial finite 1 -element countable set
(proj2 <*(TheNorSymbOf C)*>) \/ (proj2 sub2) is non empty finite countable set
((proj2 <*(TheNorSymbOf C)*>) \/ (proj2 sub2)) \/ (proj2 sub2) is non empty finite countable set
(proj2 sub2) \/ (proj2 sub2) is non empty finite countable set
(proj2 <*(TheNorSymbOf C)*>) \/ ((proj2 sub2) \/ (proj2 sub2)) is non empty finite countable set
{(TheNorSymbOf C)} is non empty trivial finite 1 -element countable Element of bool (AllSymbolsOf C)
{(TheNorSymbOf C)} \/ (proj2 sub2) is non empty finite countable set
{(TheEqSymbOf C)} \/ {(TheNorSymbOf C)} is non empty finite countable Element of bool (AllSymbolsOf C)
({(TheEqSymbOf C)} \/ {(TheNorSymbOf C)}) \/ {a} is non empty finite countable Element of bool (AllSymbolsOf C)
{(TheEqSymbOf C),(TheNorSymbOf C)} \/ {a} is non empty finite countable Element of bool (AllSymbolsOf C)
II1 is set
II2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[II1,U] is non empty V26() set
I2 is (C) (C) Element of (C)
I2 `1 is finite countable (C) set
(I2 `1) \+\ II1 is set
bool (X \/ {((S,DD) -SymbolSubstIn phi)}) is non empty set
bool X is non empty set
I1 is finite countable (C) Element of bool (X \/ {((S,DD) -SymbolSubstIn phi)})
I1 /\ X is finite countable Element of bool (X \/ {((S,DD) -SymbolSubstIn phi)})
I1 typed/\ X is finite countable (C) Element of bool I1
bool I1 is non empty finite V36() countable set
I1 /\ X is finite countable set
I1 /\typed X is Element of bool X
bool {((S,DD) -SymbolSubstIn phi)} is non empty finite V36() countable set
I1 /\ {((S,DD) -SymbolSubstIn phi)} is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (((AllSymbolsOf C) *) \ {{}})
I1 typed/\ {((S,DD) -SymbolSubstIn phi)} is finite countable (C) Element of bool I1
I1 /\ {((S,DD) -SymbolSubstIn phi)} is functional finite countable set
I1 /\typed {((S,DD) -SymbolSubstIn phi)} is trivial functional finite V36() FinSequence-membered with_non-empty_elements with_common_domain countable (C) Element of bool {((S,DD) -SymbolSubstIn phi)}
{phi} null X is finite countable (C) set
{phi} \typed/ X is Element of bool ({phi} \/ X)
{phi} \/ X is non empty set
bool ({phi} \/ X) is non empty set
X null {phi} is set
X \typed/ {phi} is Element of bool (X \/ {phi})
bool (X \/ {phi}) is non empty set
I1 is Element of bool (X \/ {phi})
bool I1 is non empty set
c26 is finite countable (C) Element of bool X
{U} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
I2 is Element of bool (X \/ {phi})
X22 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf C) *) \ {{}})
(((AllSymbolsOf C) *) \ {{}}) /\ X22 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf C) *) \ {{}})
(((AllSymbolsOf C) *) \ {{}}) typed/\ X22 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf C) *) \ {{}})
(((AllSymbolsOf C) *) \ {{}}) /\ X22 is functional set
(((AllSymbolsOf C) *) \ {{}}) /\typed X22 is functional V36() FinSequence-membered with_non-empty_elements Element of bool X22
bool X22 is non empty set
X22 null (((AllSymbolsOf C) *) \ {{}}) is set
X22 \typed/ (((AllSymbolsOf C) *) \ {{}}) is functional V36() with_non-empty_elements Element of bool (X22 \/ (((AllSymbolsOf C) *) \ {{}}))
X22 \/ (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial functional non finite V36() with_non-empty_elements non empty-membered set
bool (X22 \/ (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
SymbolsOf ((((AllSymbolsOf C) *) \ {{}}) /\ X22) is set
((((AllSymbolsOf C) *) \ {{}}) /\ X22) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf C) *) \ {{}}) /\ X22) \/ {{}} : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ X22 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf C) *) \ {{}}) /\ X22) \/ {{}} : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ X22 } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf C) *) \ {{}}) /\ X22 : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ X22 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf C) *) \ {{}}) /\ X22 : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ X22 } is set
X2 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf C) *) \ {{}})
(((AllSymbolsOf C) *) \ {{}}) /\ X2 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf C) *) \ {{}})
(((AllSymbolsOf C) *) \ {{}}) typed/\ X2 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf C) *) \ {{}})
(((AllSymbolsOf C) *) \ {{}}) /\ X2 is functional set
(((AllSymbolsOf C) *) \ {{}}) /\typed X2 is functional V36() FinSequence-membered with_non-empty_elements Element of bool X2
bool X2 is non empty set
X2 null (((AllSymbolsOf C) *) \ {{}}) is set
X2 \typed/ (((AllSymbolsOf C) *) \ {{}}) is functional V36() with_non-empty_elements Element of bool (X2 \/ (((AllSymbolsOf C) *) \ {{}}))
X2 \/ (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial functional non finite V36() with_non-empty_elements non empty-membered set
bool (X2 \/ (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
SymbolsOf ((((AllSymbolsOf C) *) \ {{}}) /\ X2) is set
((((AllSymbolsOf C) *) \ {{}}) /\ X2) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf C) *) \ {{}}) /\ X2) \/ {{}} : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ X2 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf C) *) \ {{}}) /\ X2) \/ {{}} : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ X2 } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf C) *) \ {{}}) /\ X2 : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ X2 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf C) *) \ {{}}) /\ X2 : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ X2 } is set
{phi} \/ {U} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
U is non {U} -occurring Element of AllSymbolsOf C
X1 is finite countable (C) Element of bool I1
I is literal non operational non relational termal own ofAtomicFormula non {phi} \/ {U} -occurring Element of AllSymbolsOf C
X1 \/ ({phi} \/ {U}) is non empty finite countable (C) set
c26 \/ {phi} is non empty finite countable (C) set
(c26 \/ {phi}) \/ {U} is non empty finite countable (C) set
phi is literal non operational non relational termal own ofAtomicFormula non X1 \/ ({phi} \/ {U}) -occurring Element of AllSymbolsOf C
bool FF is non empty set
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
F1 is functional Element of bool FF
F5 is functional Element of bool FF
F1 \/ F5 is functional Element of bool FF
FF \/ (F1 \/ F5) is functional set
FF null (F1 \/ F5) is set
FF \typed/ (F1 \/ F5) is functional Element of bool (FF \/ (F1 \/ F5))
bool (FF \/ (F1 \/ F5)) is non empty set
F2 is functional Element of bool FF
c26 \/ {(<*S*> ^ phi)} is non empty finite countable (C) set
I1 null (X \/ {((S,DD) -SymbolSubstIn phi)}) is finite countable (C) set
(X \/ {((S,DD) -SymbolSubstIn phi)}) /\ I1 is finite countable Element of bool (X \/ {((S,DD) -SymbolSubstIn phi)})
(X \/ {((S,DD) -SymbolSubstIn phi)}) typed/\ I1 is Element of bool (X \/ {((S,DD) -SymbolSubstIn phi)})
(X \/ {((S,DD) -SymbolSubstIn phi)}) /\ I1 is finite countable set
(X \/ {((S,DD) -SymbolSubstIn phi)}) /\typed I1 is finite countable (C) Element of bool I1
I1 \typed/ (X \/ {((S,DD) -SymbolSubstIn phi)}) is Element of bool (I1 \/ (X \/ {((S,DD) -SymbolSubstIn phi)}))
I1 \/ (X \/ {((S,DD) -SymbolSubstIn phi)}) is non empty set
bool (I1 \/ (X \/ {((S,DD) -SymbolSubstIn phi)})) is non empty set
I02 is trivial functional finite V36() FinSequence-membered with_non-empty_elements with_common_domain countable (C) Element of bool {((S,DD) -SymbolSubstIn phi)}
c26 \/ I02 is finite countable (C) set
c26 \/ {((S,DD) -SymbolSubstIn phi)} is non empty finite countable (C) set
[(c26 \/ {((S,DD) -SymbolSubstIn phi)}),U] is non empty V26() (C) (1,C,{(C)},{[c26,U]}) (C) set
[c26,U] is non empty V26() (C) (C) set
{[c26,U]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
{[(c26 \/ {((S,DD) -SymbolSubstIn phi)}),U]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
l22 is literal non operational non relational termal own ofAtomicFormula non (c26 \/ {phi}) \/ {U} -occurring Element of AllSymbolsOf C
(c26 \/ {(<*S*> ^ phi)}) null l22 is finite countable (C) set
(c26 \/ {(<*S*> ^ phi)}) \typed/ l22 is Element of bool ((c26 \/ {(<*S*> ^ phi)}) \/ l22)
(c26 \/ {(<*S*> ^ phi)}) \/ l22 is non empty set
bool ((c26 \/ {(<*S*> ^ phi)}) \/ l22) is non empty set
[((c26 \/ {(<*S*> ^ phi)}) null l22),U] is non empty V26() (C) (1,C,{(C)},{[(c26 \/ {((S,l22) -SymbolSubstIn phi)}),U]}) (C) set
(S,l22) -SymbolSubstIn phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
phi +~ (S,l22) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((S,l22) -SymbolSubstIn phi)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
c26 \/ {((S,l22) -SymbolSubstIn phi)} is non empty finite countable (C) set
[(c26 \/ {((S,l22) -SymbolSubstIn phi)}),U] is non empty V26() (C) (1,C,{(C)},{[c26,U]}) (C) set
{[(c26 \/ {((S,l22) -SymbolSubstIn phi)}),U]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[(c26 \/ I02),U] is non empty V26() (C) (1,C,{(C)},{[c26,U]}) (C) set
{[(c26 \/ I02),U]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
(c26 \/ I02) \/ {((S,DD) -SymbolSubstIn phi)} is non empty finite countable (C) set
[((c26 \/ I02) \/ {((S,DD) -SymbolSubstIn phi)}),U] is non empty V26() (C) (1,C,{(C)},{[(c26 \/ I02),U]}) (C) set
[I1,U] is non empty V26() (C) (C) Element of [:(bool (X \/ {((S,DD) -SymbolSubstIn phi)})),(((AllSymbolsOf C) *) \ {{}}):]
[:(bool (X \/ {((S,DD) -SymbolSubstIn phi)})),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
{[I1,U]} is non empty trivial Relation-like non empty-yielding bool (X \/ {((S,DD) -SymbolSubstIn phi)}) -defined ((AllSymbolsOf C) *) \ {{}} -valued Function-like constant finite 1 -element Function-yielding V156() with_non-empty_elements non empty-membered countable V208() V209() (C) Element of bool [:(bool (X \/ {((S,DD) -SymbolSubstIn phi)})),(((AllSymbolsOf C) *) \ {{}}):]
bool [:(bool (X \/ {((S,DD) -SymbolSubstIn phi)})),(((AllSymbolsOf C) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
(C,I02,{((S,DD) -SymbolSubstIn phi)}) is functional finite V36() FinSequence-membered with_non-empty_elements countable (C) Element of bool (AllFormulasOf C)
{((S,DD) -SymbolSubstIn phi)} \typed/ I02 is functional finite V36() with_non-empty_elements countable (C) Element of bool ({((S,DD) -SymbolSubstIn phi)} \/ I02)
{((S,DD) -SymbolSubstIn phi)} \/ I02 is non empty functional finite V36() with_non-empty_elements non empty-membered countable (C) set
{((S,DD) -SymbolSubstIn phi)} null I02 is finite countable (C) set
bool ({((S,DD) -SymbolSubstIn phi)} \/ I02) is non empty finite V36() countable set
c26 \/ (C,I02,{((S,DD) -SymbolSubstIn phi)}) is finite countable (C) set
[(c26 \/ (C,I02,{((S,DD) -SymbolSubstIn phi)})),U] is non empty V26() (C) (1,C,{(C)},{[c26,U]}) (C) set
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
[(c26 \/ {(<*S*> ^ phi)}),U] is non empty V26() (C) (1,C,{(C)},{[c26,U]}) (C) set
II2 + 2 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(C,{},sub2) is non empty V26() (C) (C) Element of (C)
(C,{},((<*(TheEqSymbOf C)*> ^ D2) ^ D2)) is non empty V26() (C) (C) Element of (C)
{(C,{},((<*(TheEqSymbOf C)*> ^ D2) ^ D2))} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) (C,{(C)}, {} ) (C,{(C)}) Element of bool (C)
(C,{},sub2) `1 is finite countable (C) set
((C,{},sub2) `1) \+\ {} is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
(C,{},sub2) `2 is set
((C,{},sub2) `2) \+\ sub2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
X + C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
bool (Funcs ((bool (phi)),(bool (phi)))) is non empty set
ExFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf phi) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
[:NAT,(ExFormulasOf phi):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(ExFormulasOf phi):] is non empty non trivial non finite non empty-membered set
(phi) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total (phi) (phi) Element of Funcs ((bool (phi)),(bool (phi)))
(phi) is Relation-like bool (phi) -defined (phi) -valued Element of bool [:(bool (phi)),(phi):]
[:(bool (phi)),(phi):] is non empty Relation-like set
bool [:(bool (phi)),(phi):] is non empty set
(phi,(phi)) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
(phi) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total (phi) (phi) Element of Funcs ((bool (phi)),(bool (phi)))
(phi) is Relation-like bool (phi) -defined (phi) -valued Element of bool [:(bool (phi)),(phi):]
(phi,(phi)) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
(phi) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total (phi) (phi) Element of Funcs ((bool (phi)),(bool (phi)))
(phi) is Relation-like bool (phi) -defined (phi) -valued Element of bool [:(bool (phi)),(phi):]
(phi,(phi)) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
(phi) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total (phi) (phi) Element of Funcs ((bool (phi)),(bool (phi)))
(phi) is Relation-like bool (phi) -defined (phi) -valued Element of bool [:(bool (phi)),(phi):]
(phi,(phi)) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
LettersOf phi is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf phi)
bool (AllSymbolsOf phi) is non empty non trivial non finite non empty-membered set
the U3 of phi is Element of the U1 of phi
{ the U3 of phi} is non empty trivial finite 1 -element countable set
the U1 of phi \ { the U3 of phi} is non empty Element of bool the U1 of phi
bool the U1 of phi is non empty set
the U1 of phi typed\ { the U3 of phi} is Element of bool the U1 of phi
the adicity of phi is non empty Relation-like the U1 of phi \ { the U3 of phi} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of phi \ { the U3 of phi}),INT:]
[:( the U1 of phi \ { the U3 of phi}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of phi \ { the U3 of phi}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of phi " {0} is Element of bool ( the U1 of phi \ { the U3 of phi})
bool ( the U1 of phi \ { the U3 of phi}) is non empty set
S is functional Element of bool (Funcs ((bool (phi)),(bool (phi))))
DD is functional set
DD /\ (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
DD typed/\ (((AllSymbolsOf phi) *) \ {{}}) is functional Element of bool DD
bool DD is non empty set
DD /\ (((AllSymbolsOf phi) *) \ {{}}) is functional set
DD /\typed (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf phi) *) \ {{}})
SymbolsOf (DD /\ (((AllSymbolsOf phi) *) \ {{}})) is set
(DD /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (DD /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} : b1 in DD /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (DD /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} : b1 in DD /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of DD /\ (((AllSymbolsOf phi) *) \ {{}}) : b1 in DD /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of DD /\ (((AllSymbolsOf phi) *) \ {{}}) : b1 in DD /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
(LettersOf phi) \ (SymbolsOf (DD /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (AllSymbolsOf phi)
(LettersOf phi) typed\ (SymbolsOf (DD /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (LettersOf phi)
bool (LettersOf phi) is non empty non trivial non finite non empty-membered set
(LettersOf phi) \ (SymbolsOf (DD /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (LettersOf phi)
DD \/ (AllFormulasOf phi) is non empty functional set
bool (DD \/ (AllFormulasOf phi)) is non empty Element of bool (bool (DD \/ (AllFormulasOf phi)))
bool (DD \/ (AllFormulasOf phi)) is non empty set
bool (bool (DD \/ (AllFormulasOf phi))) is non empty set
phi -firstChar is non empty Relation-like ((AllSymbolsOf phi) *) \ {{}} -defined AllSymbolsOf phi -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf phi) *) \ {{}}),(AllSymbolsOf phi):]
[:(((AllSymbolsOf phi) *) \ {{}}),(AllSymbolsOf phi):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf phi) *) \ {{}}),(AllSymbolsOf phi):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) -firstChar is non empty Relation-like ((AllSymbolsOf phi) *) \ {{}} -defined AllSymbolsOf phi -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf phi) *) \ {{}}),(AllSymbolsOf phi):]
(AllSymbolsOf phi) -pr1 is non empty Relation-like [:(AllSymbolsOf phi),(AllSymbolsOf phi):] -defined AllSymbolsOf phi -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf phi),(AllSymbolsOf phi):],(AllSymbolsOf phi):]
[:(AllSymbolsOf phi),(AllSymbolsOf phi):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf phi),(AllSymbolsOf phi):],(AllSymbolsOf phi):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf phi),(AllSymbolsOf phi):],(AllSymbolsOf phi):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf phi),(AllSymbolsOf phi)) is non empty Relation-like [:(AllSymbolsOf phi),(AllSymbolsOf phi):] -defined AllSymbolsOf phi -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf phi),(AllSymbolsOf phi):],(AllSymbolsOf phi):]
MultPlace ((AllSymbolsOf phi) -pr1) is non empty Relation-like ((AllSymbolsOf phi) *) \ {{}} -defined AllSymbolsOf phi -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf phi) *) \ {{}}),(AllSymbolsOf phi):]
m is non empty Relation-like non-empty non empty-yielding NAT -defined ExFormulasOf phi -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(ExFormulasOf phi):]
(DD,phi,S,m) is non empty Relation-like NAT -defined bool (DD \/ (AllFormulasOf phi)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (DD \/ (AllFormulasOf phi))):]
[:NAT,(bool (DD \/ (AllFormulasOf phi))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (DD \/ (AllFormulasOf phi))):] is non empty non trivial non finite non empty-membered set
(DD,phi,S,m) . X is functional Element of bool (DD \/ (AllFormulasOf phi))
(DD,phi,S,m) . (X + C) is functional Element of bool (DD \/ (AllFormulasOf phi))
(DD,phi,S,m) . C is functional Element of bool (DD \/ (AllFormulasOf phi))
((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
((DD,phi,S,m) . C) typed/\ (((AllSymbolsOf phi) *) \ {{}}) is functional Element of bool ((DD,phi,S,m) . C)
bool ((DD,phi,S,m) . C) is non empty set
((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}}) is functional set
((DD,phi,S,m) . C) /\typed (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf phi) *) \ {{}})
SymbolsOf (((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}})) is set
(((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} : b1 in ((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} : b1 in ((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}}) : b1 in ((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}}) : b1 in ((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
(LettersOf phi) \ (SymbolsOf (((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (AllSymbolsOf phi)
(LettersOf phi) typed\ (SymbolsOf (((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (LettersOf phi)
(LettersOf phi) \ (SymbolsOf (((DD,phi,S,m) . C) /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (LettersOf phi)
X + 0 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(DD,phi,S,m) . (X + 0) is functional Element of bool (DD \/ (AllFormulasOf phi))
(DD,phi,S,m) . 0 is functional Element of bool (DD \/ (AllFormulasOf phi))
((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
((DD,phi,S,m) . 0) typed/\ (((AllSymbolsOf phi) *) \ {{}}) is functional Element of bool ((DD,phi,S,m) . 0)
bool ((DD,phi,S,m) . 0) is non empty set
((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}}) is functional set
((DD,phi,S,m) . 0) /\typed (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf phi) *) \ {{}})
SymbolsOf (((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}})) is set
(((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} : b1 in ((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} : b1 in ((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}}) : b1 in ((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}}) : b1 in ((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
(LettersOf phi) \ (SymbolsOf (((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (AllSymbolsOf phi)
(LettersOf phi) typed\ (SymbolsOf (((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (LettersOf phi)
(LettersOf phi) \ (SymbolsOf (((DD,phi,S,m) . 0) /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (LettersOf phi)
HH is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
X + HH is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(DD,phi,S,m) . (X + HH) is functional Element of bool (DD \/ (AllFormulasOf phi))
(DD,phi,S,m) . HH is functional Element of bool (DD \/ (AllFormulasOf phi))
((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
((DD,phi,S,m) . HH) typed/\ (((AllSymbolsOf phi) *) \ {{}}) is functional Element of bool ((DD,phi,S,m) . HH)
bool ((DD,phi,S,m) . HH) is non empty set
((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}}) is functional set
((DD,phi,S,m) . HH) /\typed (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf phi) *) \ {{}})
SymbolsOf (((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}})) is set
(((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} : b1 in ((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} : b1 in ((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}}) : b1 in ((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}}) : b1 in ((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
(LettersOf phi) \ (SymbolsOf (((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (AllSymbolsOf phi)
(LettersOf phi) typed\ (SymbolsOf (((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (LettersOf phi)
(LettersOf phi) \ (SymbolsOf (((DD,phi,S,m) . HH) /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (LettersOf phi)
HH + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
X + (HH + 1) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(DD,phi,S,m) . (X + (HH + 1)) is functional Element of bool (DD \/ (AllFormulasOf phi))
(DD,phi,S,m) . (HH + 1) is functional Element of bool (DD \/ (AllFormulasOf phi))
((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
((DD,phi,S,m) . (HH + 1)) typed/\ (((AllSymbolsOf phi) *) \ {{}}) is functional Element of bool ((DD,phi,S,m) . (HH + 1))
bool ((DD,phi,S,m) . (HH + 1)) is non empty set
((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}}) is functional set
((DD,phi,S,m) . (HH + 1)) /\typed (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf phi) *) \ {{}})
SymbolsOf (((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}})) is set
(((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} : b1 in ((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} : b1 in ((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}}) : b1 in ((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}}) : b1 in ((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
(LettersOf phi) \ (SymbolsOf (((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (AllSymbolsOf phi)
(LettersOf phi) typed\ (SymbolsOf (((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (LettersOf phi)
(LettersOf phi) \ (SymbolsOf (((DD,phi,S,m) . (HH + 1)) /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (LettersOf phi)
D2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
m . D2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf phi
sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff wff exal Element of ((AllSymbolsOf phi) *) \ {{}}
head sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}}
SubWffsOf sub2 is set
(SubWffsOf sub2) `1 is set
(phi -firstChar) . sub2 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf phi
U is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf phi
<*U*> is non empty trivial Relation-like NAT -defined TermSymbolsOf phi -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() termal 0 -termal Element of ((AllSymbolsOf phi) *) \ {{}}
TermSymbolsOf phi is non empty set
the adicity of phi " NAT is Element of bool ( the U1 of phi \ { the U3 of phi})
[1,U] is non empty V26() set
{[1,U]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}}
<*U*> ^ inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff 1 + (Depth inf) -wff non Depth inf -wff wff exal Element of ((AllSymbolsOf phi) *) \ {{}}
Depth inf is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
1 + (Depth inf) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
tail sub2 is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued AllSymbolsOf phi -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of (AllSymbolsOf phi) *
(SubWffsOf sub2) `2 is set
(<*U*> ^ inf) ^ (tail sub2) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(<*U*> ^ inf) null (tail sub2) is Relation-like NAT -defined (tail sub2) \/ (proj1 (<*U*> ^ inf)) -defined (tail sub2) \/ (proj2 (<*U*> ^ inf)) -valued Function-like finite len (<*U*> ^ inf) -element FinSequence-like FinSubsequence-like countable V209() set
proj1 (<*U*> ^ inf) is non empty finite countable set
(tail sub2) \/ (proj1 (<*U*> ^ inf)) is non empty finite countable set
proj2 (<*U*> ^ inf) is non empty finite countable set
(tail sub2) \/ (proj2 (<*U*> ^ inf)) is non empty finite countable set
len (<*U*> ^ inf) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(<*U*> ^ inf) \typed/ (tail sub2) is Relation-like NAT -defined finite countable Element of bool ((<*U*> ^ inf) \/ (tail sub2))
(<*U*> ^ inf) \/ (tail sub2) is non empty Relation-like NAT -defined finite countable set
bool ((<*U*> ^ inf) \/ (tail sub2)) is non empty finite V36() countable set
(tail sub2) ^ (<*U*> ^ inf) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
HC is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(DD,phi,S,m) . HC is functional Element of bool (DD \/ (AllFormulasOf phi))
((DD,phi,S,m) . HC) \/ (AllFormulasOf phi) is non empty functional set
bool (((DD,phi,S,m) . HC) \/ (AllFormulasOf phi)) is non empty set
m . HC is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf phi
(phi,S,((DD,phi,S,m) . HC),(m . HC)) is functional Element of bool (((DD,phi,S,m) . HC) \/ (AllFormulasOf phi))
(DD,phi,S,m) . D2 is functional Element of bool (DD \/ (AllFormulasOf phi))
((DD,phi,S,m) . D2) \/ (AllFormulasOf phi) is non empty functional set
bool (((DD,phi,S,m) . D2) \/ (AllFormulasOf phi)) is non empty set
(phi,S,((DD,phi,S,m) . D2),(m . D2)) is functional Element of bool (((DD,phi,S,m) . D2) \/ (AllFormulasOf phi))
II1 is functional Element of bool (((DD,phi,S,m) . HC) \/ (AllFormulasOf phi))
((DD,phi,S,m) . HC) \ II1 is functional Element of bool (DD \/ (AllFormulasOf phi))
((DD,phi,S,m) . HC) typed\ II1 is functional Element of bool ((DD,phi,S,m) . HC)
bool ((DD,phi,S,m) . HC) is non empty set
((DD,phi,S,m) . HC) \ II1 is functional Element of bool ((DD,phi,S,m) . HC)
HC + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(DD,phi,S,m) . (HC + 1) is functional Element of bool (DD \/ (AllFormulasOf phi))
a is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(DD,phi,S,m) . a is functional Element of bool (DD \/ (AllFormulasOf phi))
II2 is functional Element of bool (((DD,phi,S,m) . D2) \/ (AllFormulasOf phi))
((DD,phi,S,m) . D2) \ II2 is functional Element of bool (DD \/ (AllFormulasOf phi))
((DD,phi,S,m) . D2) typed\ II2 is functional Element of bool ((DD,phi,S,m) . D2)
bool ((DD,phi,S,m) . D2) is non empty set
((DD,phi,S,m) . D2) \ II2 is functional Element of bool ((DD,phi,S,m) . D2)
bool II2 is non empty set
II2 /\ (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
II2 typed/\ (((AllSymbolsOf phi) *) \ {{}}) is functional Element of bool II2
II2 /\ (((AllSymbolsOf phi) *) \ {{}}) is functional set
II2 /\typed (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf phi) *) \ {{}})
bool (II2 /\ (((AllSymbolsOf phi) *) \ {{}})) is non empty set
I2 is functional Element of bool II2
I2 /\ (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
I2 typed/\ (((AllSymbolsOf phi) *) \ {{}}) is functional Element of bool I2
bool I2 is non empty set
I2 /\ (((AllSymbolsOf phi) *) \ {{}}) is functional set
I2 /\typed (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf phi) *) \ {{}})
II2 \ ((DD,phi,S,m) . D2) is functional Element of bool (((DD,phi,S,m) . D2) \/ (AllFormulasOf phi))
II2 typed\ ((DD,phi,S,m) . D2) is functional Element of bool II2
II2 \ ((DD,phi,S,m) . D2) is functional Element of bool II2
I1 is functional V36() FinSequence-membered Element of bool (II2 /\ (((AllSymbolsOf phi) *) \ {{}}))
SymbolsOf I1 is set
I1 \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of I1 \/ {{}} : b1 in I1 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of I1 \/ {{}} : b1 in I1 } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of I1 : b1 in I1 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of I1 : b1 in I1 } is set
(LettersOf phi) \ (SymbolsOf I1) is Element of bool (AllSymbolsOf phi)
(LettersOf phi) typed\ (SymbolsOf I1) is Element of bool (LettersOf phi)
(LettersOf phi) \ (SymbolsOf I1) is Element of bool (LettersOf phi)
c26 is trivial finite countable set
c26 /\ (((AllSymbolsOf phi) *) \ {{}}) is functional finite V36() FinSequence-membered countable Element of bool ((AllSymbolsOf phi) *)
c26 typed/\ (((AllSymbolsOf phi) *) \ {{}}) is trivial finite countable Element of bool c26
bool c26 is non empty finite V36() countable set
c26 /\ (((AllSymbolsOf phi) *) \ {{}}) is functional finite countable set
c26 /\typed (((AllSymbolsOf phi) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf phi) *) \ {{}})
I2 \/ c26 is set
SymbolsOf (II2 /\ (((AllSymbolsOf phi) *) \ {{}})) is set
(II2 /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (II2 /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} : b1 in II2 /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (II2 /\ (((AllSymbolsOf phi) *) \ {{}})) \/ {{}} : b1 in II2 /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of II2 /\ (((AllSymbolsOf phi) *) \ {{}}) : b1 in II2 /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of II2 /\ (((AllSymbolsOf phi) *) \ {{}}) : b1 in II2 /\ (((AllSymbolsOf phi) *) \ {{}}) } is set
I1 is functional finite V36() FinSequence-membered countable set
I1 \/ I1 is functional V36() set
SymbolsOf (I1 \/ I1) is set
(I1 \/ I1) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (I1 \/ I1) \/ {{}} : b1 in I1 \/ I1 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (I1 \/ I1) \/ {{}} : b1 in I1 \/ I1 } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of I1 \/ I1 : b1 in I1 \/ I1 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of I1 \/ I1 : b1 in I1 \/ I1 } is set
SymbolsOf I1 is finite countable set
I1 \/ {{}} is non empty functional finite V36() countable set
{ (proj2 b1) where b1 is Relation-like Function-like Element of I1 \/ {{}} : b1 in I1 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of I1 \/ {{}} : b1 in I1 } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of I1 : b1 in I1 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of I1 : b1 in I1 } is set
(SymbolsOf I1) \/ (SymbolsOf I1) is set
(LettersOf phi) \ (SymbolsOf (II2 /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (AllSymbolsOf phi)
(LettersOf phi) typed\ (SymbolsOf (II2 /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (LettersOf phi)
(LettersOf phi) \ (SymbolsOf (II2 /\ (((AllSymbolsOf phi) *) \ {{}}))) is Element of bool (LettersOf phi)
I02 is non empty non trivial non finite non empty-membered set
I02 \ (SymbolsOf I1) is non empty non trivial non finite non empty-membered Element of bool I02
bool I02 is non empty non trivial non finite non empty-membered set
I02 typed\ (SymbolsOf I1) is Element of bool I02
sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf phi
head sub1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}}
SubWffsOf sub1 is set
(SubWffsOf sub1) `1 is set
{(head sub1)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (phi) Element of bool (((AllSymbolsOf phi) *) \ {{}})
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
I2 \/ {(head sub1)} is non empty functional set
(((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
(((AllSymbolsOf phi) *) \ {{}}) typed/\ (I2 \/ {(head sub1)}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf phi) *) \ {{}})
(((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)}) is functional set
(((AllSymbolsOf phi) *) \ {{}}) /\typed (I2 \/ {(head sub1)}) is functional Element of bool (I2 \/ {(head sub1)})
bool (I2 \/ {(head sub1)}) is non empty set
SymbolsOf ((((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)})) is set
((((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)})) \/ {{}} : b1 in (((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)})) \/ {{}} : b1 in (((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)}) : b1 in (((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)}) : b1 in (((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)}) } is set
(LettersOf phi) \ (SymbolsOf ((((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)}))) is Element of bool (AllSymbolsOf phi)
(LettersOf phi) typed\ (SymbolsOf ((((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)}))) is Element of bool (LettersOf phi)
(LettersOf phi) \ (SymbolsOf ((((AllSymbolsOf phi) *) \ {{}}) /\ (I2 \/ {(head sub1)}))) is Element of bool (LettersOf phi)
{sub1} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (phi) Element of bool (ExFormulasOf phi)
bool (ExFormulasOf phi) is non empty set
I2 \/ {sub1} is non empty functional set
I2 is Element of bool (LettersOf phi)
X1 is non empty Element of bool (LettersOf phi)
the Element of X1 is Element of X1
{(<*U*> ^ inf)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (phi) Element of bool (((AllSymbolsOf phi) *) \ {{}})
I2 \/ {(<*U*> ^ inf)} is non empty functional set
{inf} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (phi) Element of bool (((AllSymbolsOf phi) *) \ {{}})
I2 \/ {inf} is non empty functional set
X22 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf phi
(U,X22) -SymbolSubstIn inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}}
inf +~ (U,X22) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
{((U,X22) -SymbolSubstIn inf)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (phi) Element of bool (((AllSymbolsOf phi) *) \ {{}})
I2 \/ {((U,X22) -SymbolSubstIn inf)} is non empty functional set
{sub1} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (phi) Element of bool (ExFormulasOf phi)
bool (ExFormulasOf phi) is non empty set
I2 \/ {sub1} is non empty functional set
I2 is Element of bool (LettersOf phi)
{sub1} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (phi) Element of bool (ExFormulasOf phi)
bool (ExFormulasOf phi) is non empty set
I2 \/ {sub1} is non empty functional set
I2 is Element of bool (LettersOf phi)
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
ExFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
[:NAT,(ExFormulasOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(ExFormulasOf C):] is non empty non trivial non finite non empty-membered set
X is functional set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S is non empty Relation-like non-empty non empty-yielding NAT -defined ExFormulasOf C -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(ExFormulasOf C):]
(X,C,phi,S) is non empty Relation-like NAT -defined bool (X \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (X \/ (AllFormulasOf C))):]
X \/ (AllFormulasOf C) is non empty functional set
bool (X \/ (AllFormulasOf C)) is non empty Element of bool (bool (X \/ (AllFormulasOf C)))
bool (X \/ (AllFormulasOf C)) is non empty set
bool (bool (X \/ (AllFormulasOf C))) is non empty set
[:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial non finite non empty-membered set
proj2 (X,C,phi,S) is non empty set
union (proj2 (X,C,phi,S)) is set
bool (bool (X \/ (AllFormulasOf C))) is non empty set
Y is Element of bool (bool (X \/ (AllFormulasOf C)))
union Y is functional Element of bool (X \/ (AllFormulasOf C))
(union Y) \ (X \/ (AllFormulasOf C)) is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (X \/ (AllFormulasOf C))
(union Y) typed\ (X \/ (AllFormulasOf C)) is functional Element of bool (union Y)
bool (union Y) is non empty set
(union Y) \ (X \/ (AllFormulasOf C)) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (union Y)
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
ExFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
[:NAT,(ExFormulasOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(ExFormulasOf C):] is non empty non trivial non finite non empty-membered set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
ExFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
[:NAT,(ExFormulasOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(ExFormulasOf X):] is non empty non trivial non finite non empty-membered set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
LettersOf X is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
C is functional Element of bool (Funcs ((bool (X)),(bool (X))))
phi is functional set
phi /\ (((AllSymbolsOf X) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi typed/\ (((AllSymbolsOf X) *) \ {{}}) is functional Element of bool phi
bool phi is non empty set
phi /\ (((AllSymbolsOf X) *) \ {{}}) is functional set
phi /\typed (((AllSymbolsOf X) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf X) *) \ {{}})
SymbolsOf (phi /\ (((AllSymbolsOf X) *) \ {{}})) is set
(phi /\ (((AllSymbolsOf X) *) \ {{}})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (phi /\ (((AllSymbolsOf X) *) \ {{}})) \/ {{}} : b1 in phi /\ (((AllSymbolsOf X) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (phi /\ (((AllSymbolsOf X) *) \ {{}})) \/ {{}} : b1 in phi /\ (((AllSymbolsOf X) *) \ {{}}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of phi /\ (((AllSymbolsOf X) *) \ {{}}) : b1 in phi /\ (((AllSymbolsOf X) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of phi /\ (((AllSymbolsOf X) *) \ {{}}) : b1 in phi /\ (((AllSymbolsOf X) *) \ {{}}) } is set
(LettersOf X) \ (SymbolsOf (phi /\ (((AllSymbolsOf X) *) \ {{}}))) is Element of bool (AllSymbolsOf X)
(LettersOf X) typed\ (SymbolsOf (phi /\ (((AllSymbolsOf X) *) \ {{}}))) is Element of bool (LettersOf X)
bool (LettersOf X) is non empty non trivial non finite non empty-membered set
(LettersOf X) \ (SymbolsOf (phi /\ (((AllSymbolsOf X) *) \ {{}}))) is Element of bool (LettersOf X)
D is non empty Relation-like non-empty non empty-yielding NAT -defined ExFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(ExFormulasOf X):]
(phi,X,C,D) is functional Element of bool (phi \/ (AllFormulasOf X))
phi \/ (AllFormulasOf X) is non empty functional set
bool (phi \/ (AllFormulasOf X)) is non empty set
(phi,X,C,D) is non empty Relation-like NAT -defined bool (phi \/ (AllFormulasOf X)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (phi \/ (AllFormulasOf X))):]
bool (phi \/ (AllFormulasOf X)) is non empty Element of bool (bool (phi \/ (AllFormulasOf X)))
bool (bool (phi \/ (AllFormulasOf X))) is non empty set
[:NAT,(bool (phi \/ (AllFormulasOf X))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (phi \/ (AllFormulasOf X))):] is non empty non trivial non finite non empty-membered set
proj2 (phi,X,C,D) is non empty set
union (proj2 (phi,X,C,D)) is set
dom (phi,X,C,D) is non empty countable Element of bool NAT
HC is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(phi,X,C,D) . HC is functional Element of bool (phi \/ (AllFormulasOf X))
a is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(phi,X,C,D) . a is functional Element of bool (phi \/ (AllFormulasOf X))
HC - HC is complex ext-real finite V40() V41() countable set
a - HC is complex ext-real finite V40() V41() countable set
sub2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
HC + sub2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(phi,X,C,D) . (HC + sub2) is functional Element of bool (phi \/ (AllFormulasOf X))
bool (phi,X,C,D) is non empty set
HC is functional finite countable Element of bool (phi,X,C,D)
a is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(phi,X,C,D) . a is functional Element of bool (phi \/ (AllFormulasOf X))
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
ExFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
[:NAT,(ExFormulasOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(ExFormulasOf C):] is non empty non trivial non finite non empty-membered set
X is functional set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S is non empty Relation-like non-empty non empty-yielding NAT -defined ExFormulasOf C -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(ExFormulasOf C):]
(X,C,phi,S) is functional Element of bool (X \/ (AllFormulasOf C))
X \/ (AllFormulasOf C) is non empty functional set
bool (X \/ (AllFormulasOf C)) is non empty set
(X,C,phi,S) is non empty Relation-like NAT -defined bool (X \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (X \/ (AllFormulasOf C))):]
bool (X \/ (AllFormulasOf C)) is non empty Element of bool (bool (X \/ (AllFormulasOf C)))
bool (bool (X \/ (AllFormulasOf C))) is non empty set
[:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial non finite non empty-membered set
proj2 (X,C,phi,S) is non empty set
union (proj2 (X,C,phi,S)) is set
X \ (X,C,phi,S) is functional Element of bool X
bool X is non empty set
X typed\ (X,C,phi,S) is functional Element of bool X
[:NAT,(proj2 (X,C,phi,S)):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(proj2 (X,C,phi,S)):] is non empty non trivial non finite non empty-membered set
Y is non empty Relation-like NAT -defined proj2 (X,C,phi,S) -valued Function-like total quasi_total Element of bool [:NAT,(proj2 (X,C,phi,S)):]
Y . 0 is Element of proj2 (X,C,phi,S)
phii is set
X is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
ExFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
[:NAT,(ExFormulasOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(ExFormulasOf C):] is non empty non trivial non finite non empty-membered set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
LettersOf C is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C " {0} is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S is functional set
S /\ (((AllSymbolsOf C) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
S typed/\ (((AllSymbolsOf C) *) \ {{}}) is functional Element of bool S
bool S is non empty set
S /\ (((AllSymbolsOf C) *) \ {{}}) is functional set
S /\typed (((AllSymbolsOf C) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf C) *) \ {{}})
SymbolsOf (S /\ (((AllSymbolsOf C) *) \ {{}})) is set
(S /\ (((AllSymbolsOf C) *) \ {{}})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (S /\ (((AllSymbolsOf C) *) \ {{}})) \/ {{}} : b1 in S /\ (((AllSymbolsOf C) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (S /\ (((AllSymbolsOf C) *) \ {{}})) \/ {{}} : b1 in S /\ (((AllSymbolsOf C) *) \ {{}}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of S /\ (((AllSymbolsOf C) *) \ {{}}) : b1 in S /\ (((AllSymbolsOf C) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of S /\ (((AllSymbolsOf C) *) \ {{}}) : b1 in S /\ (((AllSymbolsOf C) *) \ {{}}) } is set
(LettersOf C) \ (SymbolsOf (S /\ (((AllSymbolsOf C) *) \ {{}}))) is Element of bool (AllSymbolsOf C)
(LettersOf C) typed\ (SymbolsOf (S /\ (((AllSymbolsOf C) *) \ {{}}))) is Element of bool (LettersOf C)
bool (LettersOf C) is non empty non trivial non finite non empty-membered set
(LettersOf C) \ (SymbolsOf (S /\ (((AllSymbolsOf C) *) \ {{}}))) is Element of bool (LettersOf C)
C -firstChar is non empty Relation-like ((AllSymbolsOf C) *) \ {{}} -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):]
[:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) -firstChar is non empty Relation-like ((AllSymbolsOf C) *) \ {{}} -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):]
(AllSymbolsOf C) -pr1 is non empty Relation-like [:(AllSymbolsOf C),(AllSymbolsOf C):] -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):]
[:(AllSymbolsOf C),(AllSymbolsOf C):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf C),(AllSymbolsOf C)) is non empty Relation-like [:(AllSymbolsOf C),(AllSymbolsOf C):] -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):]
MultPlace ((AllSymbolsOf C) -pr1) is non empty Relation-like ((AllSymbolsOf C) *) \ {{}} -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):]
Y is non empty Relation-like non-empty non empty-yielding NAT -defined ExFormulasOf C -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(ExFormulasOf C):]
(S,C,phi,Y) is functional Element of bool (S \/ (AllFormulasOf C))
S \/ (AllFormulasOf C) is non empty functional set
bool (S \/ (AllFormulasOf C)) is non empty set
(S,C,phi,Y) is non empty Relation-like NAT -defined bool (S \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (S \/ (AllFormulasOf C))):]
bool (S \/ (AllFormulasOf C)) is non empty Element of bool (bool (S \/ (AllFormulasOf C)))
bool (bool (S \/ (AllFormulasOf C))) is non empty set
[:NAT,(bool (S \/ (AllFormulasOf C))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (S \/ (AllFormulasOf C))):] is non empty non trivial non finite non empty-membered set
proj2 (S,C,phi,Y) is non empty set
union (proj2 (S,C,phi,Y)) is set
proj2 Y is non empty with_non-empty_elements non empty-membered set
S \ (S,C,phi,Y) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool S
S typed\ (S,C,phi,Y) is functional Element of bool S
seqt is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf C
<*seqt*> is non empty trivial Relation-like NAT -defined TermSymbolsOf C -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() termal 0 -termal Element of ((AllSymbolsOf C) *) \ {{}}
TermSymbolsOf C is non empty set
the adicity of C " NAT is Element of bool ( the U1 of C \ { the U3 of C})
[1,seqt] is non empty V26() set
{[1,seqt]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
<*seqt*> ^ HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff 1 + (Depth HH) -wff non Depth HH -wff wff exal Element of ((AllSymbolsOf C) *) \ {{}}
Depth HH is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
1 + (Depth HH) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
proj2 HH is non empty finite countable set
(<*seqt*> ^ HH) ^ {} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(<*seqt*> ^ HH) null {} is Relation-like NAT -defined {} \/ (proj1 (<*seqt*> ^ HH)) -defined {} \/ (proj2 (<*seqt*> ^ HH)) -valued Function-like finite len (<*seqt*> ^ HH) -element FinSequence-like FinSubsequence-like countable V209() set
proj1 (<*seqt*> ^ HH) is non empty finite countable set
{} \/ (proj1 (<*seqt*> ^ HH)) is non empty finite countable set
proj2 (<*seqt*> ^ HH) is non empty finite countable set
{} \/ (proj2 (<*seqt*> ^ HH)) is non empty finite countable set
len (<*seqt*> ^ HH) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable Element of NAT
(<*seqt*> ^ HH) \typed/ {} is Relation-like NAT -defined finite countable Element of bool ((<*seqt*> ^ HH) \/ {})
(<*seqt*> ^ HH) \/ {} is non empty Relation-like NAT -defined finite countable set
bool ((<*seqt*> ^ HH) \/ {}) is non empty finite V36() countable set
{} ^ (<*seqt*> ^ HH) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
(C -firstChar) . (<*seqt*> ^ HH) is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf C
head (<*seqt*> ^ HH) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
SubWffsOf (<*seqt*> ^ HH) is set
(SubWffsOf (<*seqt*> ^ HH)) `1 is set
dom Y is non empty countable Element of bool NAT
a is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff exal Element of ExFormulasOf C
D2 is set
Y . D2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
sub1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
sub1 + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(S,C,phi,Y) . sub1 is functional Element of bool (S \/ (AllFormulasOf C))
{HH} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
((S,C,phi,Y) . sub1) \/ {HH} is non empty functional set
(((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
(((AllSymbolsOf C) *) \ {{}}) typed/\ (((S,C,phi,Y) . sub1) \/ {HH}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf C) *) \ {{}})
(((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH}) is functional set
(((AllSymbolsOf C) *) \ {{}}) /\typed (((S,C,phi,Y) . sub1) \/ {HH}) is functional Element of bool (((S,C,phi,Y) . sub1) \/ {HH})
bool (((S,C,phi,Y) . sub1) \/ {HH}) is non empty set
SymbolsOf ((((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH})) is set
((((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH})) \/ {{}} : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH})) \/ {{}} : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH}) : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH}) : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH}) } is set
bool {HH} is non empty finite V36() countable set
(((AllSymbolsOf C) *) \ {{}}) /\ {HH} is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (((AllSymbolsOf C) *) \ {{}})
(((AllSymbolsOf C) *) \ {{}}) typed/\ {HH} is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf C) *) \ {{}})
(((AllSymbolsOf C) *) \ {{}}) /\ {HH} is functional finite countable set
(((AllSymbolsOf C) *) \ {{}}) /\typed {HH} is trivial functional finite V36() FinSequence-membered with_non-empty_elements with_common_domain countable (C) Element of bool {HH}
{HH} null (((AllSymbolsOf C) *) \ {{}}) is finite countable (C) set
(((AllSymbolsOf C) *) \ {{}}) /\ {HH} is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool (((AllSymbolsOf C) *) \ {{}})
{HH} \typed/ (((AllSymbolsOf C) *) \ {{}}) is functional V36() with_non-empty_elements Element of bool ({HH} \/ (((AllSymbolsOf C) *) \ {{}}))
{HH} \/ (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial functional non finite V36() with_non-empty_elements non empty-membered set
bool ({HH} \/ (((AllSymbolsOf C) *) \ {{}})) is non empty non trivial non finite non empty-membered set
II1 is trivial functional finite V36() FinSequence-membered with_non-empty_elements with_common_domain countable (C) Element of bool {HH}
SymbolsOf II1 is finite countable set
II1 \/ {{}} is non empty functional finite V36() countable set
{ (proj2 b1) where b1 is Relation-like Function-like Element of II1 \/ {{}} : b1 in II1 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of II1 \/ {{}} : b1 in II1 } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of II1 : b1 in II1 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of II1 : b1 in II1 } is set
((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
((S,C,phi,Y) . sub1) typed/\ (((AllSymbolsOf C) *) \ {{}}) is functional Element of bool ((S,C,phi,Y) . sub1)
bool ((S,C,phi,Y) . sub1) is non empty set
((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}}) is functional set
((S,C,phi,Y) . sub1) /\typed (((AllSymbolsOf C) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf C) *) \ {{}})
SymbolsOf (((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}})) is set
(((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}})) \/ {{}} : b1 in ((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}})) \/ {{}} : b1 in ((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}}) : b1 in ((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}}) : b1 in ((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}}) } is set
(LettersOf C) \ (SymbolsOf (((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}}))) is Element of bool (AllSymbolsOf C)
(LettersOf C) typed\ (SymbolsOf (((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}}))) is Element of bool (LettersOf C)
(LettersOf C) \ (SymbolsOf (((S,C,phi,Y) . sub1) /\ (((AllSymbolsOf C) *) \ {{}}))) is Element of bool (LettersOf C)
(((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1) is functional Element of bool (S \/ (AllFormulasOf C))
(((AllSymbolsOf C) *) \ {{}}) typed/\ ((S,C,phi,Y) . sub1) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf C) *) \ {{}})
(((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1) is functional set
(((AllSymbolsOf C) *) \ {{}}) /\typed ((S,C,phi,Y) . sub1) is functional Element of bool ((S,C,phi,Y) . sub1)
((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ ((((AllSymbolsOf C) *) \ {{}}) /\ {HH}) is functional set
SymbolsOf (((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ ((((AllSymbolsOf C) *) \ {{}}) /\ {HH})) is set
(((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ ((((AllSymbolsOf C) *) \ {{}}) /\ {HH})) \/ {{}} is non empty functional set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ ((((AllSymbolsOf C) *) \ {{}}) /\ {HH})) \/ {{}} : b1 in ((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ ((((AllSymbolsOf C) *) \ {{}}) /\ {HH}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ ((((AllSymbolsOf C) *) \ {{}}) /\ {HH})) \/ {{}} : b1 in ((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ ((((AllSymbolsOf C) *) \ {{}}) /\ {HH}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ ((((AllSymbolsOf C) *) \ {{}}) /\ {HH}) : b1 in ((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ ((((AllSymbolsOf C) *) \ {{}}) /\ {HH}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ ((((AllSymbolsOf C) *) \ {{}}) /\ {HH}) : b1 in ((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ ((((AllSymbolsOf C) *) \ {{}}) /\ {HH}) } is set
SymbolsOf ((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) is set
((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ {{}} is non empty functional set
{ (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ {{}} : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of ((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1)) \/ {{}} : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1) : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1) : b1 in (((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1) } is set
(SymbolsOf ((((AllSymbolsOf C) *) \ {{}}) /\ ((S,C,phi,Y) . sub1))) \/ (SymbolsOf II1) is set
(LettersOf C) \ (SymbolsOf ((((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH}))) is Element of bool (AllSymbolsOf C)
(LettersOf C) typed\ (SymbolsOf ((((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH}))) is Element of bool (LettersOf C)
(LettersOf C) \ (SymbolsOf ((((AllSymbolsOf C) *) \ {{}}) /\ (((S,C,phi,Y) . sub1) \/ {HH}))) is Element of bool (LettersOf C)
I2 is non empty non trivial non finite non empty-membered Element of bool (LettersOf C)
II2 is finite countable set
I2 \ II2 is non empty non trivial non finite non empty-membered Element of bool (LettersOf C)
I2 typed\ II2 is Element of bool I2
bool I2 is non empty non trivial non finite non empty-membered set
I2 \ II2 is non empty non trivial non finite non empty-membered Element of bool I2
I1 is non empty Element of bool (LettersOf C)
the Element of I1 is Element of I1
I02 is literal non operational non relational termal own ofAtomicFormula Element of AllSymbolsOf C
(seqt,I02) -SymbolSubstIn HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
HH +~ (seqt,I02) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
dom (S,C,phi,Y) is non empty countable Element of bool NAT
sub2 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(S,C,phi,Y) . sub2 is functional Element of bool (S \/ (AllFormulasOf C))
{(<*seqt*> ^ HH)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
((S,C,phi,Y) . sub1) \/ {(<*seqt*> ^ HH)} is non empty functional set
{((seqt,I02) -SymbolSubstIn HH)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
((S,C,phi,Y) . sub1) \/ {((seqt,I02) -SymbolSubstIn HH)} is non empty functional set
(C,phi,((S,C,phi,Y) . sub1),a) is functional Element of bool (((S,C,phi,Y) . sub1) \/ (AllFormulasOf C))
((S,C,phi,Y) . sub1) \/ (AllFormulasOf C) is non empty functional set
bool (((S,C,phi,Y) . sub1) \/ (AllFormulasOf C)) is non empty set
(S,C,phi,Y) . (sub1 + 1) is functional Element of bool (S \/ (AllFormulasOf C))
{((seqt,I02) -SymbolSubstIn HH)} null ((S,C,phi,Y) . sub1) is finite countable (C) set
{((seqt,I02) -SymbolSubstIn HH)} \typed/ ((S,C,phi,Y) . sub1) is functional Element of bool ({((seqt,I02) -SymbolSubstIn HH)} \/ ((S,C,phi,Y) . sub1))
{((seqt,I02) -SymbolSubstIn HH)} \/ ((S,C,phi,Y) . sub1) is non empty functional set
bool ({((seqt,I02) -SymbolSubstIn HH)} \/ ((S,C,phi,Y) . sub1)) is non empty set
SymbolsOf {HH} is finite countable set
{HH} \/ {{}} is non empty functional finite V36() countable set
{ (proj2 b1) where b1 is Relation-like Function-like Element of {HH} \/ {{}} : b1 in {HH} } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of {HH} \/ {{}} : b1 in {HH} } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of {HH} : b1 in {HH} } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of {HH} : b1 in {HH} } is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
X is set
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf C
xnot S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ S) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth S),(Depth S)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot S),(xnot S)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth S is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth S),(Depth S)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot S),(xnot S)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{S} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (AllFormulasOf C)
X \/ {S} is non empty set
{(xnot S)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
X \/ {(xnot S)} is non empty set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
X is set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf C
(X,C,phi,S) is set
X \/ (AllFormulasOf C) is non empty set
bool (X \/ (AllFormulasOf C)) is non empty set
C -firstChar is non empty Relation-like ((AllSymbolsOf C) *) \ {{}} -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):]
[:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):] is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) -firstChar is non empty Relation-like ((AllSymbolsOf C) *) \ {{}} -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):]
(AllSymbolsOf C) -pr1 is non empty Relation-like [:(AllSymbolsOf C),(AllSymbolsOf C):] -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):]
[:(AllSymbolsOf C),(AllSymbolsOf C):] is non empty non trivial Relation-like non finite non empty-membered set
[:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):] is non empty non trivial non finite non empty-membered set
K474((AllSymbolsOf C),(AllSymbolsOf C)) is non empty Relation-like [:(AllSymbolsOf C),(AllSymbolsOf C):] -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:[:(AllSymbolsOf C),(AllSymbolsOf C):],(AllSymbolsOf C):]
MultPlace ((AllSymbolsOf C) -pr1) is non empty Relation-like ((AllSymbolsOf C) *) \ {{}} -defined AllSymbolsOf C -valued Function-like total quasi_total Element of bool [:(((AllSymbolsOf C) *) \ {{}}),(AllSymbolsOf C):]
Y is non empty set
bool Y is non empty set
X null (AllFormulasOf C) is set
X \typed/ (AllFormulasOf C) is Element of bool (X \/ (AllFormulasOf C))
(AllFormulasOf C) null X is set
(AllFormulasOf C) \typed/ X is Element of bool ((AllFormulasOf C) \/ X)
(AllFormulasOf C) \/ X is non empty set
bool ((AllFormulasOf C) \/ X) is non empty set
xnot S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ S) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth S),(Depth S)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot S),(xnot S)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth S is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth S),(Depth S)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot S),(xnot S)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
psi is non empty Element of bool Y
H is Element of Y
{H} is non empty trivial finite 1 -element countable Element of bool Y
m is Element of Y
{m} is non empty trivial finite 1 -element countable Element of bool Y
phii is Element of bool Y
seqt is Element of bool Y
phii \/ seqt is Element of bool Y
HH is Element of bool Y
phii \/ HH is Element of bool Y
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
X is set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf C
(X,C,phi,S) is Element of bool (X \/ (AllFormulasOf C))
X \/ (AllFormulasOf C) is non empty set
bool (X \/ (AllFormulasOf C)) is non empty set
X \ (X,C,phi,S) is Element of bool X
bool X is non empty set
X typed\ (X,C,phi,S) is Element of bool X
xnot S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ S) ^ S is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth S),(Depth S)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot S),(xnot S)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth S is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth S),(Depth S)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot S),(xnot S)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{S} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (AllFormulasOf C)
X \/ {S} is non empty set
{(xnot S)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
X \/ {(xnot S)} is non empty set
X null {S} is set
X \typed/ {S} is Element of bool (X \/ {S})
bool (X \/ {S}) is non empty set
X null {(xnot S)} is set
X \typed/ {(xnot S)} is Element of bool (X \/ {(xnot S)})
bool (X \/ {(xnot S)}) is non empty set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
[:NAT,(AllFormulasOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(AllFormulasOf C):] is non empty non trivial non finite non empty-membered set
X is set
X \/ (AllFormulasOf C) is non empty set
bool (X \/ (AllFormulasOf C)) is non empty Element of bool (bool (X \/ (AllFormulasOf C)))
bool (X \/ (AllFormulasOf C)) is non empty set
bool (bool (X \/ (AllFormulasOf C))) is non empty set
[:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial non finite non empty-membered set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S is non empty Relation-like non-empty non empty-yielding NAT -defined AllFormulasOf C -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(AllFormulasOf C):]
X null (AllFormulasOf C) is set
X \typed/ (AllFormulasOf C) is Element of bool (X \/ (AllFormulasOf C))
phii is Element of bool (X \/ (AllFormulasOf C))
psi is non empty Relation-like NAT -defined bool (X \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (X \/ (AllFormulasOf C))):]
psi . 0 is Element of bool (X \/ (AllFormulasOf C))
H is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
psi . m is Element of bool (X \/ (AllFormulasOf C))
S . m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf C
((psi . m),C,phi,(S . m)) is Element of bool ((psi . m) \/ (AllFormulasOf C))
(psi . m) \/ (AllFormulasOf C) is non empty set
bool ((psi . m) \/ (AllFormulasOf C)) is non empty set
(AllFormulasOf C) \/ (psi . m) is non empty set
(AllFormulasOf C) \/ (X \/ (AllFormulasOf C)) is non empty set
(AllFormulasOf C) \/ (AllFormulasOf C) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) \ {{}})
((AllFormulasOf C) \/ (AllFormulasOf C)) \/ X is non empty set
H + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
psi . (H + 1) is Element of bool (X \/ (AllFormulasOf C))
seqt is Element of bool (X \/ (AllFormulasOf C))
seqt null (X \/ (AllFormulasOf C)) is set
(X \/ (AllFormulasOf C)) /\ seqt is Element of bool (X \/ (AllFormulasOf C))
(X \/ (AllFormulasOf C)) typed/\ seqt is Element of bool (X \/ (AllFormulasOf C))
(X \/ (AllFormulasOf C)) /\ seqt is set
(X \/ (AllFormulasOf C)) /\typed seqt is Element of bool seqt
bool seqt is non empty set
seqt \typed/ (X \/ (AllFormulasOf C)) is Element of bool (seqt \/ (X \/ (AllFormulasOf C)))
seqt \/ (X \/ (AllFormulasOf C)) is non empty set
bool (seqt \/ (X \/ (AllFormulasOf C))) is non empty set
psi . H is Element of bool (X \/ (AllFormulasOf C))
S . H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf C
((psi . H),C,phi,(S . H)) is Element of bool ((psi . H) \/ (AllFormulasOf C))
(psi . H) \/ (AllFormulasOf C) is non empty set
bool ((psi . H) \/ (AllFormulasOf C)) is non empty set
H is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
H + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
psi . (H + 1) is Element of bool (X \/ (AllFormulasOf C))
psi . H is Element of bool (X \/ (AllFormulasOf C))
S . H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf C
((psi . H),C,phi,(S . H)) is Element of bool ((psi . H) \/ (AllFormulasOf C))
(psi . H) \/ (AllFormulasOf C) is non empty set
bool ((psi . H) \/ (AllFormulasOf C)) is non empty set
phii is non empty Relation-like NAT -defined bool (X \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (X \/ (AllFormulasOf C))):]
phii . 0 is Element of bool (X \/ (AllFormulasOf C))
psi is non empty Relation-like NAT -defined bool (X \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (X \/ (AllFormulasOf C))):]
psi . 0 is Element of bool (X \/ (AllFormulasOf C))
H is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
H + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
phii . (H + 1) is Element of bool (X \/ (AllFormulasOf C))
phii . H is Element of bool (X \/ (AllFormulasOf C))
S . H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf C
((phii . H),C,phi,(S . H)) is Element of bool ((phii . H) \/ (AllFormulasOf C))
(phii . H) \/ (AllFormulasOf C) is non empty set
bool ((phii . H) \/ (AllFormulasOf C)) is non empty set
H is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
H + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
psi . (H + 1) is Element of bool (X \/ (AllFormulasOf C))
psi . H is Element of bool (X \/ (AllFormulasOf C))
S . H is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf C
((psi . H),C,phi,(S . H)) is Element of bool ((psi . H) \/ (AllFormulasOf C))
(psi . H) \/ (AllFormulasOf C) is non empty set
bool ((psi . H) \/ (AllFormulasOf C)) is non empty set
dom phii is non empty countable Element of bool NAT
dom psi is non empty countable Element of bool NAT
X is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
X + C is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
phi is set
S is V51() V53() eligible Language-like
(S) is non empty Relation-like set
AllFormulasOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
the U1 of S is set
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf S) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf S), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}} : b1 is finite } is set
bool (S) is non empty Element of bool (bool (S))
bool (S) is non empty set
bool (bool (S)) is non empty set
Funcs ((bool (S)),(bool (S))) is non empty functional FUNCTION_DOMAIN of bool (S), bool (S)
bool (Funcs ((bool (S)),(bool (S)))) is non empty set
[:NAT,(AllFormulasOf S):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(AllFormulasOf S):] is non empty non trivial non finite non empty-membered set
(S) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total (S) (S) Element of Funcs ((bool (S)),(bool (S)))
(S) is Relation-like bool (S) -defined (S) -valued Element of bool [:(bool (S)),(S):]
[:(bool (S)),(S):] is non empty Relation-like set
bool [:(bool (S)),(S):] is non empty set
(S,(S)) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
(S) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total (S) (S) Element of Funcs ((bool (S)),(bool (S)))
(S) is Relation-like bool (S) -defined (S) -valued Element of bool [:(bool (S)),(S):]
(S,(S)) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
phi \/ (AllFormulasOf S) is non empty set
bool (phi \/ (AllFormulasOf S)) is non empty Element of bool (bool (phi \/ (AllFormulasOf S)))
bool (phi \/ (AllFormulasOf S)) is non empty set
bool (bool (phi \/ (AllFormulasOf S))) is non empty set
DD is functional Element of bool (Funcs ((bool (S)),(bool (S))))
D is non empty Relation-like non-empty non empty-yielding NAT -defined AllFormulasOf S -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(AllFormulasOf S):]
(phi,S,DD,D) is non empty Relation-like NAT -defined bool (phi \/ (AllFormulasOf S)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (phi \/ (AllFormulasOf S))):]
[:NAT,(bool (phi \/ (AllFormulasOf S))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (phi \/ (AllFormulasOf S))):] is non empty non trivial non finite non empty-membered set
(phi,S,DD,D) . X is Element of bool (phi \/ (AllFormulasOf S))
(phi,S,DD,D) . (X + C) is Element of bool (phi \/ (AllFormulasOf S))
(phi,S,DD,D) . C is Element of bool (phi \/ (AllFormulasOf S))
X + 0 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(phi,S,DD,D) . (X + 0) is Element of bool (phi \/ (AllFormulasOf S))
(phi,S,DD,D) . 0 is Element of bool (phi \/ (AllFormulasOf S))
phii is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
X + phii is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(phi,S,DD,D) . (X + phii) is Element of bool (phi \/ (AllFormulasOf S))
(phi,S,DD,D) . phii is Element of bool (phi \/ (AllFormulasOf S))
phii + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
X + (phii + 1) is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(phi,S,DD,D) . (X + (phii + 1)) is Element of bool (phi \/ (AllFormulasOf S))
(phi,S,DD,D) . (phii + 1) is Element of bool (phi \/ (AllFormulasOf S))
D . (X + phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf S
(((phi,S,DD,D) . (X + phii)),S,DD,(D . (X + phii))) is Element of bool (((phi,S,DD,D) . (X + phii)) \/ (AllFormulasOf S))
((phi,S,DD,D) . (X + phii)) \/ (AllFormulasOf S) is non empty set
bool (((phi,S,DD,D) . (X + phii)) \/ (AllFormulasOf S)) is non empty set
((phi,S,DD,D) . (X + phii)) \ (((phi,S,DD,D) . (X + phii)),S,DD,(D . (X + phii))) is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (phi \/ (AllFormulasOf S))
((phi,S,DD,D) . (X + phii)) typed\ (((phi,S,DD,D) . (X + phii)),S,DD,(D . (X + phii))) is Element of bool ((phi,S,DD,D) . (X + phii))
bool ((phi,S,DD,D) . (X + phii)) is non empty set
((phi,S,DD,D) . (X + phii)) \ (((phi,S,DD,D) . (X + phii)),S,DD,(D . (X + phii))) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool ((phi,S,DD,D) . (X + phii))
(X + phii) + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(phi,S,DD,D) . ((X + phii) + 1) is Element of bool (phi \/ (AllFormulasOf S))
D . phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf S
m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf S
seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}}
xnot seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}}
TheNorSymbOf S is non literal non low-compounding non relational non own Element of AllSymbolsOf S
the U3 of S is Element of the U1 of S
<*(TheNorSymbOf S)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}}
[1,(TheNorSymbOf S)] is non empty V26() set
{[1,(TheNorSymbOf S)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf S)*> ^ seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf S) *) \ {{}}
(<*(TheNorSymbOf S)*> ^ seqt) ^ seqt is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth seqt),(Depth seqt)) -wff wff non exal (S,{(S)} \/ {(S)},{(xnot seqt),(xnot seqt)}) Element of ((AllSymbolsOf S) *) \ {{}}
Depth seqt is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth seqt),(Depth seqt)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(S) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total (S) (S) Element of Funcs ((bool (S)),(bool (S)))
(S) is Relation-like bool (S) -defined (S) -valued Element of bool [:(bool (S)),(S):]
(S,(S)) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
{(S)} is non empty trivial functional finite 1 -element with_common_domain countable (S) (S) Element of bool (Funcs ((bool (S)),(bool (S))))
(S) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total (S) (S) Element of Funcs ((bool (S)),(bool (S)))
(S) is Relation-like bool (S) -defined (S) -valued Element of bool [:(bool (S)),(S):]
(S,(S)) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
{(S)} is non empty trivial functional finite 1 -element with_common_domain countable (S) (S) Element of bool (Funcs ((bool (S)),(bool (S))))
{(S)} \/ {(S)} is non empty functional finite countable (S) Element of bool (Funcs ((bool (S)),(bool (S))))
{(xnot seqt),(xnot seqt)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf S) *) \ {{}})
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
HH is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}}
(((phi,S,DD,D) . phii),S,DD,(D . phii)) is Element of bool (((phi,S,DD,D) . phii) \/ (AllFormulasOf S))
((phi,S,DD,D) . phii) \/ (AllFormulasOf S) is non empty set
bool (((phi,S,DD,D) . phii) \/ (AllFormulasOf S)) is non empty set
xnot m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}}
<*(TheNorSymbOf S)*> ^ m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf S) *) \ {{}}
(<*(TheNorSymbOf S)*> ^ m) ^ m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth m),(Depth m)) -wff wff non exal (S,{(S)} \/ {(S)},{(xnot m),(xnot m)}) Element of ((AllSymbolsOf S) *) \ {{}}
Depth m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth m),(Depth m)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot m),(xnot m)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf S) *) \ {{}})
{m} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (S) Element of bool (AllFormulasOf S)
((phi,S,DD,D) . phii) \/ {m} is non empty set
{(xnot m)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (S) Element of bool (((AllSymbolsOf S) *) \ {{}})
((phi,S,DD,D) . phii) \/ {(xnot m)} is non empty set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
[:NAT,(AllFormulasOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(AllFormulasOf C):] is non empty non trivial non finite non empty-membered set
X is set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S is non empty Relation-like non-empty non empty-yielding NAT -defined AllFormulasOf C -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(AllFormulasOf C):]
(X,C,phi,S) is non empty Relation-like NAT -defined bool (X \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (X \/ (AllFormulasOf C))):]
X \/ (AllFormulasOf C) is non empty set
bool (X \/ (AllFormulasOf C)) is non empty Element of bool (bool (X \/ (AllFormulasOf C)))
bool (X \/ (AllFormulasOf C)) is non empty set
bool (bool (X \/ (AllFormulasOf C))) is non empty set
[:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial non finite non empty-membered set
proj2 (X,C,phi,S) is non empty set
union (proj2 (X,C,phi,S)) is set
bool (bool (X \/ (AllFormulasOf C))) is non empty set
Y is Element of bool (bool (X \/ (AllFormulasOf C)))
union Y is Element of bool (X \/ (AllFormulasOf C))
(union Y) \ (X \/ (AllFormulasOf C)) is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (X \/ (AllFormulasOf C))
(union Y) typed\ (X \/ (AllFormulasOf C)) is Element of bool (union Y)
bool (union Y) is non empty set
(union Y) \ (X \/ (AllFormulasOf C)) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (union Y)
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
[:NAT,(AllFormulasOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(AllFormulasOf C):] is non empty non trivial non finite non empty-membered set
X is set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
S is non empty Relation-like non-empty non empty-yielding NAT -defined AllFormulasOf C -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(AllFormulasOf C):]
(X,C,phi,S) is Element of bool (X \/ (AllFormulasOf C))
X \/ (AllFormulasOf C) is non empty set
bool (X \/ (AllFormulasOf C)) is non empty set
(X,C,phi,S) is non empty Relation-like NAT -defined bool (X \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (X \/ (AllFormulasOf C))):]
bool (X \/ (AllFormulasOf C)) is non empty Element of bool (bool (X \/ (AllFormulasOf C)))
bool (bool (X \/ (AllFormulasOf C))) is non empty set
[:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial non finite non empty-membered set
proj2 (X,C,phi,S) is non empty set
union (proj2 (X,C,phi,S)) is set
X \ (X,C,phi,S) is Element of bool X
bool X is non empty set
X typed\ (X,C,phi,S) is Element of bool X
[:NAT,(proj2 (X,C,phi,S)):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(proj2 (X,C,phi,S)):] is non empty non trivial non finite non empty-membered set
D is non empty Relation-like NAT -defined proj2 (X,C,phi,S) -valued Function-like total quasi_total Element of bool [:NAT,(proj2 (X,C,phi,S)):]
D . 0 is Element of proj2 (X,C,phi,S)
(X,C,phi,S) . 0 is Element of bool (X \/ (AllFormulasOf C))
Y is set
X is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
[:NAT,(AllFormulasOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(AllFormulasOf C):] is non empty non trivial non finite non empty-membered set
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
DD is non empty Relation-like non-empty non empty-yielding NAT -defined AllFormulasOf C -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(AllFormulasOf C):]
proj2 DD is non empty with_non-empty_elements non empty-membered set
(X,C,phi,DD) is Element of bool (X \/ (AllFormulasOf C))
X \/ (AllFormulasOf C) is non empty set
bool (X \/ (AllFormulasOf C)) is non empty set
(X,C,phi,DD) is non empty Relation-like NAT -defined bool (X \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (X \/ (AllFormulasOf C))):]
bool (X \/ (AllFormulasOf C)) is non empty Element of bool (bool (X \/ (AllFormulasOf C)))
bool (bool (X \/ (AllFormulasOf C))) is non empty set
[:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial non finite non empty-membered set
proj2 (X,C,phi,DD) is non empty set
union (proj2 (X,C,phi,DD)) is set
[:NAT,(proj2 (X,C,phi,DD)):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(proj2 (X,C,phi,DD)):] is non empty non trivial non finite non empty-membered set
phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
dom DD is non empty countable Element of bool NAT
psi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf C
H is set
DD . H is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() set
m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
m + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(X,C,phi,DD) . (m + 1) is Element of bool (X \/ (AllFormulasOf C))
(X,C,phi,DD) . m is Element of bool (X \/ (AllFormulasOf C))
DD . m is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of AllFormulasOf C
(((X,C,phi,DD) . m),C,phi,(DD . m)) is Element of bool (((X,C,phi,DD) . m) \/ (AllFormulasOf C))
((X,C,phi,DD) . m) \/ (AllFormulasOf C) is non empty set
bool (((X,C,phi,DD) . m) \/ (AllFormulasOf C)) is non empty set
{phii} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
((X,C,phi,DD) . m) \/ {phii} is non empty set
xnot phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ phii) ^ phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phii),(Depth phii)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot phii),(xnot phii)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth phii is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth phii),(Depth phii)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot phii),(xnot phii)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
{(xnot phii)} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
((X,C,phi,DD) . m) \/ {(xnot phii)} is non empty set
{phii} null ((X,C,phi,DD) . m) is finite countable (C) set
{phii} \typed/ ((X,C,phi,DD) . m) is Element of bool ({phii} \/ ((X,C,phi,DD) . m))
{phii} \/ ((X,C,phi,DD) . m) is non empty set
bool ({phii} \/ ((X,C,phi,DD) . m)) is non empty set
seqt is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(X,C,phi,DD) . seqt is Element of bool (X \/ (AllFormulasOf C))
{(xnot phii)} null ((X,C,phi,DD) . m) is finite countable (C) set
{(xnot phii)} \typed/ ((X,C,phi,DD) . m) is Element of bool ({(xnot phii)} \/ ((X,C,phi,DD) . m))
{(xnot phii)} \/ ((X,C,phi,DD) . m) is non empty set
bool ({(xnot phii)} \/ ((X,C,phi,DD) . m)) is non empty set
Y is non empty Relation-like NAT -defined proj2 (X,C,phi,DD) -valued Function-like total quasi_total Element of bool [:NAT,(proj2 (X,C,phi,DD)):]
Y . seqt is Element of proj2 (X,C,phi,DD)
X is set
C is V51() V53() eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
[:NAT,(AllFormulasOf C):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(AllFormulasOf C):] is non empty non trivial non finite non empty-membered set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
phi is functional Element of bool (Funcs ((bool (C)),(bool (C))))
ExFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf C) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
LettersOf C is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
the U3 of C is Element of the U1 of C
{ the U3 of C} is non empty trivial finite 1 -element countable set
the U1 of C \ { the U3 of C} is non empty Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U3 of C} is Element of bool the U1 of C
the adicity of C is non empty Relation-like the U1 of C \ { the U3 of C} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of C \ { the U3 of C}),INT:]
[:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of C \ { the U3 of C}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of C " {0} is Element of bool ( the U1 of C \ { the U3 of C})
bool ( the U1 of C \ { the U3 of C}) is non empty set
D is non empty Relation-like non-empty non empty-yielding NAT -defined AllFormulasOf C -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(AllFormulasOf C):]
(X,C,phi,D) is Element of bool (X \/ (AllFormulasOf C))
X \/ (AllFormulasOf C) is non empty set
bool (X \/ (AllFormulasOf C)) is non empty set
(X,C,phi,D) is non empty Relation-like NAT -defined bool (X \/ (AllFormulasOf C)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (X \/ (AllFormulasOf C))):]
bool (X \/ (AllFormulasOf C)) is non empty Element of bool (bool (X \/ (AllFormulasOf C)))
bool (bool (X \/ (AllFormulasOf C))) is non empty set
[:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (X \/ (AllFormulasOf C))):] is non empty non trivial non finite non empty-membered set
proj2 (X,C,phi,D) is non empty set
union (proj2 (X,C,phi,D)) is set
dom (X,C,phi,D) is non empty countable Element of bool NAT
HH is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(X,C,phi,D) . HH is Element of bool (X \/ (AllFormulasOf C))
HC is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(X,C,phi,D) . HC is Element of bool (X \/ (AllFormulasOf C))
HH - HH is complex ext-real finite V40() V41() countable set
HC - HH is complex ext-real finite V40() V41() countable set
sub1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
HH + sub1 is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
(X,C,phi,D) . (HH + sub1) is Element of bool (X \/ (AllFormulasOf C))
bool (X,C,phi,D) is non empty set
HH is finite countable Element of bool (X,C,phi,D)
HC is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable Element of NAT
(X,C,phi,D) . HC is Element of bool (X \/ (AllFormulasOf C))
phi is V51() V53() eligible Language-like
(phi) is non empty Relation-like set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf phi) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf phi), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}} : b1 is finite } is set
bool (phi) is non empty Element of bool (bool (phi))
bool (phi) is non empty set
bool (bool (phi)) is non empty set
[:(bool (phi)),(phi):] is non empty Relation-like set
bool [:(bool (phi)),(phi):] is non empty set
D is V51() V53() eligible Language-like
(D) is non empty Relation-like set
AllFormulasOf D is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf D -prefix D -prefix Element of bool (((AllSymbolsOf D) *) \ {{}})
AllSymbolsOf D is non empty non trivial non finite non empty-membered set
the U1 of D is set
AllSymbolsOf D is non empty non trivial non finite non empty-membered set
(AllSymbolsOf D) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf D
((AllSymbolsOf D) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf D) *)
bool ((AllSymbolsOf D) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf D) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf D) *)
bool (((AllSymbolsOf D) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf D) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf D
((AllSymbolsOf D) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf D) *)
bool ((AllSymbolsOf D) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf D) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf D) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf D) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf D) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf D), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf D) *) \ {{}} : b1 is finite } is set
bool (D) is non empty Element of bool (bool (D))
bool (D) is non empty set
bool (bool (D)) is non empty set
[:(bool (D)),(D):] is non empty Relation-like set
bool [:(bool (D)),(D):] is non empty set
X is set
S is Relation-like bool (phi) -defined (phi) -valued Element of bool [:(bool (phi)),(phi):]
(phi,S) is Relation-like bool (phi) -defined bool (phi) -valued Function-like total quasi_total Element of Funcs ((bool (phi)),(bool (phi)))
Funcs ((bool (phi)),(bool (phi))) is non empty functional FUNCTION_DOMAIN of bool (phi), bool (phi)
C is set
(phi,S) . C is set
[C,X] is non empty V26() set
DD is set
FF is set
[FF,DD] is non empty V26() set
Y is Relation-like bool (D) -defined (D) -valued Element of bool [:(bool (D)),(D):]
(D,Y) is Relation-like bool (D) -defined bool (D) -valued Function-like total quasi_total Element of Funcs ((bool (D)),(bool (D)))
Funcs ((bool (D)),(bool (D))) is non empty functional FUNCTION_DOMAIN of bool (D), bool (D)
(D,Y) . FF is set
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
LettersOf X is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U3 of X is Element of the U1 of X
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
the U2 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
C is functional (2,X) Element of bool (Funcs ((bool (X)),(bool (X))))
phi is functional set
phi /\ (((AllSymbolsOf X) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi typed/\ (((AllSymbolsOf X) *) \ {{}}) is functional Element of bool phi
bool phi is non empty set
phi /\ (((AllSymbolsOf X) *) \ {{}}) is functional set
phi /\typed (((AllSymbolsOf X) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf X) *) \ {{}})
SymbolsOf (phi /\ (((AllSymbolsOf X) *) \ {{}})) is set
(phi /\ (((AllSymbolsOf X) *) \ {{}})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (phi /\ (((AllSymbolsOf X) *) \ {{}})) \/ {{}} : b1 in phi /\ (((AllSymbolsOf X) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (phi /\ (((AllSymbolsOf X) *) \ {{}})) \/ {{}} : b1 in phi /\ (((AllSymbolsOf X) *) \ {{}}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of phi /\ (((AllSymbolsOf X) *) \ {{}}) : b1 in phi /\ (((AllSymbolsOf X) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of phi /\ (((AllSymbolsOf X) *) \ {{}}) : b1 in phi /\ (((AllSymbolsOf X) *) \ {{}}) } is set
(LettersOf X) \ (SymbolsOf (phi /\ (((AllSymbolsOf X) *) \ {{}}))) is Element of bool (AllSymbolsOf X)
(LettersOf X) typed\ (SymbolsOf (phi /\ (((AllSymbolsOf X) *) \ {{}}))) is Element of bool (LettersOf X)
bool (LettersOf X) is non empty non trivial non finite non empty-membered set
(LettersOf X) \ (SymbolsOf (phi /\ (((AllSymbolsOf X) *) \ {{}}))) is Element of bool (LettersOf X)
ExFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool (((AllSymbolsOf X) *) \ {{}})
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ( b1 is wff & b1 is exal ) } is set
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
[:NAT,(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(((AllSymbolsOf X) *) \ {{}}):] is non empty non trivial non finite non empty-membered set
I2 is countable set
I1 is non empty Relation-like non-empty non empty-yielding NAT -defined ((AllSymbolsOf X) *) \ {{}} -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(((AllSymbolsOf X) *) \ {{}}):]
proj2 I1 is non empty with_non-empty_elements non empty-membered set
[:NAT,(AllFormulasOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(AllFormulasOf X):] is non empty non trivial non finite non empty-membered set
(ExFormulasOf X) \ I2 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf X) *) \ {{}})
(ExFormulasOf X) typed\ I2 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (ExFormulasOf X)
bool (ExFormulasOf X) is non empty set
(ExFormulasOf X) \ I2 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (ExFormulasOf X)
bool I2 is non empty set
[:NAT,I2:] is Relation-like set
bool [:NAT,I2:] is non empty set
I02 is countable Element of bool I2
I1 is Relation-like NAT -defined I2 -valued Function-like quasi_total Element of bool [:NAT,I2:]
proj2 I1 is set
[:NAT,(ExFormulasOf X):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(ExFormulasOf X):] is non empty non trivial non finite non empty-membered set
II2 is non empty functional (1,X) ( 0 ,X) Element of bool (Funcs ((bool (X)),(bool (X))))
I2 is non empty Relation-like non-empty non empty-yielding NAT -defined ExFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(ExFormulasOf X):]
(phi,X,II2,I2) is functional Element of bool (phi \/ (AllFormulasOf X))
phi \/ (AllFormulasOf X) is non empty functional set
bool (phi \/ (AllFormulasOf X)) is non empty set
(phi,X,II2,I2) is non empty Relation-like NAT -defined bool (phi \/ (AllFormulasOf X)) -valued Function-like total quasi_total Element of bool [:NAT,(bool (phi \/ (AllFormulasOf X))):]
bool (phi \/ (AllFormulasOf X)) is non empty Element of bool (bool (phi \/ (AllFormulasOf X)))
bool (bool (phi \/ (AllFormulasOf X))) is non empty set
[:NAT,(bool (phi \/ (AllFormulasOf X))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool (phi \/ (AllFormulasOf X))):] is non empty non trivial non finite non empty-membered set
proj2 (phi,X,II2,I2) is non empty set
union (proj2 (phi,X,II2,I2)) is set
c26 is non empty Relation-like non-empty non empty-yielding NAT -defined AllFormulasOf X -valued Function-like total quasi_total Function-yielding V156() V208() Element of bool [:NAT,(AllFormulasOf X):]
((phi,X,II2,I2),X,II2,c26) is functional Element of bool ((phi,X,II2,I2) \/ (AllFormulasOf X))
(phi,X,II2,I2) \/ (AllFormulasOf X) is non empty functional set
bool ((phi,X,II2,I2) \/ (AllFormulasOf X)) is non empty set
((phi,X,II2,I2),X,II2,c26) is non empty Relation-like NAT -defined bool ((phi,X,II2,I2) \/ (AllFormulasOf X)) -valued Function-like total quasi_total Element of bool [:NAT,(bool ((phi,X,II2,I2) \/ (AllFormulasOf X))):]
bool ((phi,X,II2,I2) \/ (AllFormulasOf X)) is non empty Element of bool (bool ((phi,X,II2,I2) \/ (AllFormulasOf X)))
bool (bool ((phi,X,II2,I2) \/ (AllFormulasOf X))) is non empty set
[:NAT,(bool ((phi,X,II2,I2) \/ (AllFormulasOf X))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:NAT,(bool ((phi,X,II2,I2) \/ (AllFormulasOf X))):] is non empty non trivial non finite non empty-membered set
proj2 ((phi,X,II2,I2),X,II2,c26) is non empty set
union (proj2 ((phi,X,II2,I2),X,II2,c26)) is set
AllTermsOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered Element of bool (bool (((AllSymbolsOf X) *) \ {{}}))
bool (bool (((AllSymbolsOf X) *) \ {{}})) is non empty non trivial non finite non empty-membered set
X -termsOfMaxDepth is Relation-like Function-like set
proj2 (X -termsOfMaxDepth) is set
union (proj2 (X -termsOfMaxDepth)) is set
X22 is (X,II2) set
(X,II2,X22) is Relation-like AllTermsOf X -defined AllTermsOf X -valued total quasi_total reflexive symmetric transitive Element of bool [:(AllTermsOf X),(AllTermsOf X):]
[:(AllTermsOf X),(AllTermsOf X):] is non empty Relation-like set
bool [:(AllTermsOf X),(AllTermsOf X):] is non empty set
TermSymbolsOf X is non empty set
the adicity of X " NAT is Element of bool ( the U1 of X \ { the U3 of X})
TheEqSymbOf X is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf X
<*(TheEqSymbOf X)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}}
[1,(TheEqSymbOf X)] is non empty V26() set
{[1,(TheEqSymbOf X)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
{ [b1,b2] where b1, b2 is non empty Relation-like NAT -defined TermSymbolsOf X -valued Function-like finite FinSequence-like FinSubsequence-like countable V209() termal Element of ((AllSymbolsOf X) *) \ {{}} : (<*(TheEqSymbOf X)*> ^ b1) ^ b2 is (X,II2,X22) } is set
Class (X,II2,X22) is non empty with_non-empty_elements non empty-membered a_partition of AllTermsOf X
U is non empty with_non-empty_elements non empty-membered a_partition of AllTermsOf X
U * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of U
U \/ BOOLEAN is non empty set
K491((U *),(U \/ BOOLEAN)) is non empty functional M30(U * ,U \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491((U *),(U \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491((U *),(U \/ BOOLEAN))
U -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491((U *),(U \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491((U *),(U \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491((U *),(U \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491((U *),(U \/ BOOLEAN))) : b1 is X,U -interpreter-like } is set
(X,II2,X22) is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, Class (X,II2,X22) -interpreter-like Element of (Class (X,II2,X22)) -InterpretersOf X
(Class (X,II2,X22)) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of Class (X,II2,X22)
(Class (X,II2,X22)) \/ BOOLEAN is non empty set
K491(((Class (X,II2,X22)) *),((Class (X,II2,X22)) \/ BOOLEAN)) is non empty functional M30((Class (X,II2,X22)) * ,(Class (X,II2,X22)) \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491(((Class (X,II2,X22)) *),((Class (X,II2,X22)) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491(((Class (X,II2,X22)) *),((Class (X,II2,X22)) \/ BOOLEAN))
(Class (X,II2,X22)) -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491(((Class (X,II2,X22)) *),((Class (X,II2,X22)) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491(((Class (X,II2,X22)) *),((Class (X,II2,X22)) \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491(((Class (X,II2,X22)) *),((Class (X,II2,X22)) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491(((Class (X,II2,X22)) *),((Class (X,II2,X22)) \/ BOOLEAN))) : b1 is X, Class (X,II2,X22) -interpreter-like } is set
(X,X22) -freeInterpreter is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X, AllTermsOf X -interpreter-like (X,II2,X22) -respecting Element of (AllTermsOf X) -InterpretersOf X
(AllTermsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllTermsOf X
(AllTermsOf X) \/ BOOLEAN is non empty set
K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) is non empty functional M30((AllTermsOf X) * ,(AllTermsOf X) \/ BOOLEAN)
Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf X,K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))
(AllTermsOf X) -InterpretersOf X is non empty functional Element of bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf X -defined K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf X),K491(((AllTermsOf X) *),((AllTermsOf X) \/ BOOLEAN))) : b1 is X, AllTermsOf X -interpreter-like } is set
((X,X22) -freeInterpreter) quotient (X,II2,X22) is Relation-like OwnSymbolsOf X -defined Function-like Function-yielding V156() X, Class (X,II2,X22) -interpreter-like set
I is Relation-like OwnSymbolsOf X -defined Function-like total Function-yielding V156() X,U -interpreter-like Element of U -InterpretersOf X
phi \ (phi,X,II2,I2) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool phi
phi typed\ (phi,X,II2,I2) is functional Element of bool phi
(phi,X,II2,I2) \ ((phi,X,II2,I2),X,II2,c26) is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (phi \/ (AllFormulasOf X))
(phi,X,II2,I2) typed\ ((phi,X,II2,I2),X,II2,c26) is functional Element of bool (phi,X,II2,I2)
bool (phi,X,II2,I2) is non empty set
(phi,X,II2,I2) \ ((phi,X,II2,I2),X,II2,c26) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (phi,X,II2,I2)
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}}
I -TruthEval phi is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
OwnSymbolsOf X is non empty Element of bool (AllSymbolsOf X)
bool (AllSymbolsOf X) is non empty non trivial non finite non empty-membered set
the U2 of X is Element of the U1 of X
the U3 of X is Element of the U1 of X
{ the U2 of X, the U3 of X} is non empty finite countable set
the U1 of X \ { the U2 of X, the U3 of X} is Element of bool the U1 of X
bool the U1 of X is non empty set
the U1 of X typed\ { the U2 of X, the U3 of X} is Element of bool the U1 of X
C is functional (2,X) Element of bool (Funcs ((bool (X)),(bool (X))))
phi is functional set
LettersOf X is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf X)
{ the U3 of X} is non empty trivial finite 1 -element countable set
the U1 of X \ { the U3 of X} is non empty Element of bool the U1 of X
the U1 of X typed\ { the U3 of X} is Element of bool the U1 of X
the adicity of X is non empty Relation-like the U1 of X \ { the U3 of X} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of X \ { the U3 of X}),INT:]
[:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of X \ { the U3 of X}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of X " {0} is Element of bool ( the U1 of X \ { the U3 of X})
bool ( the U1 of X \ { the U3 of X}) is non empty set
phi /\ (((AllSymbolsOf X) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
phi typed/\ (((AllSymbolsOf X) *) \ {{}}) is functional Element of bool phi
bool phi is non empty set
phi /\ (((AllSymbolsOf X) *) \ {{}}) is functional set
phi /\typed (((AllSymbolsOf X) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((AllSymbolsOf X) *) \ {{}})
SymbolsOf (phi /\ (((AllSymbolsOf X) *) \ {{}})) is set
(phi /\ (((AllSymbolsOf X) *) \ {{}})) \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of (phi /\ (((AllSymbolsOf X) *) \ {{}})) \/ {{}} : b1 in phi /\ (((AllSymbolsOf X) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of (phi /\ (((AllSymbolsOf X) *) \ {{}})) \/ {{}} : b1 in phi /\ (((AllSymbolsOf X) *) \ {{}}) } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of phi /\ (((AllSymbolsOf X) *) \ {{}}) : b1 in phi /\ (((AllSymbolsOf X) *) \ {{}}) } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of phi /\ (((AllSymbolsOf X) *) \ {{}}) : b1 in phi /\ (((AllSymbolsOf X) *) \ {{}}) } is set
phii is functional finite V36() FinSequence-membered countable set
SymbolsOf phii is finite countable set
phii \/ {{}} is non empty functional finite V36() countable set
{ (proj2 b1) where b1 is Relation-like Function-like Element of phii \/ {{}} : b1 in phii } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of phii \/ {{}} : b1 in phii } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of phii : b1 in phii } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of phii : b1 in phii } is set
(LettersOf X) \ (SymbolsOf (phi /\ (((AllSymbolsOf X) *) \ {{}}))) is Element of bool (AllSymbolsOf X)
(LettersOf X) typed\ (SymbolsOf (phi /\ (((AllSymbolsOf X) *) \ {{}}))) is Element of bool (LettersOf X)
bool (LettersOf X) is non empty non trivial non finite non empty-membered set
(LettersOf X) \ (SymbolsOf (phi /\ (((AllSymbolsOf X) *) \ {{}}))) is Element of bool (LettersOf X)
X is non empty set
X * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of X
X \/ BOOLEAN is non empty set
K491((X *),(X \/ BOOLEAN)) is non empty functional M30(X * ,X \/ BOOLEAN)
C is set
phi is V51() V53() eligible Language-like
OwnSymbolsOf phi is non empty Element of bool (AllSymbolsOf phi)
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
the U1 of phi is set
bool (AllSymbolsOf phi) is non empty non trivial non finite non empty-membered set
the U2 of phi is Element of the U1 of phi
the U3 of phi is Element of the U1 of phi
{ the U2 of phi, the U3 of phi} is non empty finite countable set
the U1 of phi \ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
bool the U1 of phi is non empty set
the U1 of phi typed\ { the U2 of phi, the U3 of phi} is Element of bool the U1 of phi
Funcs ((OwnSymbolsOf phi),K491((X *),(X \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf phi,K491((X *),(X \/ BOOLEAN))
X -InterpretersOf phi is non empty functional Element of bool (Funcs ((OwnSymbolsOf phi),K491((X *),(X \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf phi),K491((X *),(X \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf phi -defined K491((X *),(X \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf phi),K491((X *),(X \/ BOOLEAN))) : b1 is phi,X -interpreter-like } is set
AllFormulasOf phi is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf phi -prefix phi -prefix Element of bool (((AllSymbolsOf phi) *) \ {{}})
AllSymbolsOf phi is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
bool (((AllSymbolsOf phi) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf phi
((AllSymbolsOf phi) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf phi) *)
bool ((AllSymbolsOf phi) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf phi) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf phi) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf phi) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
S is V51() V53() eligible Language-like
OwnSymbolsOf S is non empty Element of bool (AllSymbolsOf S)
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
the U1 of S is set
bool (AllSymbolsOf S) is non empty non trivial non finite non empty-membered 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 countable 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),K491((X *),(X \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf S,K491((X *),(X \/ BOOLEAN))
X -InterpretersOf S is non empty functional Element of bool (Funcs ((OwnSymbolsOf S),K491((X *),(X \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf S),K491((X *),(X \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf S -defined K491((X *),(X \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf S),K491((X *),(X \/ BOOLEAN))) : b1 is S,X -interpreter-like } is set
the adicity of phi is non empty Relation-like the U1 of phi \ { the U3 of phi} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of phi \ { the U3 of phi}),INT:]
{ the U3 of phi} is non empty trivial finite 1 -element countable set
the U1 of phi \ { the U3 of phi} is non empty Element of bool the U1 of phi
the U1 of phi typed\ { the U3 of phi} is Element of bool the U1 of phi
[:( the U1 of phi \ { the U3 of phi}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of phi \ { the U3 of phi}),INT:] is non empty non trivial non finite non empty-membered set
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 countable 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 non empty-membered set
bool [:( the U1 of S \ { the U3 of S}),INT:] is non empty non trivial non finite non empty-membered set
TheEqSymbOf phi is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf phi
TheEqSymbOf S is low-compounding relational non own ofAtomicFormula Element of AllSymbolsOf S
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
TheNorSymbOf phi is non literal non low-compounding non relational non own Element of AllSymbolsOf phi
TheNorSymbOf S is non literal non low-compounding non relational non own Element of AllSymbolsOf S
AtomicFormulaSymbolsOf phi is non empty Element of bool (AllSymbolsOf phi)
TheNorSymbOf phi is set
{(TheNorSymbOf phi)} is non empty trivial finite 1 -element countable set
(AllSymbolsOf phi) \ {(TheNorSymbOf phi)} is non empty non trivial non finite non empty-membered Element of bool (AllSymbolsOf phi)
bool (AllSymbolsOf phi) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf phi) typed\ {(TheNorSymbOf phi)} is Element of bool (AllSymbolsOf phi)
dom the adicity of phi is non empty Element of bool ( the U1 of phi \ { the U3 of phi})
bool ( the U1 of phi \ { the U3 of phi}) is non empty set
bool (dom the adicity of phi) is non empty set
D2 is Relation-like OwnSymbolsOf phi -defined Function-like total Function-yielding V156() phi,X -interpreter-like Element of X -InterpretersOf phi
D2 | (OwnSymbolsOf phi) is Relation-like OwnSymbolsOf phi -defined OwnSymbolsOf phi -defined OwnSymbolsOf phi -defined K491((X *),(X \/ BOOLEAN)) -valued Function-like total Function-yielding V156() phi,X -interpreter-like set
D2 null (OwnSymbolsOf phi) is Relation-like (OwnSymbolsOf phi) \/ (proj1 D2) -defined (OwnSymbolsOf phi) \/ (proj2 D2) -valued Function-like set
proj1 D2 is set
(OwnSymbolsOf phi) \/ (proj1 D2) is non empty set
proj2 D2 is set
(OwnSymbolsOf phi) \/ (proj2 D2) is non empty set
D2 \typed/ (OwnSymbolsOf phi) is Element of bool (D2 \/ (OwnSymbolsOf phi))
D2 \/ (OwnSymbolsOf phi) is non empty set
bool (D2 \/ (OwnSymbolsOf phi)) is non empty set
sub1 is Relation-like OwnSymbolsOf S -defined Function-like total Function-yielding V156() S,X -interpreter-like Element of X -InterpretersOf S
sub1 | (OwnSymbolsOf phi) is Relation-like OwnSymbolsOf phi -defined OwnSymbolsOf S -defined Function-like Function-yielding V156() set
the adicity of phi | (OwnSymbolsOf phi) is Relation-like OwnSymbolsOf phi -defined the U1 of phi \ { the U3 of phi} -defined INT -valued Function-like Element of bool [:( the U1 of phi \ { the U3 of phi}),INT:]
the adicity of S | (dom the adicity of phi) is Relation-like the U1 of S \ { the U3 of S} -defined dom the adicity of phi -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 | (dom the adicity of phi)) | (OwnSymbolsOf phi) is Relation-like OwnSymbolsOf phi -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:]
a is Element of bool (dom the adicity of phi)
a null (dom the adicity of phi) is set
(dom the adicity of phi) /\ a is Element of bool (dom the adicity of phi)
(dom the adicity of phi) typed/\ a is Element of bool (dom the adicity of phi)
(dom the adicity of phi) /\ a is set
(dom the adicity of phi) /\typed a is Element of bool a
bool a is non empty set
a \typed/ (dom the adicity of phi) is Element of bool (a \/ (dom the adicity of phi))
a \/ (dom the adicity of phi) is non empty set
bool (a \/ (dom the adicity of phi)) is non empty set
the adicity of S | (a null (dom the adicity of phi)) is Relation-like the U1 of S \ { the U3 of S} -defined a null (dom the adicity of phi) -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 | (OwnSymbolsOf phi) is Relation-like OwnSymbolsOf phi -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:]
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}}
inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}}
D2 -TruthEval inf is boolean Element of BOOLEAN
U is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}}
sub1 -TruthEval U is boolean Element of BOOLEAN
sub1 -TruthEval sub2 is boolean Element of BOOLEAN
sub2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf phi) *) \ {{}}
D2 -TruthEval sub2 is boolean Element of BOOLEAN
inf is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}}
sub1 -TruthEval inf is boolean Element of BOOLEAN
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
phi is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
{C,phi} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
{C} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{phi} is non empty trivial functional finite 1 -element with_common_domain countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{C} \/ {phi} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
S is functional Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
C is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
phi is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
S is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
DD is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) Element of Funcs ((bool (X)),(bool (X)))
{C,phi,S,DD} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
{C,phi} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{S,DD} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{C,phi} \/ {S,DD} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
FF is functional Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is functional (2,X) (X) Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X),(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X),(X),(X),(X),(X),(X),(X),(X)} \/ {(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
{(X),(X),(X),(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X),(X),(X),(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X),(X),(X),(X)} \/ {(X),(X),(X),(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
DD is functional (X) Element of bool (Funcs ((bool (X)),(bool (X))))
DD \/ {(X),(X),(X),(X)} is non empty functional (X) Element of bool (Funcs ((bool (X)),(bool (X))))
FF is functional Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is functional (X) (2,X) (X) Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X),(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X),(X),(X),(X),(X),(X),(X),(X)} \/ {(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() eligible Language-like
(X) is non empty Relation-like set
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf X) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf X), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf X) *) \ {{}} : b1 is finite } is set
bool (X) is non empty Element of bool (bool (X))
bool (X) is non empty set
bool (bool (X)) is non empty set
Funcs ((bool (X)),(bool (X))) is non empty functional FUNCTION_DOMAIN of bool (X), bool (X)
bool (Funcs ((bool (X)),(bool (X)))) is non empty set
(X) is functional (X) (2,X) (X) Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
[:(bool (X)),(X):] is non empty Relation-like set
bool [:(bool (X)),(X):] is non empty set
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X),(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total (X) (X) Element of Funcs ((bool (X)),(bool (X)))
(X) is Relation-like bool (X) -defined (X) -valued Element of bool [:(bool (X)),(X):]
(X,(X)) is Relation-like bool (X) -defined bool (X) -valued Function-like total quasi_total Element of Funcs ((bool (X)),(bool (X)))
{(X),(X),(X),(X)} is non empty functional finite countable (X) Element of bool (Funcs ((bool (X)),(bool (X))))
{(X),(X),(X),(X),(X),(X),(X),(X)} \/ {(X),(X),(X),(X)} is non empty functional finite countable Element of bool (Funcs ((bool (X)),(bool (X))))
X is V51() V53() countable eligible Language-like
AllFormulasOf X is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered countable AllSymbolsOf X -prefix X -prefix Element of bool (((AllSymbolsOf X) *) \ {{}})
AllSymbolsOf X is non empty non trivial non finite non empty-membered countable denumerable set
the U1 of X is set
AllSymbolsOf X is non empty non trivial non finite non empty-membered countable denumerable set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable denumerable Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
bool (((AllSymbolsOf X) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf X
((AllSymbolsOf X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable denumerable Element of bool ((AllSymbolsOf X) *)
bool ((AllSymbolsOf X) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf X) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf X) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf X) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
X is set
C is V51() V53() countable eligible Language-like
(C) is non empty Relation-like set
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered countable AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered countable denumerable set
the U1 of C is set
AllSymbolsOf C is non empty non trivial non finite non empty-membered countable denumerable set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable denumerable Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable denumerable Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
OwnSymbolsOf C is non empty countable Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
the U2 of C is Element of the U1 of C
the U3 of C is Element of the U1 of C
{ the U2 of C, the U3 of C} is non empty finite countable set
the U1 of C \ { the U2 of C, the U3 of C} is Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U2 of C, the U3 of C} is Element of bool the U1 of C
S is functional Element of bool (Funcs ((bool (C)),(bool (C))))
FF is functional V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf C)
C addLettersNotIn FF is V51() V53() countable eligible C -extending Language-like
SymbolsOf FF is set
FF \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of FF \/ {{}} : b1 in FF } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of FF \/ {{}} : b1 in FF } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of FF : b1 in FF } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of FF : b1 in FF } is set
(AllSymbolsOf C) \/ (SymbolsOf FF) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) \/ (SymbolsOf FF)) -freeCountableSet is non empty non trivial non finite non empty-membered countable denumerable set
proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)) is set
bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF))) is non empty set
bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF))) is non empty Element of bool (bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF))))
bool (bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) is non empty set
(bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) \ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF))) is non empty Element of bool (bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF))))
(bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) typed\ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF))) is Element of bool (bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF))))
bool (bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) is non empty set
(bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) \ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF))) is non empty Element of bool (bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF))))
the Element of (bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) \ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF))) is Element of (bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) \ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))
{ the Element of (bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) \ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))} is non empty trivial finite 1 -element countable Element of bool ((bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) \ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF))))
bool ((bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) \ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) is non empty set
[:NAT,{ the Element of (bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) \ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))}:] is non empty non trivial Relation-like REAL -defined (bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) \ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF))) -valued non finite non empty-membered Element of bool [:REAL,((bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) \ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))):]
[:REAL,((bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) \ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))):] is non empty non trivial Relation-like non finite non empty-membered set
bool [:REAL,((bool (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))) \ (proj2 ((AllSymbolsOf C) \/ (SymbolsOf FF)))):] is non empty non trivial non finite non empty-membered set
(((AllSymbolsOf C) \/ (SymbolsOf FF)) -freeCountableSet) --> 0 is non empty non trivial Relation-like ((AllSymbolsOf C) \/ (SymbolsOf FF)) -freeCountableSet -defined NAT -valued INT -valued Function-like constant total quasi_total non finite Function-yielding V156() non empty-membered Cardinal-yielding Element of bool [:(((AllSymbolsOf C) \/ (SymbolsOf FF)) -freeCountableSet),NAT:]
[:(((AllSymbolsOf C) \/ (SymbolsOf FF)) -freeCountableSet),NAT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:(((AllSymbolsOf C) \/ (SymbolsOf FF)) -freeCountableSet),NAT:] is non empty non trivial non finite non empty-membered set
[:(((AllSymbolsOf C) \/ (SymbolsOf FF)) -freeCountableSet),{0}:] is non empty non trivial Relation-like non finite non empty-membered set
C extendWith ((((AllSymbolsOf C) \/ (SymbolsOf FF)) -freeCountableSet) --> 0) is V47() strict Language-like
OwnSymbolsOf (C addLettersNotIn FF) is non empty countable Element of bool (AllSymbolsOf (C addLettersNotIn FF))
AllSymbolsOf (C addLettersNotIn FF) is non empty non trivial non finite non empty-membered countable denumerable set
the U1 of (C addLettersNotIn FF) is set
bool (AllSymbolsOf (C addLettersNotIn FF)) is non empty non trivial non finite non empty-membered set
the U2 of (C addLettersNotIn FF) is Element of the U1 of (C addLettersNotIn FF)
the U3 of (C addLettersNotIn FF) is Element of the U1 of (C addLettersNotIn FF)
{ the U2 of (C addLettersNotIn FF), the U3 of (C addLettersNotIn FF)} is non empty finite countable set
the U1 of (C addLettersNotIn FF) \ { the U2 of (C addLettersNotIn FF), the U3 of (C addLettersNotIn FF)} is Element of bool the U1 of (C addLettersNotIn FF)
bool the U1 of (C addLettersNotIn FF) is non empty set
the U1 of (C addLettersNotIn FF) typed\ { the U2 of (C addLettersNotIn FF), the U3 of (C addLettersNotIn FF)} is Element of bool the U1 of (C addLettersNotIn FF)
AllFormulasOf (C addLettersNotIn FF) is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered countable AllSymbolsOf (C addLettersNotIn FF) -prefix C addLettersNotIn FF -prefix Element of bool (((AllSymbolsOf (C addLettersNotIn FF)) *) \ {{}})
AllSymbolsOf (C addLettersNotIn FF) is non empty non trivial non finite non empty-membered countable denumerable set
(AllSymbolsOf (C addLettersNotIn FF)) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf (C addLettersNotIn FF)
((AllSymbolsOf (C addLettersNotIn FF)) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable denumerable Element of bool ((AllSymbolsOf (C addLettersNotIn FF)) *)
bool ((AllSymbolsOf (C addLettersNotIn FF)) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf (C addLettersNotIn FF)) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf (C addLettersNotIn FF)) *)
bool (((AllSymbolsOf (C addLettersNotIn FF)) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf (C addLettersNotIn FF)) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf (C addLettersNotIn FF)
((AllSymbolsOf (C addLettersNotIn FF)) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable denumerable Element of bool ((AllSymbolsOf (C addLettersNotIn FF)) *)
bool ((AllSymbolsOf (C addLettersNotIn FF)) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf (C addLettersNotIn FF)) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf (C addLettersNotIn FF)) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf (C addLettersNotIn FF)) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
LettersOf (C addLettersNotIn FF) is non empty non trivial non finite non empty-membered countable denumerable Element of bool (AllSymbolsOf (C addLettersNotIn FF))
{ the U3 of (C addLettersNotIn FF)} is non empty trivial finite 1 -element countable set
the U1 of (C addLettersNotIn FF) \ { the U3 of (C addLettersNotIn FF)} is non empty Element of bool the U1 of (C addLettersNotIn FF)
the U1 of (C addLettersNotIn FF) typed\ { the U3 of (C addLettersNotIn FF)} is Element of bool the U1 of (C addLettersNotIn FF)
the adicity of (C addLettersNotIn FF) is non empty Relation-like the U1 of (C addLettersNotIn FF) \ { the U3 of (C addLettersNotIn FF)} -defined INT -valued Function-like total quasi_total Element of bool [:( the U1 of (C addLettersNotIn FF) \ { the U3 of (C addLettersNotIn FF)}),INT:]
[:( the U1 of (C addLettersNotIn FF) \ { the U3 of (C addLettersNotIn FF)}),INT:] is non empty non trivial Relation-like non finite non empty-membered set
bool [:( the U1 of (C addLettersNotIn FF) \ { the U3 of (C addLettersNotIn FF)}),INT:] is non empty non trivial non finite non empty-membered set
the adicity of (C addLettersNotIn FF) " {0} is Element of bool ( the U1 of (C addLettersNotIn FF) \ { the U3 of (C addLettersNotIn FF)})
bool ( the U1 of (C addLettersNotIn FF) \ { the U3 of (C addLettersNotIn FF)}) is non empty set
(OwnSymbolsOf C) \ (OwnSymbolsOf (C addLettersNotIn FF)) is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (AllSymbolsOf C)
(OwnSymbolsOf C) typed\ (OwnSymbolsOf (C addLettersNotIn FF)) is countable Element of bool (OwnSymbolsOf C)
bool (OwnSymbolsOf C) is non empty set
(OwnSymbolsOf C) \ (OwnSymbolsOf (C addLettersNotIn FF)) is empty trivial proper V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() Element of bool (OwnSymbolsOf C)
bool (OwnSymbolsOf (C addLettersNotIn FF)) is non empty set
((C addLettersNotIn FF)) is non empty Relation-like set
bool (AllFormulasOf (C addLettersNotIn FF)) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf (C addLettersNotIn FF)), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf (C addLettersNotIn FF)) *) \ {{}} : b1 is finite } is set
bool ((C addLettersNotIn FF)) is non empty Element of bool (bool ((C addLettersNotIn FF)))
bool ((C addLettersNotIn FF)) is non empty set
bool (bool ((C addLettersNotIn FF))) is non empty set
Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF)))) is non empty functional FUNCTION_DOMAIN of bool ((C addLettersNotIn FF)), bool ((C addLettersNotIn FF))
bool (Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))) is non empty set
((C addLettersNotIn FF)) is functional (C addLettersNotIn FF) (2,C addLettersNotIn FF) (C addLettersNotIn FF) Element of bool (Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF)))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total (C addLettersNotIn FF) (C addLettersNotIn FF) Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined ((C addLettersNotIn FF)) -valued Element of bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):]
[:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):] is non empty Relation-like set
bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):] is non empty set
((C addLettersNotIn FF),((C addLettersNotIn FF))) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total (C addLettersNotIn FF) (C addLettersNotIn FF) Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined ((C addLettersNotIn FF)) -valued Element of bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):]
((C addLettersNotIn FF),((C addLettersNotIn FF))) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total (C addLettersNotIn FF) (C addLettersNotIn FF) Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined ((C addLettersNotIn FF)) -valued Element of bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):]
((C addLettersNotIn FF),((C addLettersNotIn FF))) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total (C addLettersNotIn FF) (C addLettersNotIn FF) Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined ((C addLettersNotIn FF)) -valued Element of bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):]
((C addLettersNotIn FF),((C addLettersNotIn FF))) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total (C addLettersNotIn FF) (C addLettersNotIn FF) Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined ((C addLettersNotIn FF)) -valued Element of bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):]
((C addLettersNotIn FF),((C addLettersNotIn FF))) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total (C addLettersNotIn FF) (C addLettersNotIn FF) Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined ((C addLettersNotIn FF)) -valued Element of bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):]
((C addLettersNotIn FF),((C addLettersNotIn FF))) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total (C addLettersNotIn FF) (C addLettersNotIn FF) Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined ((C addLettersNotIn FF)) -valued Element of bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):]
((C addLettersNotIn FF),((C addLettersNotIn FF))) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total (C addLettersNotIn FF) (C addLettersNotIn FF) Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined ((C addLettersNotIn FF)) -valued Element of bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):]
((C addLettersNotIn FF),((C addLettersNotIn FF))) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
{((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF))} is non empty functional finite countable Element of bool (Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF)))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total (C addLettersNotIn FF) (C addLettersNotIn FF) Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined ((C addLettersNotIn FF)) -valued Element of bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):]
((C addLettersNotIn FF),((C addLettersNotIn FF))) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total (C addLettersNotIn FF) (C addLettersNotIn FF) Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined ((C addLettersNotIn FF)) -valued Element of bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):]
((C addLettersNotIn FF),((C addLettersNotIn FF))) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total (C addLettersNotIn FF) (C addLettersNotIn FF) Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined ((C addLettersNotIn FF)) -valued Element of bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):]
((C addLettersNotIn FF),((C addLettersNotIn FF))) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total (C addLettersNotIn FF) (C addLettersNotIn FF) Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
((C addLettersNotIn FF)) is Relation-like bool ((C addLettersNotIn FF)) -defined ((C addLettersNotIn FF)) -valued Element of bool [:(bool ((C addLettersNotIn FF))),((C addLettersNotIn FF)):]
((C addLettersNotIn FF),((C addLettersNotIn FF))) is Relation-like bool ((C addLettersNotIn FF)) -defined bool ((C addLettersNotIn FF)) -valued Function-like total quasi_total Element of Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF))))
{((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF))} is non empty functional finite countable (C addLettersNotIn FF) Element of bool (Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF)))))
{((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF))} \/ {((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF)),((C addLettersNotIn FF))} is non empty functional finite countable Element of bool (Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF)))))
bool FF is non empty set
FF /\ (((AllSymbolsOf (C addLettersNotIn FF)) *) \ {{}}) is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf (C addLettersNotIn FF)) *)
FF typed/\ (((AllSymbolsOf (C addLettersNotIn FF)) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements countable Element of bool FF
FF /\ (((AllSymbolsOf (C addLettersNotIn FF)) *) \ {{}}) is functional set
FF /\typed (((AllSymbolsOf (C addLettersNotIn FF)) *) \ {{}}) is functional V36() FinSequence-membered with_non-empty_elements countable Element of bool (((AllSymbolsOf (C addLettersNotIn FF)) *) \ {{}})
bool (SymbolsOf FF) is non empty set
sub1 is functional V36() FinSequence-membered with_non-empty_elements countable Element of bool FF
SymbolsOf sub1 is set
sub1 \/ {{}} is non empty functional V36() set
{ (proj2 b1) where b1 is Relation-like Function-like Element of sub1 \/ {{}} : b1 in sub1 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of sub1 \/ {{}} : b1 in sub1 } is set
{ (proj2 b1) where b1 is Relation-like Function-like Element of sub1 : b1 in sub1 } is set
union { (proj2 b1) where b1 is Relation-like Function-like Element of sub1 : b1 in sub1 } is set
sub2 is Element of bool (SymbolsOf FF)
(LettersOf (C addLettersNotIn FF)) \ sub2 is countable Element of bool (AllSymbolsOf (C addLettersNotIn FF))
(LettersOf (C addLettersNotIn FF)) typed\ sub2 is countable Element of bool (LettersOf (C addLettersNotIn FF))
bool (LettersOf (C addLettersNotIn FF)) is non empty non trivial non finite non empty-membered set
(LettersOf (C addLettersNotIn FF)) \ sub2 is countable Element of bool (LettersOf (C addLettersNotIn FF))
bool ((LettersOf (C addLettersNotIn FF)) \ sub2) is non empty set
(LettersOf (C addLettersNotIn FF)) \ (SymbolsOf FF) is non empty non trivial non finite non empty-membered countable denumerable Element of bool (AllSymbolsOf (C addLettersNotIn FF))
(LettersOf (C addLettersNotIn FF)) typed\ (SymbolsOf FF) is countable Element of bool (LettersOf (C addLettersNotIn FF))
(LettersOf (C addLettersNotIn FF)) \ (SymbolsOf FF) is non empty non trivial non finite non empty-membered countable denumerable Element of bool (LettersOf (C addLettersNotIn FF))
inf is countable Element of bool ((LettersOf (C addLettersNotIn FF)) \ sub2)
sub2 null inf is set
sub2 \typed/ inf is Element of bool (sub2 \/ inf)
sub2 \/ inf is set
bool (sub2 \/ inf) is non empty set
(LettersOf (C addLettersNotIn FF)) \ (sub2 null inf) is countable Element of bool (AllSymbolsOf (C addLettersNotIn FF))
(LettersOf (C addLettersNotIn FF)) typed\ (sub2 null inf) is countable Element of bool (LettersOf (C addLettersNotIn FF))
(LettersOf (C addLettersNotIn FF)) \ (sub2 null inf) is countable Element of bool (LettersOf (C addLettersNotIn FF))
U is functional finite V36() FinSequence-membered with_non-empty_elements countable Element of bool FF
II1 is functional set
HC is functional (2,C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
I2 is non empty set
I2 * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of I2
I2 \/ BOOLEAN is non empty set
K491((I2 *),(I2 \/ BOOLEAN)) is non empty functional M30(I2 * ,I2 \/ BOOLEAN)
Funcs ((OwnSymbolsOf C),K491((I2 *),(I2 \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf C,K491((I2 *),(I2 \/ BOOLEAN))
I2 -InterpretersOf C is non empty functional Element of bool (Funcs ((OwnSymbolsOf C),K491((I2 *),(I2 \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf C),K491((I2 *),(I2 \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf C -defined K491((I2 *),(I2 \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf C),K491((I2 *),(I2 \/ BOOLEAN))) : b1 is C,I2 -interpreter-like } is set
I2 -InterpretersOf (C addLettersNotIn FF) is non empty functional Element of bool (Funcs ((OwnSymbolsOf (C addLettersNotIn FF)),K491((I2 *),(I2 \/ BOOLEAN))))
Funcs ((OwnSymbolsOf (C addLettersNotIn FF)),K491((I2 *),(I2 \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf (C addLettersNotIn FF),K491((I2 *),(I2 \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf (C addLettersNotIn FF)),K491((I2 *),(I2 \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf (C addLettersNotIn FF) -defined K491((I2 *),(I2 \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf (C addLettersNotIn FF)),K491((I2 *),(I2 \/ BOOLEAN))) : b1 is C addLettersNotIn FF,I2 -interpreter-like } is set
the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set is Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set
II2 is functional V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf C)
I1 is Relation-like OwnSymbolsOf C -defined Function-like total Function-yielding V156() C,I2 -interpreter-like Element of I2 -InterpretersOf C
I1 is Relation-like OwnSymbolsOf C -defined Function-like total Function-yielding V156() C,I2 -interpreter-like Element of I2 -InterpretersOf C
the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set +* I1 is Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set
( the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set +* I1) | (OwnSymbolsOf (C addLettersNotIn FF)) is Relation-like OwnSymbolsOf (C addLettersNotIn FF) -defined OwnSymbolsOf (C addLettersNotIn FF) -defined K491((I2 *),(I2 \/ BOOLEAN)) -valued Function-like total Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set
I2 is Relation-like OwnSymbolsOf (C addLettersNotIn FF) -defined Function-like total Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like Element of I2 -InterpretersOf (C addLettersNotIn FF)
I2 | (OwnSymbolsOf C) is Relation-like OwnSymbolsOf C -defined OwnSymbolsOf (C addLettersNotIn FF) -defined Function-like Function-yielding V156() C,I2 -interpreter-like set
a is non empty countable Element of bool (OwnSymbolsOf (C addLettersNotIn FF))
a null (OwnSymbolsOf (C addLettersNotIn FF)) is set
(OwnSymbolsOf (C addLettersNotIn FF)) /\ a is countable Element of bool (OwnSymbolsOf (C addLettersNotIn FF))
(OwnSymbolsOf (C addLettersNotIn FF)) typed/\ a is countable Element of bool (OwnSymbolsOf (C addLettersNotIn FF))
(OwnSymbolsOf (C addLettersNotIn FF)) /\ a is set
(OwnSymbolsOf (C addLettersNotIn FF)) /\typed a is countable Element of bool a
bool a is non empty set
a \typed/ (OwnSymbolsOf (C addLettersNotIn FF)) is Element of bool (a \/ (OwnSymbolsOf (C addLettersNotIn FF)))
a \/ (OwnSymbolsOf (C addLettersNotIn FF)) is non empty set
bool (a \/ (OwnSymbolsOf (C addLettersNotIn FF))) is non empty set
( the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set +* I1) | (a null (OwnSymbolsOf (C addLettersNotIn FF))) is Relation-like a null (OwnSymbolsOf (C addLettersNotIn FF)) -defined Function-like Function-yielding V156() set
the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set | (OwnSymbolsOf C) is Relation-like OwnSymbolsOf C -defined Function-like Function-yielding V156() C,I2 -interpreter-like set
I1 | (OwnSymbolsOf C) is Relation-like OwnSymbolsOf C -defined OwnSymbolsOf C -defined OwnSymbolsOf C -defined K491((I2 *),(I2 \/ BOOLEAN)) -valued Function-like total Function-yielding V156() C,I2 -interpreter-like set
I1 null (OwnSymbolsOf C) is Relation-like (OwnSymbolsOf C) \/ (proj1 I1) -defined (OwnSymbolsOf C) \/ (proj2 I1) -valued Function-like set
proj1 I1 is set
(OwnSymbolsOf C) \/ (proj1 I1) is non empty set
proj2 I1 is set
(OwnSymbolsOf C) \/ (proj2 I1) is non empty set
I1 \typed/ (OwnSymbolsOf C) is Element of bool (I1 \/ (OwnSymbolsOf C))
I1 \/ (OwnSymbolsOf C) is non empty set
bool (I1 \/ (OwnSymbolsOf C)) is non empty set
( the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set | (OwnSymbolsOf C)) +* (I1 | (OwnSymbolsOf C)) is Relation-like OwnSymbolsOf C -defined Function-like total Function-yielding V156() set
(I1 | (OwnSymbolsOf C)) null ( the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set | (OwnSymbolsOf C)) is Relation-like ( the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set | (OwnSymbolsOf C)) \/ (proj1 (I1 | (OwnSymbolsOf C))) -defined ( the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set | (OwnSymbolsOf C)) \/ (proj2 (I1 | (OwnSymbolsOf C))) -valued Function-like set
proj1 (I1 | (OwnSymbolsOf C)) is set
( the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set | (OwnSymbolsOf C)) \/ (proj1 (I1 | (OwnSymbolsOf C))) is set
proj2 (I1 | (OwnSymbolsOf C)) is set
( the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set | (OwnSymbolsOf C)) \/ (proj2 (I1 | (OwnSymbolsOf C))) is set
(I1 | (OwnSymbolsOf C)) \typed/ ( the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set | (OwnSymbolsOf C)) is Relation-like OwnSymbolsOf C -defined Element of bool ((I1 | (OwnSymbolsOf C)) \/ ( the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set | (OwnSymbolsOf C)))
(I1 | (OwnSymbolsOf C)) \/ ( the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set | (OwnSymbolsOf C)) is Relation-like OwnSymbolsOf C -defined set
bool ((I1 | (OwnSymbolsOf C)) \/ ( the Relation-like Function-like Function-yielding V156() C addLettersNotIn FF,I2 -interpreter-like set | (OwnSymbolsOf C))) is non empty set
D2 is functional (C addLettersNotIn FF) (2,C addLettersNotIn FF) (C addLettersNotIn FF) Element of bool (Funcs ((bool ((C addLettersNotIn FF))),(bool ((C addLettersNotIn FF)))))
U is non empty set
U * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of U
U \/ BOOLEAN is non empty set
K491((U *),(U \/ BOOLEAN)) is non empty functional M30(U * ,U \/ BOOLEAN)
Funcs ((OwnSymbolsOf (C addLettersNotIn FF)),K491((U *),(U \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf (C addLettersNotIn FF),K491((U *),(U \/ BOOLEAN))
U -InterpretersOf (C addLettersNotIn FF) is non empty functional Element of bool (Funcs ((OwnSymbolsOf (C addLettersNotIn FF)),K491((U *),(U \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf (C addLettersNotIn FF)),K491((U *),(U \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf (C addLettersNotIn FF) -defined K491((U *),(U \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf (C addLettersNotIn FF)),K491((U *),(U \/ BOOLEAN))) : b1 is C addLettersNotIn FF,U -interpreter-like } is set
U -InterpretersOf C is non empty functional Element of bool (Funcs ((OwnSymbolsOf C),K491((U *),(U \/ BOOLEAN))))
Funcs ((OwnSymbolsOf C),K491((U *),(U \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf C,K491((U *),(U \/ BOOLEAN))
bool (Funcs ((OwnSymbolsOf C),K491((U *),(U \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf C -defined K491((U *),(U \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf C),K491((U *),(U \/ BOOLEAN))) : b1 is C,U -interpreter-like } is set
I2 is Relation-like OwnSymbolsOf (C addLettersNotIn FF) -defined Function-like total Function-yielding V156() C addLettersNotIn FF,U -interpreter-like Element of U -InterpretersOf (C addLettersNotIn FF)
I2 is Relation-like OwnSymbolsOf (C addLettersNotIn FF) -defined Function-like total Function-yielding V156() C addLettersNotIn FF,U -interpreter-like Element of U -InterpretersOf (C addLettersNotIn FF)
I2 | (OwnSymbolsOf C) is Relation-like OwnSymbolsOf C -defined OwnSymbolsOf (C addLettersNotIn FF) -defined Function-like Function-yielding V156() C,U -interpreter-like set
I1 is Relation-like OwnSymbolsOf C -defined Function-like total Function-yielding V156() C,U -interpreter-like Element of U -InterpretersOf C
I1 | (OwnSymbolsOf C) is Relation-like OwnSymbolsOf C -defined OwnSymbolsOf C -defined OwnSymbolsOf C -defined K491((U *),(U \/ BOOLEAN)) -valued Function-like total Function-yielding V156() C,U -interpreter-like set
I1 null (OwnSymbolsOf C) is Relation-like (OwnSymbolsOf C) \/ (proj1 I1) -defined (OwnSymbolsOf C) \/ (proj2 I1) -valued Function-like set
proj1 I1 is set
(OwnSymbolsOf C) \/ (proj1 I1) is non empty set
proj2 I1 is set
(OwnSymbolsOf C) \/ (proj2 I1) is non empty set
I1 \typed/ (OwnSymbolsOf C) is Element of bool (I1 \/ (OwnSymbolsOf C))
I1 \/ (OwnSymbolsOf C) is non empty set
bool (I1 \/ (OwnSymbolsOf C)) is non empty set
(I2 | (OwnSymbolsOf C)) null (OwnSymbolsOf C) is Relation-like (OwnSymbolsOf C) \/ (proj1 (I2 | (OwnSymbolsOf C))) -defined (OwnSymbolsOf C) \/ (proj2 (I2 | (OwnSymbolsOf C))) -valued Function-like set
proj1 (I2 | (OwnSymbolsOf C)) is set
(OwnSymbolsOf C) \/ (proj1 (I2 | (OwnSymbolsOf C))) is non empty set
proj2 (I2 | (OwnSymbolsOf C)) is set
(OwnSymbolsOf C) \/ (proj2 (I2 | (OwnSymbolsOf C))) is non empty set
(I2 | (OwnSymbolsOf C)) \typed/ (OwnSymbolsOf C) is Element of bool ((I2 | (OwnSymbolsOf C)) \/ (OwnSymbolsOf C))
(I2 | (OwnSymbolsOf C)) \/ (OwnSymbolsOf C) is non empty set
bool ((I2 | (OwnSymbolsOf C)) \/ (OwnSymbolsOf C)) is non empty set
(I2 | (OwnSymbolsOf C)) | (OwnSymbolsOf C) is Relation-like OwnSymbolsOf C -defined OwnSymbolsOf C -defined OwnSymbolsOf C -defined K491((U *),(U \/ BOOLEAN)) -valued Function-like total Function-yielding V156() C,U -interpreter-like set
X is set
C is V51() V53() countable eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered countable denumerable set
the U1 of C is set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable denumerable Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered countable AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered countable denumerable set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable denumerable Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
(C) is functional (C) (2,C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is non empty Relation-like set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C),(C),(C),(C),(C),(C),(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C),(C),(C),(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C),(C),(C),(C),(C),(C),(C),(C)} \/ {(C),(C),(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
xnot DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ DD) ^ DD is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth DD),(Depth DD)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot DD),(xnot DD)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth DD is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth DD),(Depth DD)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot DD),(xnot DD)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{DD} is non empty trivial functional finite V36() 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (C) Element of bool (((AllSymbolsOf C) *) \ {{}})
FF is functional V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf C)
Y is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (AllFormulasOf C)
FF \/ Y is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (AllFormulasOf C)
phii is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (AllFormulasOf C)
bool phii is non empty set
FF null Y is set
FF \typed/ Y is functional V36() with_non-empty_elements Element of bool (FF \/ Y)
FF \/ Y is non empty functional V36() with_non-empty_elements non empty-membered set
bool (FF \/ Y) is non empty set
Y null FF is set
Y \typed/ FF is functional V36() with_non-empty_elements Element of bool (Y \/ FF)
Y \/ FF is non empty functional V36() with_non-empty_elements non empty-membered set
bool (Y \/ FF) is non empty set
OwnSymbolsOf C is non empty countable Element of bool (AllSymbolsOf C)
bool (AllSymbolsOf C) is non empty non trivial non finite non empty-membered set
the U2 of C is Element of the U1 of C
{ the U2 of C, the U3 of C} is non empty finite countable set
the U1 of C \ { the U2 of C, the U3 of C} is Element of bool the U1 of C
bool the U1 of C is non empty set
the U1 of C typed\ { the U2 of C, the U3 of C} is Element of bool the U1 of C
m is non empty set
m * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of m
m \/ BOOLEAN is non empty set
K491((m *),(m \/ BOOLEAN)) is non empty functional M30(m * ,m \/ BOOLEAN)
Funcs ((OwnSymbolsOf C),K491((m *),(m \/ BOOLEAN))) is non empty functional FUNCTION_DOMAIN of OwnSymbolsOf C,K491((m *),(m \/ BOOLEAN))
m -InterpretersOf C is non empty functional Element of bool (Funcs ((OwnSymbolsOf C),K491((m *),(m \/ BOOLEAN))))
bool (Funcs ((OwnSymbolsOf C),K491((m *),(m \/ BOOLEAN)))) is non empty set
{ b1 where b1 is Relation-like OwnSymbolsOf C -defined K491((m *),(m \/ BOOLEAN)) -valued Function-like total quasi_total Function-yielding V156() Element of Funcs ((OwnSymbolsOf C),K491((m *),(m \/ BOOLEAN))) : b1 is C,m -interpreter-like } is set
seqt is Relation-like OwnSymbolsOf C -defined Function-like total Function-yielding V156() C,m -interpreter-like Element of m -InterpretersOf C
seqt -TruthEval (xnot DD) is boolean Element of BOOLEAN
seqt -TruthEval DD is boolean Element of BOOLEAN
'not' (seqt -TruthEval DD) is boolean Element of BOOLEAN
1 - (seqt -TruthEval DD) is set
(seqt -TruthEval (xnot DD)) \+\ ('not' (seqt -TruthEval DD)) is empty trivial V4() V5() V6() V8() V9() V10() complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element V40() V41() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V156() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable V208() V209() set
psi is functional V36() FinSequence-membered with_non-empty_elements countable Element of bool phii
phii /\ psi is functional V36() FinSequence-membered with_non-empty_elements countable Element of bool phii
phii typed/\ psi is functional V36() FinSequence-membered with_non-empty_elements countable Element of bool phii
phii /\ psi is functional set
phii /\typed psi is functional V36() FinSequence-membered with_non-empty_elements countable Element of bool psi
bool psi is non empty set
psi null phii is set
psi \typed/ phii is functional V36() with_non-empty_elements Element of bool (psi \/ phii)
psi \/ phii is non empty functional V36() with_non-empty_elements non empty-membered set
bool (psi \/ phii) is non empty set
H is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool phii
'not' (seqt -TruthEval (xnot DD)) is boolean Element of BOOLEAN
1 - (seqt -TruthEval (xnot DD)) is set
X is set
C is V51() V53() countable eligible Language-like
AllSymbolsOf C is non empty non trivial non finite non empty-membered countable denumerable set
the U1 of C is set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable denumerable Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
AllFormulasOf C is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered countable AllSymbolsOf C -prefix C -prefix Element of bool (((AllSymbolsOf C) *) \ {{}})
AllSymbolsOf C is non empty non trivial non finite non empty-membered countable denumerable set
(AllSymbolsOf C) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf C
((AllSymbolsOf C) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable denumerable Element of bool ((AllSymbolsOf C) *)
bool ((AllSymbolsOf C) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf C) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf C) *)
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
S is V51() V53() eligible Language-like
(S) is non empty Relation-like set
AllFormulasOf S is non empty functional V36() FinSequence-membered with_non-empty_elements non empty-membered AllSymbolsOf S -prefix S -prefix Element of bool (((AllSymbolsOf S) *) \ {{}})
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
the U1 of S is set
AllSymbolsOf S is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
bool (((AllSymbolsOf S) *) \ {{}}) is non empty non trivial non finite non empty-membered set
(AllSymbolsOf S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of AllSymbolsOf S
((AllSymbolsOf S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((AllSymbolsOf S) *)
bool ((AllSymbolsOf S) *) is non empty non trivial non finite non empty-membered set
((AllSymbolsOf S) *) typed\ {{}} is functional V36() FinSequence-membered Element of bool ((AllSymbolsOf S) *)
{ b1 where b1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf S) *) \ {{}} : ex b2 being V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set st b1 is b2 -wff } is set
bool (AllFormulasOf S) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf S), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf S) *) \ {{}} : b1 is finite } is set
bool (S) is non empty Element of bool (bool (S))
bool (S) is non empty set
bool (bool (S)) is non empty set
Funcs ((bool (S)),(bool (S))) is non empty functional FUNCTION_DOMAIN of bool (S), bool (S)
bool (Funcs ((bool (S)),(bool (S)))) is non empty set
(S) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total (S) Element of Funcs ((bool (S)),(bool (S)))
(S) is Relation-like bool (S) -defined (S) -valued Element of bool [:(bool (S)),(S):]
[:(bool (S)),(S):] is non empty Relation-like set
bool [:(bool (S)),(S):] is non empty set
(S,(S)) is Relation-like bool (S) -defined bool (S) -valued Function-like total quasi_total Element of Funcs ((bool (S)),(bool (S)))
{(S)} is non empty trivial functional finite 1 -element with_common_domain countable (S) Element of bool (Funcs ((bool (S)),(bool (S))))
(C) is functional (C) (2,C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is non empty Relation-like set
bool (AllFormulasOf C) is non empty set
{ [b1,b2] where b1 is functional V36() FinSequence-membered with_non-empty_elements Element of bool (AllFormulasOf C), b2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}} : b1 is finite } is set
bool (C) is non empty Element of bool (bool (C))
bool (C) is non empty set
bool (bool (C)) is non empty set
Funcs ((bool (C)),(bool (C))) is non empty functional FUNCTION_DOMAIN of bool (C), bool (C)
bool (Funcs ((bool (C)),(bool (C)))) is non empty set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
[:(bool (C)),(C):] is non empty Relation-like set
bool [:(bool (C)),(C):] is non empty set
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C),(C),(C),(C),(C),(C),(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C),(C),(C),(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C),(C),(C),(C),(C),(C),(C),(C)} \/ {(C),(C),(C),(C)} is non empty functional finite countable Element of bool (Funcs ((bool (C)),(bool (C))))
phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff X -implied Element of ((AllSymbolsOf C) *) \ {{}}
xnot phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
TheNorSymbOf C is non literal non low-compounding non relational non own Element of AllSymbolsOf C
the U3 of C is Element of the U1 of C
<*(TheNorSymbOf C)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable V209() Element of ((AllSymbolsOf C) *) \ {{}}
[1,(TheNorSymbOf C)] is non empty V26() set
{[1,(TheNorSymbOf C)]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() set
<*(TheNorSymbOf C)*> ^ phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ phii) ^ phii is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phii),(Depth phii)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot phii),(xnot phii)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth phii is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth phii),(Depth phii)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(C)} \/ {(C)} is non empty functional finite countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
{(xnot phii),(xnot phii)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
bool (((AllSymbolsOf C) *) \ {{}}) is non empty non trivial non finite non empty-membered set
xnot (xnot phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff X -implied Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheNorSymbOf C)*> ^ (xnot phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ (xnot phii)) ^ (xnot phii) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth (xnot phii)),(Depth (xnot phii))) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot (xnot phii)),(xnot (xnot phii))}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth (xnot phii) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth (xnot phii)),(Depth (xnot phii))) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot (xnot phii)),(xnot (xnot phii))} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
Y is functional V36() FinSequence-membered with_non-empty_elements countable Element of bool (AllFormulasOf C)
H is set
m is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
[H,(xnot (xnot phii))] is non empty V26() set
seqt is (C) (C) set
seqt `1 is finite countable (C) set
(seqt `1) \+\ H is set
(C) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total (C) Element of Funcs ((bool (C)),(bool (C)))
(C) is Relation-like bool (C) -defined (C) -valued Element of bool [:(bool (C)),(C):]
(C,(C)) is Relation-like bool (C) -defined bool (C) -valued Function-like total quasi_total Element of Funcs ((bool (C)),(bool (C)))
{(C)} is non empty trivial functional finite 1 -element with_common_domain countable (C) Element of bool (Funcs ((bool (C)),(bool (C))))
HC is finite countable (C) set
xnot phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheNorSymbOf C)*> ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ phi) ^ phi is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth phi),(Depth phi)) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot phi),(xnot phi)}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth phi is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth phi),(Depth phi)) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot phi),(xnot phi)} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
xnot (xnot phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() wff Element of ((AllSymbolsOf C) *) \ {{}}
<*(TheNorSymbOf C)*> ^ (xnot phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non exal Element of ((AllSymbolsOf C) *) \ {{}}
(<*(TheNorSymbOf C)*> ^ (xnot phi)) ^ (xnot phi) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable V209() non 0wff non max ((Depth (xnot phi)),(Depth (xnot phi))) -wff wff non exal (C,{(C)} \/ {(C)},{(xnot (xnot phi)),(xnot (xnot phi))}) Element of ((AllSymbolsOf C) *) \ {{}}
Depth (xnot phi) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
max ((Depth (xnot phi)),(Depth (xnot phi))) is V4() V5() V6() V10() complex ext-real non negative finite cardinal V40() V41() countable set
{(xnot (xnot phi)),(xnot (xnot phi))} is non empty functional finite V36() FinSequence-membered with_non-empty_elements non empty-membered countable Element of bool (((AllSymbolsOf C) *) \ {{}})
[HC,(xnot (xnot phi))] is non empty V26() (C) (C) set
{[HC,(xnot (xnot phi))]} is non empty trivial Relation-like Function-like constant finite 1 -element with_non-empty_elements non empty-membered countable V209() (C) set
[HC,phi] is non empty V26() (C) (C) set
[HC,phi] null 1 is (C) (1,C,{(C)},{[HC,(xnot (xnot phi))]}) (C) set
[HC,phi] \typed/ 1 is Element of bool ([HC,phi] \/ 1)
[HC,phi] \/ 1 is non empty set
bool ([HC,phi] \/ 1) is non empty set
m + 1 is non empty V4() V5() V6() V10() complex ext-real positive non negative finite cardinal V40() V41() countable set
(C) \/ {(C)} is non empty functional (C) Element of bool (Funcs ((bool (C)),(bool (C))))